METHOD AND SYSTEM FOR REAL-TIME MONITORING NOISE SQUEEZING EFFECTS OF A NONLINEAR DEVICE AND/OR SYSTEM

Abstract

 The present invention relates to a method and system for real-time monitoring noise squeezing effects of a nonlinear device and/or system (1). The method comprises the following steps:
- applying a drive signal S_d having a drive frequency f_d to an input (3) of the nonlinear device and/or system (1) for driving the nonlinear device and/or system (1) in a nonlinear state
- applying an additional probe signal S_p to the input of the nonlinear device and/or system (1);
- capturing an output signal S_out of the nonlinear device and/or system (1);
- determining, based on the captured output signal S_out, a frequency spectrum of the output signal S_out;
- determining, based on the frequency spectrum of the output signal S_out, an antiresonance frequency f_ar, the antiresonance frequency f_ar being a measure for the noise squeezing effects of the nonlinear device and/or system (1); wherein:
the additional probe signal S_p comprises a multi-tone signal having a plurality of different probe frequencies, and/or
the additional probe signal S_p comprises white noise having a frequency bandwidth that is smaller than the drive frequency f_d.

Description

[0001] The present invention relates to a method and a system for real-time monitoring of noise squeezing effects of a nonlinear device and/or system such as an oscillator, a resonator, a microelectromechanical system (MEMS) or a nanoelectromechanical system (NEMS). In particular, the present invention relates to a method and a system for reducing noise, particularly in-phase noise, of a nonlinear device and/or system in real-time. In particular, the present invention relates to a method and a system for enhancing the signal-to-noise ratio, particularly the in-phase signal-to-noise-ratio, of a nonlinear device and/or system in real-time. In particular, the present invention relates to a method and a system for improving the sensitivity and/or performance of oscillators and/or resonators in real-time, particularly in wide applications such as NEMS/MEMS sensors, mechanical filters, and similar devices and/or systems.

[0002] Oscillators and resonators show noise due to several sources including temperature, material defects, boundary conditions or other sources of irregularities. In addition, irregularities and sources of noise may change over time so that noise is not a constant parameter. Hence, the measurement of noise is difficult because it requires complicated characterization and an extremely stable environment (which is almost impossible to achieve), and it is time-consuming as well.

[0003] So-called noise squeezing effects can break the limit of noise in nonlinear devices and/or systems by redistributing the noise in two conjugates of the observables. One direction (in-phase) is compressed, and the other direction (quadrature) is enlarged. Particularly if the signal detection and measurement of a device and/or system is performed in the in-phase direction, noise can be suppressed by means of such squeezing effects, and the signal-to-noise ratio and/or the accuracy of the device and/or system can be enhanced.

[0004] Oscillators and resonators in the nonlinear regime show noise squeezing effects under certain conditions (e.g. at a particular excitation level or detuning frequency). This property of nonlinear oscillators or resonators can be utilized to reduce the noise floor and thus improve the sensitivity or performance of oscillators and/or resonators in wide applications such as NEMS/MEMS sensors, mechanical filters and similar devices and/or systems. To dynamically adjust the oscillators and/or resonators into the best working conditions with lowest noise floor, the real-time monitoring of noise squeezing effects, and particularly the real-time monitoring of the squeezing factors, of the oscillators and/or resonators becomes important.

[0005] Traditionally, the squeezing effects are characterized by drawing a distribution of in-phase and its quadrature (phase-space) by homodyne measurements, as described, for example, in D. Rugar and P. Gruetter: "Mechanical parametric amplification and thermomechanical noise squeezing", Phys. Rev. Lett. 67, 699 (1991). However, the homodyne measurements need to be conducted for a long time, usually at least several tens of seconds for mechanical resonators, because of a time-consuming calculation or integration process of the distribution. This method suffers from temperature and/or frequency drifts and other difficult to control impacts, particularly in ultrasensitive MEMS/NEMS in engineering applications. Therefore, the integration requires the system to be extremely stable and requires active stabilization of temperature, pressure and/or other environmental parameters on short as well as on long time scales (no drifts allowed).

[0006] Recently, a method by sideband fitting of thermal noise has been developed to characterize the squeezing effect without the homodyne measurement. In this method, which is described in J. S. Huber, G. Rastelli, M. J. Seitner, J. Koelbl, W. Belzig, M. I. Dykman, and E. M. Weig: "Spectral evidence of squeezing of a weakly damped driven nanomechanical mode, Phys. Rev. X 10, 021066 (2020), the thermal noise whose frequency is close to that of the drive tone helps to form one pair of sidebands around the response of resonators to the drive tone in the frequency spectrum. The difference of the spectral weight determined by integrating the response curves can be used to calculate the squeezing effects after a complicated post analysis. This complicated post analysis makes the characterization hard or even impossible to be applied in real-time scenarios. Besides, in that method, the resonator is required to work on resonance or very close to the resonance state. Hence, there is no possibility to optimize the driving point. Furthermore, the method described in the above-mentioned publication of J. S. Huber et al. is limited to resonators with extremely high-quality factor, because otherwise the thermal fluctuations are unmeasurably small in amplitude.

[0007] In the publication F. Yang, M. Fu, B. Bosnjak, R. H. Blick, Y. Jiang, and E. Scheer: "Mechanically Modulated Sideband and Squeezing Effects of Membrane Resonators", Phys. Rev. Lett. 127, 184301 (2021), which is referred to herein as publication [3] and which is hereby incorporated by reference, it is described that antiresonance sidebands are formed by modulating a resonator with low-frequency signals. If the eigenfrequency of a nonlinear system is modulated at a low frequency (for instance, < 1 kHz), the sidebands will have anti-resonance behavior in the frequency spectrum. At one frequency, the intensity of the modulated sideband is severely suppressed, and this frequency is called antiresonance frequency f_ar (or "M-point" in publication [3], see particularly FIG. 2a of publication [3]). As shown in publication [3] (see equation 5 therein), the antiresonance frequency f_ar (or "M-point") can be used to calculate the squeezing of noise in the system through the following direct relationship between a squeezing factor φ (also referred to herein as squeezing parameter) and the antiresonance frequency f_ar:

wherein ω_ar = 2πf_ar is the angular antiresonance frequency, Γ is a damping parameter of the nonlinear device and/or system, and δω = (ω_d - ω₀)/Γ with ω_d being a specified (i.e. predetermined or predeterminable) angular drive frequency, and ω₀ being an angular eigenfrequency of the nonlinear device and/or system. The parameters Γ and δω are both known as they are characteristic parameters of the nonlinear device and/or system. Thus, by monitoring the antiresonance frequency f_ar (or M-point), the squeezing factor φ of the nonlinear device and/or system can directly be obtained. Furthermore, as described in publication [3] and particularly shown in FIG. 3 of publication [3], by adjusting the drive signal, particularly the drive frequency (detuning) and/or the drive power, the antiresonance effect and thus the squeezing can be controlled.

[0008] Thus, it is an object of the present invention to achieve real-time monitoring of squeezing effects of a nonlinear device and/or system (such as a nonlinear oscillator and/or resonator, i.e. an oscillator and/or a resonator operated in a nonlinear state). This object is solved by the subject-matters of the independent claims. Preferred embodiments are defined by the dependent claims.

[0009] According to one aspect of the present invention, a method for real-time monitoring noise squeezing effects of a nonlinear device and/or system is provided. The method comprises the following steps:

• applying a drive signal S_d having a drive frequency f_d to an input of the nonlinear device and/or system for driving the nonlinear device and/or system in a nonlinear state
• applying an additional probe signal S_p to the input of the nonlinear device and/or system;
• capturing an output signal S_out of the nonlinear device and/or system;
• determining, based on the captured output signal S_out, a frequency spectrum of the output signal S_out;
• determining, based on the frequency spectrum of the output signal S_out, an antiresonance frequency f_ar, the antiresonance frequency f_ar being a measure for the noise squeezing effects of the nonlinear device and/or system;
  wherein:

  the additional probe signal S_p comprises a multi-tone signal having a plurality of different probe frequencies, and/or

  the additional probe signal S_p comprises white noise having a frequency bandwidth that is smaller than the drive frequency f_d.

[0010] A "nonlinear device" within the present invention may be a resonator or an oscillator, particular a resonator or an oscillator that is operated and/or driven in a nonlinear state. A "nonlinear system" within the present invention may be a MEMS or NEMS. For example, a nonlinear system may be a gyroscope, a mass detector, an inertial sensor, an accelerator, etc.

[0011] "Real-time monitoring noise squeezing effects" or "real-time monitoring of a noise squeezing" of a nonlinear device and/or system" particularly means within the present invention that it is determined how strong the squeezing of the nonlinear device and/or system is at a distinct time or within a distinct time period. In particular, monitoring noise squeezing effects of a nonlinear device and/or system means monitoring (and/or determining) an intensity, a degree and/or a strength of noise squeezing effects present in the nonlinear device and/or system. The noise squeezing effects of a nonlinear device and/or system are monitored based on the determined antiresonance frequency f_ar which is obtained from the frequency (sideband) spectrum of the output signal of the nonlinear device and/or system. This is possible, because according to equation 1 above the presence of squeezing effects can be quantized by means of a squeezing factor φ which is directly related with the antiresonance frequency f_ar. Therefore, the antiresonance frequency f_ar is a measure of the squeezing factor φ, and thus a measure for the presence of noise squeezing effects in the nonlinear device and/or system. Hence, monitoring noise squeezing (or noise squeezing effects) may comprise monitoring the squeezing factor φ. However, it is noted that for monitoring the noise squeezing (or noise squeezing effects), it is not necessary to determine the squeezing factor φ. Rather, the antiresonance frequency can also be used directly to monitor noise squeezing effects (without calculating the squeezing factor φ). This can be done by determining if the current working status of the nonlinear device and/or system has the lowest noise floor. For example, in some nonlinear devices and/or systems, it is the on-resonance state which provides the best squeezing state for enhancing the signal. Further, the antiresonance frequency of on-resonance states is known to be close to zero (i.e. 0 Hz). Therefore, for monitoring the noise squeezing effects, the determined antiresonance frequency may be compared with zero (i.e. 0 Hz), and the comparison result, i.e. the difference between the determined antiresonance frequency and zero (i.e. 0 Hz), is a measure for the noise squeezing effects. In particular, the smaller the difference of the antiresonance frequency from 0 Hz, the larger the noise squeezing effects. In addition or alternatively, for monitoring the noise squeezing effects, the determined antiresonance frequency f_ar may be compared with the driving frequency f_d. The comparison result, i.e. the difference between the determined antiresonance frequency f_ar and the driving frequency f_d, is a measure for the noise squeezing effects. In particular, the larger the difference of the antiresonance frequency f_ar from the driving frequency f_d, the larger the noise squeezing effects.

[0012] A drive signal having a drive frequency f_d (also referred to herein as working frequency) is applied to an input of the nonlinear device and/or system. For example, the input of the nonlinear device and/or system may comprise contacts or electrodes of a piezo actuator.

[0013] Further, an additional probe signal, particularly a pulse of an additional probe signal, is applied to the input of the nonlinear device and/or system. In particular, the probe signal has a plurality of different probe frequencies, wherein the plurality of different probe frequencies comprises a plurality of predefined probe frequencies, or wherein the plurality of different probe frequencies relates to a white noise signal (and/or the frequencies present in a white noise signal). Preferably, each of the probe frequencies is lower than the drive frequency f_d.

[0014] An output signal (also referred to herein as a response signal) of the nonlinear device and/or system is captured, and a frequency spectrum, particularly a frequency sideband spectrum, of the output signal is determined (particularly calculated) based on the captured output signal. In particular, the output signal of the nonlinear device and/or system is analyzed in real-time by means of a fast Fourier transformation (FFT), i.e., by applying a FFT to the output signal, thereby obtaining a frequency spectrum of the output signal. For example, in case that the nonlinear device and/or system is a membrane resonator, the output signal may be detected by means of detection contacts or electrodes of the membrane resonator.

[0015] Based on the frequency spectrum of the output signal, an antiresonance frequency f_ar is determined. The antiresonance frequency f_ar is a frequency at which an intensity of a corresponding sideband of the output signal is suppressed so that the intensity of said sideband of the output signal causes a minimum in the sideband frequency spectrum.

[0016] According to one alternative, the additional probe signal comprises or particularly is a multi-tone signal having a plurality of different probe frequencies. Within the present disclosure, a multi-tone signal is particularly a well-defined signal, i.e., a signal that can be defined by a mathematical function. Accordingly, a multi-tone signal in the sense of the present invention differs from a noise signal. In particular, the multi-tone signal is periodic, i.e., the additional probe signal particularly comprises or is a periodic multi-tone signal. Preferably, but not necessarily, the multi-tone signal has equal amplitudes, i.e., the amplitude of each tone of the probe signal is equal. Preferably, each tone of the multi-tone signal has a distinct frequency which differs from another tone of the multi-tone signal. In particular, the probe signal comprises a basic probe frequency and at least one further probe frequency being a multiple of the basic probe frequency. In particular, the probe signal comprises a plurality of further probe frequencies, each being a multiple of the basic probe frequency. Preferably, but not necessarily, the frequency spacing of the multi-tone signal is equal, i.e., the differences between any two subsequent probe frequencies of the multi-tone signal may be equal.

[0017] For example, the probe signal may comprise or be a non-sinusoidal wave function having multiple frequencies with a frequency bandwidth (BD) that is smaller than the drive frequency f_d. In particular, the frequency of the non-sinusoidal wave function may range from zero to BD. In other words, any frequency f_{non-sinusoidal} of the non-sinusoidal wave function may in particular be between zero and the drive frequency, i.e. 0 < f_{non-sinusoidal} < f_d. It is noted that any non-sinusoidal wave function can be written as a superposition of sinusoidal probe tones or multi-tones. For example, the non-sinusoidal wave function may be a pulse-train. In particular, the probe signal may be a series of pulses of relatively short duration t₁, which are repeated after a longer cycle time t₂ (for example, a cycle time of t₂ = 500*t₁). In this case, the probe signal contains both low frequency and high frequency components. In particular, a filter may be added to reduce the amplitude of high frequency components.

[0018] In addition or alternatively, the probe signal comprises or particularly is white noise having a frequency bandwidth (BD) that is smaller than the drive frequency. In particular, the frequency of the white noise probe signal ranges from zero to BD. In other words, any frequency f_{white noise} of the white noise is in particular between zero and the drive frequency, i.e. 0 < f_{white noise} < f_d. Contrary to a multi-tone signal which is a well-defined or definable signal, white noise relates to a random signal.

[0019] By the present invention, the antiresonance frequency and thus the noise squeezing of a nonlinear device and/or system can be determined fast and easy without the need of subsequently scanning a broad range of probe frequencies. Thus, by the present invention, a disturbance of the nonlinear device and/or system due to complex and time intensive measurements can be avoided. Moreover, contrary to conventional methods, the present invention enables monitoring noise squeezing effects of a nonlinear device and/or system in real-time.

[0020] Particularly due to the special design of the additional probe signal according to the present invention, it is sufficient that the steps of capturing an output signal of the nonlinear device and/or system and determining a frequency spectrum of the output signal are performed only once for monitoring noise squeezing effects at a distinct time. The measurement time of anti-resonance shaped sidebands can therefore be drastically reduced. In particular, contrary to existing methods such as described in publication [3], the frequency spectrum obtained by the method according to the present invention, from which the antiresonance frequency is determined, is not obtained by overlaying individual frequency spectra as disclosed in publication [3]. In particular, contrary to the method described in publication [3], the frequency spectrum of the output signal, from which the antiresonance frequency is determined, is obtained by applying only one and the same additional probe signal (particularly a pulse thereof). In other words, the additional probe signal is not changed (particularly not swept) for determining the antiresonance frequency. In particular, contrary to what is described in publication [3], namely that the anti-resonance shaped sidebands are obtained by a time intensive integration of a plurality (e.g. hundreds) of frequency spectra, the present invention enables to obtain the anti-resonance shaped sidebands in short time (for instance < 0.1 s), thus making a real-time monitoring of the noise squeezing possible. Advantageously, according to the present invention, no time-consuming sweeping and/or overlaying of individual frequency spectra is necessary.

[0021] In particular, by monitoring the antiresonance frequency, the squeezing parameter of a nonlinear device and/or system can directly be acquired, i.e. in real-time. Further, by adjusting the excitation level or/and detuning frequency, the squeezing can be optimized. For example, real-time monitoring of squeezing effects of resonators working in the nonlinear state improves detector performance in the following aspects: low noise, high sensitivity and stability enhancement, as well as real-time characterization.

[0022] In a preferred embodiment, the multi-tone signal S_multi is defined as follows:

wherein V_k denotes amplitudes, t denotes the time, ϕ_k denotes arbitrary phases, and wherein n is an integer with n ≥ 2. Preferably, ω₁ is below 100·2π Hz, more preferably below 50·2π Hz, and particularly about 10·2π Hz. Alternatively, one or more of the individual sub-tones present in equation 2 may be missing. For example, a multi-tone signal with sub-sequential tones 1ω₁, 2ω₁, 4ω₁, 5ω₁, 6ω₁, 7ω₁, and 8ω₁ is also possible. Thus, as an alternative to equation 2, the multi-tone signal S_multi may be defined as follows:

wherein m is an integer with m ≥ 3, wherein a_k is equal to 1 for at least two different values of k, and wherein a_k is equal to 0 for at least one another value of k (i.e., for at least one further different value of k). For example, according to the above-mentioned exemplary multi-tone signal, where the third subtone is missing, the parameters are as follows: m = 8, a₁ = a₂ = a₄ = a₅ = a₆ = a₇ = a₈ = 1, and a₃ = 0 . It is to be understood that instead of or in addition to the third subtone also one or more other subtones may be missing in the multi-tone signal according to equation 3. Preferably, but not necessarily, the amplitudes V_k are equal for each k, i.e., V_k may correspond to a constant probe signal amplitude V_p for each k.

[0023] In particular, the multi-tone signal S_multi may be written as follows:

or

[0024] As a non-limiting example, n and/or m may be equal to 10, 20, or 100. However, it is noted that the value of n and/or m may be determined based on parameters of the nonlinear device and/or system (e.g. based on the damping or the quality factor of the nonlinear device and/or system). In particular, n may be chosen so that the frequency of the highest subtone is equal to or below 10% of the drive frequency f_d, i.e. nω₁ ≤ 0,1 · 2πf_d. Similarly, m may particularly be chosen so that the frequency of the highest subtone is equal to or below 10% of the drive frequency f_d, i.e. mω₁ ≤ 0,1 · 2πf_d.

[0025] In a further preferred embodiment, the frequency bandwidth BD of the non-sinusoidal wave function and/or the frequency bandwidth BD of the white noise is below 0.1 of the drive frequency f_d, preferably below 0.05 of the drive frequency f_d, and more preferably equal to or below 0.02 of the drive frequency f_d. Preferably, the frequency of the non-sinusoidal wave function and/or the frequency bandwidth BD of the white noise probe signal ranges from zero to 0.1 of the drive frequency f_d (i.e. 0 < f_{white noise} < 0.1f_d), more preferably from zero to 0.05 of the drive frequency f_d (i.e. 0 < f_{white noise} < 0.05f_d), and most preferably from zero to 0.02 of the drive frequency f_d (i.e. 0 < f_{white noise} ≤ 0.02f_d). Noise around the drive frequency can stimulate additional sidebands. These additional sidebands may be overlaid with the sidebands excited by low-frequency noise, and thus the antiresonance dip might be submerged or hidden. Within the present invention, it has been found that the above-mentioned ranges for the frequency bandwidth BD can lead to a suppression or prevention of further noise introduced to the working or drive frequency range. In particular, a low bandwidth noise merely modulates the eigen-frequency (far away from the working frequency) without noise contamination. This makes it possible to reduce noise of the nonlinear device and/or system in a very effective manner.

[0026] In a further preferred embodiment, the additional probe signal, which is applied to the input of the nonlinear device and/or system, is not changed for determining the antiresonance frequency (and particularly for determining the squeezing factor). In particular, the antiresonance frequency is determined based on only one frequency spectrum. In particular, the frequency spectrum, from which the antiresonance frequency is determined, is directly obtained from the detected output signal. The expression "directly obtained" shall mean in this context that the frequency spectrum, from which the antiresonance frequency is determined, is not a composed or overlaid frequency spectrum, i.e. a frequency spectrum that is a composition of several individual frequency spectra. In addition or alternatively, the expression "directly obtained" shall mean in this context that the frequency spectrum of the output signal, from which the antiresonance frequency is determined, is obtained by applying one and the same additional probe signal, i.e. without changing (particularly without sweeping) the additional probe signal. By directly obtaining the frequency spectrum, based on which the antiresonance frequency is determined, from the output signal, a fast monitoring of noise squeezing effects is possible.

[0027] In a further preferred embodiment, the antiresonance frequency f_ar is determined by using a fast-fitting process, for example a combination of a real-time Fourier transformation with error minimalization. Preferably, by means of the fast-fitting process, an envelope of anti-resonance sidebands present in the frequency spectrum of the output signal is found and/or determined. More preferably, an envelope of anti-resonance sidebands present in the frequency spectrum of the output signal is found and/or determined in a frequency region that is defined by (1 ± 0.02)f_d.

[0028] In a further preferred embodiment, the steps of capturing an output signal of the nonlinear device and/or system, determining a frequency spectrum of the output signal, and determining an antiresonance frequency f_ar, are repeated, in the given order, continuously and/or based on (i.e. by or in response to) a request. For example, the steps mentioned above may be repeated after a predefined repetition time in order to continuously monitor the noise squeezing of the nonlinear device and/or system. In addition or alternatively, the steps mentioned above may be repeated on demand.

[0029] In a further preferred embodiment, the method further comprises the step of determining a squeezing factor of the nonlinear device and/or system based on the determined antiresonance frequency f_ar. In particular, the squeezing factor φ is determined by means of equation 1 provided above.

[0030] In a further preferred embodiment, the method serves for reducing noise of the nonlinear device and/or system in real-time and further comprises the step of adjusting the drive signal, particularly the drive frequency f_d and/or a drive power of the drive signal, applied to the input of the nonlinear device and/or system based on the determined antiresonance frequency, particularly based on the determined squeezing factor φ. In particular, the drive frequency f_d and/or the drive power of the drive signal may be changed and/or adjusted such that the squeezing factor and thus the noise squeezing effects increase. Thereby, a reduction of noise, particularly a reduction of the in-phase noise (i.e. the noise of an in-phase signal), of a nonlinear device and/or system is possible in real-time. Further, the signal-to-noise ratio of a nonlinear device and/or system can be enhanced in real-time. In particular, the sensitivity and/or performance of a nonlinear device and/or system can be improved in real-time.

[0031] Preferably, the steps of capturing an output signal of the nonlinear device and/or system, determining a frequency spectrum of the output signal, determining an antiresonance frequency and/or determining a squeezing factor, and adjusting the drive signal based on the determined antiresonance frequency and/or the determined squeezing factor are repeated, in the given order, continuously and/or based on (i.e. by or in response to) a request.

[0032] According to a further aspect of the present invention, a real-time monitoring system for real-time monitoring noise squeezing effects of a nonlinear device and/or system is provided. The real-time monitoring system comprises:

• a drive signal source configured to apply a drive signal S_d having a drive frequency f_d to an input of the nonlinear device and/or system for driving the nonlinear device and/or system in a nonlinear state;

• a probe signal source configured to apply an additional probe signal S_p to the input of the nonlinear device and/or system;
• a signal capturing unit for capturing an output signal S_out of the nonlinear device and/or system;
• a frequency spectrum determination unit being coupled with the signal capturing unit and configured to determine, based on the captured output signal S_out, a frequency spectrum of the output signal S_out;
• an antiresonance frequency determination unit being configured to determine, based on the frequency spectrum of the output signal S_out, an antiresonance frequency f_ar, the antiresonance frequency f_ar being a measure for the noise squeezing effects of the nonlinear device and/or system;
  wherein:

  the additional probe signal S_p comprises a multi-tone signal having a plurality of different probe frequencies, and/or

  the additional probe signal S_p comprises white noise having a frequency bandwidth that is smaller than the drive frequency f_d.

[0033] In particular, the real-time monitoring system is configured to real-time monitor a squeezing factor. In particular, the real-time monitoring system may further comprise the nonlinear device and/or system.

[0034] The frequency spectrum determination unit and/or the antiresonance frequency determination unit may comprise or be a computer and/or processor. In particular, the frequency spectrum determination unit may comprise or be a spectrum analyzer. In particular, the frequency spectrum determination unit may be based on performing a fast Fourier transformation (FFT). In this case, the frequency spectrum determination unit may also be referred to as FFT-unit.

[0035] That two or more units are "coupled" particularly means in the context of the present invention that these units are able to exchange information. The coupling may be done by a physical connection, i.e., the term "coupled" particularly encompasses the term "connected". In addition or alternatively, the coupling may be done by means of a wireless technique. In the latter case, each of the coupled units comprises wireless communication means.

[0036] In a preferred embodiment, the real-time monitoring system further comprises a calculation unit being coupled with the antiresonance frequency determination unit and configured to determine a squeezing factor of the nonlinear device and/or system based on the determined antiresonance frequency f_ar. The calculation unit may comprise or be a computer and/or processor.

[0037] In a further preferred embodiment, the real-time monitoring system comprises a signal acquisition unit being coupled with the signal capturing unit and configured to acquire, based on the captured output signal, an in-phase signal of the nonlinear device and/or system. The signal acquisition unit may comprise or be a computer and/or processor.

[0038] In a further preferred embodiment, the real-time monitoring system comprises an in-phase signal processing unit being coupled with the signal acquisition unit and configured to process and/or analyze the in-phase signal of the nonlinear device and/or system. The in-phase signal processing unit may comprise or be a computer and/or processor.

[0039] In a further preferred embodiment, the real-time monitoring system comprises a feedback unit being coupled with the drive signal unit and configured to adjust, based on the determined antiresonance frequency (particularly based on the determined squeezing factor), the drive signal applied to the input of the nonlinear device and/or system. The feedback unit may comprise or be a computer and/or processor. Preferably, a controlling unit controls the feedback unit. The feedback unit may be coupled and/or connected, particularly via the controlling unit, to the antiresonance frequency determination unit and/or the calculation unit.

[0040] In a further preferred embodiment, the real-time monitoring system comprises a command unit for requesting the determination of the antiresonance frequency, particularly the determination of the squeezing factor. The controlling unit preferably controls the command unit. The command unit may be coupled and/or connected, particularly via the controlling unit, to the antiresonance frequency determination unit and/or the calculation unit.

[0041] In particular, the real-time monitoring system comprises a controlling unit configured to control a feedback unit and/or a command unit based on the determined antiresonance frequency and/or based on the determined squeezing factor. In particular, the controlling unit comprises or is a computer and/or a processor.

[0042] For the above mentioned further independent aspect and in particular for preferred embodiments in this regard, the explanations given above or below concerning the embodiments of the first aspect also hold true. In particular, for one independent aspect of the present invention and for preferred embodiments in this regard, the explanations given above and below concerning the embodiments of the respective other aspects also hold true.

[0043] Individual embodiments for solving the problem are described by way of example below with reference to the figures. In this case, the individual embodiments described have in part features which are not absolutely necessary for implementing the claimed subject matter, but which provide desired properties in specific applications. In this regard embodiments which do not have all the features of the embodiments described below are also intended to be regarded as disclosed in a manner coming under the technical teaching described. Furthermore, in order to avoid unnecessary repetitions, specific features are mentioned only with regard to individual embodiments from among the embodiments described below. It is pointed out that the individual embodiments are therefore intended to be considered not only by themselves but also in a joint consideration. On the basis of this joint consideration the person skilled in the art will recognize that individual embodiments can also be modified by inclusion of individual or a plurality of features of other embodiments. It is pointed out that a systematic combination of the individual embodiments with individual or a plurality of features described with regard to other embodiments may be desirable and expedient and is therefore intended to be taken into account and also to be regarded as encompassed by the description.

Brief description of the figures

[0044] The above and other objects, features and advantages of the present invention will become more apparent upon reading of the following description of preferred embodiments and accompanying drawings. Other features and advantages of the subject-matter described herein will be apparent from the description and the drawings and from the claims. It should be understood that even though embodiments are separately described, single features and functionalities thereof may be combined without prejudice to additional embodiments. The present disclosure is illustrated by way of example and not limited by the accompanying figures.

[0045] Preferred embodiments of the present invention are exemplarily described regarding the following figures:

Fig. 1

shows a schematic representation illustrating the principle of noise squeezing in nonlinear systems;

Fig. 2

shows a schematic representation of a prior art membrane resonator as an example for a nonlinear device, and a detection scheme for determining an antiresonance frequency;

Fig. 3a

shows a measured power spectrum of a two-tone experiment according to the prior art;

Fig. 3b

shows overlaid power spectra obtained from a plurality of two-tone experiments according to the prior art;

Fig. 4

shows a schematic representation illustrating the principle of a preferred embodiment of the method according to the present invention;

Fig. 5

shows a schematic representation for illustrating a preferred embodiment of a system for real-time monitoring the squeezing effects of a nonlinear device and/or system according to the present invention.

Detailed description of the figures

[0046] The following detailed description particularly relates to exemplary embodiments of the present invention. Other embodiments of the invention are possible within the scope of the invention as defined by the appended claims. Throughout the figures, same reference signs are used for the same or similar elements.

[0047] Micro- and nanomechanical oscillators and resonators in the nonlinear regime, which have been shown to be ultra-sensitive for charge, force and mass measurements, show noise squeezing effects. By exploiting these noise squeezing effects, it is possible to circumvent limitations due to environmental fluctuations such as thermal noise or molecular motion. Fig. 1 shows a corresponding schematic representation illustrating the principle of noise squeezing in nonlinear systems such as oscillators and resonators. As can be seen from Fig. 1, squeezing effects are characterized in that the fluctuation of one quadrature is reduced at the expense of that in its conjugate.

[0048] If the signal detection and measurement is performed in the in-phase direction, the noise can be compressed and the signal to noise ratio can be enhanced. As already mentioned above, a homodyne measurement of the noise, as it is conventionally used, is difficult because it requires a complicated characterization and an extremely stable environment. Moreover, it is very time consuming.

[0049] The squeezing effect in the quadrature is usually very subtle and requires sensitive measurements and careful analysis to enable its detection, particularly in systems of high quality-factors. As already mentioned above, publication [3] describes a sideband response of a nonlinear vibrating membrane resonator using a two-tone measurement.

[0050] Fig. 2 shows a schematic representation of the nonlinear vibrating membrane resonator 1 as disclosed in publication [3] (see FIG. 1 therein). The nonlinear device 1 is composed of a ~ 500 nm thick silicon nitride (Si-N) membrane suspended on a massive silicon frame attached to a piezo ring. The vibration of the freestanding membrane is excited by applying a drive signal S_d = V_exc sin(2π f_dt) onto the piezo ring (i.e. an input 3 of the nonlinear device 1) at a drive frequency f_d close to the eigenfrequency f₀ of the membrane resonator 1. By means of detection contacts 4 (particularly detection pads 4), which are electrically connected with one or more detection leads arranged on the membrane resonator 1, an output signal S_out of the nonlinear device 1 being a measure of the vibrations is detected. In the present example, the output signal S_out is an inductive voltage V_out across the structures which is measured at an output 5 of the nonlinear device 1 under an external uniform magnetic field B. As illustrated in Fig. 2, the output voltage V_out and thus the output signal S_out may be measured by a measuring device 8, for example by using a lock-in amplifier (Lock-in) and/or an oscilloscope (OSC) and/or a spectrum analyzer (SA). Further, a pre-amplifier 7 may be used. In addition to the drive tone, that resonantly excites the system, also an additional probe tone V_p sin(2π f_pt) with a very low frequency (f_p<1 kHz) is applied to the input 3 of the nonlinear device 1. It was found that that this probe tone modulates the eigenfrequency of the nonlinear device 1 and leads to a sideband response markedly different from previous studies. The application of a single drive tone and an additional single probe tone is referred to herein as "two-tone experiment".

[0051] If in such a two-tone experiment the nonlinear output signal is observed in the frequency domain, the noise squeezing effects appear as two sidebands, as it is indicated by the two arrows in Fig. 3a showing a measured power spectrum (power P in dependence of frequency f). In the two-tone experiment shown in Fig. 3a, the following parameters were used: f_d = 251 kHz, V_exc = 0.5 V, f_p = 380 Hz, and V_p = 0.5 V. If the probe tone is changed or swept from 10 to 1000 Hz with a step size of 10 Hz under a fixed drive tone, and the respective sideband responses are plotted, this results in an overlaid power spectrum as shown in Fig. 3b. The overlaid power spectrum of Fig. 3b is obtained from a plurality of two-tone experiments described above, wherein for each two-tone experiment a different probe tone (i.e. a different probe frequency) was used.

[0052] The power P reaches a maximum at a peak frequency f_pk = ± 380 Hz and starts to decrease if the probe frequency f_p further increases. More importantly, there is a prominent silent region where the sideband signals are strongly suppressed below a noise floor. In publication [3], it is shown that the two-tone experiments performed on nonlinear devices and/or systems show a typical antiresonance response in the frequency domain. In particular, there exists a minimum point M in the silent region, wherein this minimum point M refers to an antiresonance frequency f_ar and a corresponding antiresonance amplitude or power P_ar.

[0053] In particular, the overlaid power spectrum of Fig. 3b was obtained with a sweeping probe frequency f_p increasing from 10 to 1000 Hz in steps of 10 Hz and V_p = 0.5 V under a given drive signal with V_exc = 0.5 V and f_d = 251 kHz. The dashed line in Fig. 3b shows a parameter free sideband calculation. The coordinate M(f_ar, P_ar) marks the calculated minimum point of the silent region. It is noted that the overlaid power spectrum of Fig. 3b is a black-and-white version of color FIG. 2 (a) disclosed in publication [3]. The color coding shown in FIG. 2 (a) of publication [3], which cannot be seen in the black-and-white version of Fig. 3b, indicates different probe frequencies f_p.

[0054] Thus, in view of the above, if a nonlinear device and/or system is parametrically modulated, the sidebands will have anti-resonance behavior, and the antiresonance frequency (M point) can be used to characterize the squeezing effects (particularly a squeezing factor).

[0055] In particular, the present invention is based on the antiresonance sidebands formed by modulating the nonlinear device and/or system with low-frequency signals. As mentioned before, if the eigenfrequency of a nonlinear device and/or system is modulated at a low frequency (for instance f_p < 1 kHz), the sidebands have anti-resonance behavior in the frequency spectrum. At the antiresonance frequency the intensity of the modulated sideband is severely suppressed. And the antiresonance frequency can be used to calculate the squeezing of noise in the system, for example by the direct relationship between the antiresonance frequency and the squeezing factor Φ, see equation 1 above. The calculation from antiresonance frequency to squeezing factor is quite simple and the determination of the antiresonance frequency can be based on the frequency spectrum instead of sophisticated phase space characterization.

[0056] In particular, within the present invention, it was found that if the injected low-frequency probe signal is designed different compared to the probe signal disclosed in publication [3], one can obtain the anti-resonance shaped sidebands in short time (for instance < 0.1 s) and make a real-time monitoring on the noise squeezing possible.

[0057] Fig. 4 shows a schematic representation which serves to illustrate the principle of a preferred embodiment of the method according to the present invention. As shown in Fig. 4, instead of using a single-tone signal as suggested by publication [3], a multi-tone signal with a plurality of tones and/or frequencies is used as probe signal S_p. This is indicated by the plurality of arrows marked with ω_p on the bottom left side of Fig. 4. The multi-tone probe signal S_p may be defined by equation 2 or 3 provided above. Accordingly, the probe signal S_p may comprise a plurality of probe frequencies f_p, particularly with equal amplitudes. The drive signal may be defined as in publication [3], i.e. by S_d = V_exc sin(2π f_dt) with an excitation voltage V_exc and a drive frequency f_d. As illustrated in Fig. 4, the probe frequencies ω_p = 2nf_p are low frequencies, i.e. smaller than the drive frequency f_d. For example, a basic frequency f₁ of the probe signal may be below 100 Hz, more preferably below 50 Hz, and particularly equal to about 10 Hz, while the drive frequency f_d may be equal to about 251 kHz. It is to be understood that the above values merely serve as an example and that any other values, particularly for the drive frequency, are possible. Any other frequencies of the multi-tone probe signal S_p, which are multiples of the probe signal's basic frequency f₁, are below the drive frequency f_d, preferably below 10% of the drive frequency f_d, and more preferably below 5% of the drive frequency f_d.

[0058] Since the power density of the modulated signal decreases dramatically around the antiresonance dip as shown in Fig. 3b, the antiresonance dip can be determined even if the amplitude of the individual probe tones or multi-tones is not constant. For example, when the amplitudes of the probe tones differ within 6 dB, the frequency spectrum of the modulated signal will be slightly distorted compared with Fig. 3b. Hence, the distortions are within 6 dB, which will result in a small uncertainty of the antiresonance. If the amplitude of probe tones varies monotonically, the inaccuracy is even smaller. In addition, because of the linear relationship between probe tones and modulated signal, it is easy to perform a post analysis on the modulated signal by multiplying or dividing with a factor or function to normalize the modulated signal.

[0059] Alternatively or in addition to a multi-tone signal, the probe signal S_p may comprise or be white noise. In this case, it turned out within the present invention that real-time monitoring of noise squeezing is possible, if the white noise signal has a frequency bandwidth BW that is smaller than the drive frequency f_d. Preferably, any frequency of the white noise probe signal is smaller than the drive frequency f_d, wherein the frequencies of the white noise probe signal range from zero to BW. Preferably, the frequency bandwidth BW of the white noise probe signal is below 0.1 of the drive frequency f_d, more preferably below 0.05 of the drive frequency f_d, and most preferably equal to or below 0.02 of the drive frequency f_d.

[0060] By capturing the response signal S_out of the nonlinear device and/or system (not explicitly shown in Fig. 4) and applying a fast Fourier transformation to the captured response signal (which is fast enough for a real-time scenario), the frequency spectrum of the response or output signal is obtained. Due to the probe signal comprising a multi-tone signal and/or white noise (having a limited frequency bandwidth), as described above, the obtained frequency spectrum comprises, besides a pronounced amplitude at the drive frequency f_d, a plurality of sidebands showing an antiresonance behavior. Based on the obtained frequency spectrum, the antiresonance frequency being a measure for the noise squeezing effects can be determined, particularly by using a fast-fitting process. Thus, by using a probe signal as proposed by the present invention, there is no need any more for a complex and time-consuming integration over a plurality of individual frequency spectra which are obtained, step by step, by sweeping the probe frequency, as described in publication [3]. In particular, by using a probe signal as proposed by the present invention, a real-time monitoring of the squeezing effects in a nonlinear device and/or system is possible.

[0061] For example, a preferred embodiment about how to fast locate the antiresonance frequency comprises the following steps:

(1) Drive the system oscillating in a nonlinear state, at a working frequency of f_d;

(2) Simultaneously send additional signal S_p with low-frequencies, the low frequency signal S_p can in particular be periodic or noise, e.g.,

(i)

wherein ω₁ ~ 10×2π Hz, and phase of each frequency can be random, as sketched in Fig. 4, or

(ii) low-frequency white noise, with a frequency range of 0 - BW, and with a bandwidth BW of ~ 0.02 f_d;

(3) Send response signal to a processor for FFT analysis; Find the envelope of anti-resonance sideband (in the region between the dashed vertical line of Fig. 4, (1±0.02)ω_d), extract the antiresonance frequency ω_ar by fast fitting process;

(4) Then, the squeezing factor φ can be calculated by equation 1 provided above.

[0062] Fig. 5 shows a schematic representation for illustrating a preferred embodiment of a real-time monitoring system 100 for real-time monitoring squeezing effects of a nonlinear device and/or system according to the present invention. The real-time monitoring system 100 comprises a drive signal source 10 configured to apply a drive signal S_d having a drive frequency f_d to an input of the nonlinear device and/or system 1 for driving the nonlinear device and/or system 1 in a nonlinear state. Further, the monitoring system 100 comprises a probe signal source 20 configured to apply an additional probe signal S_p to the input of the nonlinear device and/or system 1. Further, the monitoring system 100 comprises a signal capturing unit 30 for capturing an output signal S_out of the nonlinear device and/or system 1. Further, the monitoring system 100 comprises a frequency spectrum determination unit 40 being coupled with the signal capturing unit 30 and configured to determine, based on the captured output signal S_out, a frequency spectrum of the output signal S_out. For example, the frequency spectrum determination unit 40 may comprise a spectrum analyzer. Further, the monitoring system 100 comprises an antiresonance frequency determination unit 50 being configured to determine, based on the frequency spectrum of the output signal S_out , an antiresonance frequency f_ar, the antiresonance frequency f_ar being a measure for the noise squeezing effects of the nonlinear device and/or system 1. Further, the monitoring system 100 comprises a calculation unit 60 being coupled with the antiresonance frequency determination unit 50 and configured to determine a squeezing factor of the nonlinear device and/or system 1 based on the determined antiresonance frequency f_ar. Further, the monitoring system 100 comprises a signal acquisition unit 32 being coupled with the signal capturing unit 30 and configured to acquire, based on the captured output signal S_out, an in-phase signal of the nonlinear device and/or system 1. Further, the monitoring system 100 comprises an in-phase signal processing unit 34 being coupled with the signal acquisition unit 32 and configured to process and/or analyze the in-phase signal of the nonlinear device and/or system 1. Further, the monitoring system 100 comprises a feedback unit 80 being coupled with the drive signal unit 10 and configured to adjust, based on the determined antiresonance frequency f_ar, the drive signal S_d applied to the input 3 of the nonlinear device and/or system 1. Further, the monitoring system 100 comprises a command unit 90 for requesting the determination of the antiresonance frequency f_ar. The feedback unit 80 and the command unit 90 are controlled by a controlling unit 70, wherein the controlling unit 70 comprises or is a computer and/or a processor.

[0063] Thus, in the embodiment illustrated in Fig. 5, the signal used for further data processing or detection is the in-phase signal of the vibration of a nonlinear device and/or system 1. The present invention enables to reduce the noise floor of the in-phase signal and thus to improve the resolution or sensitivity of the nonlinear device and/or system 1. To achieve this goal, the nonlinear device and/or system 1 is driven by a drive signal into a nonlinear state. The nonlinear device and/or system 1, for example, can be a NEMS/MEMS gyroscope, mass detector, Inertial sensor, accelerator. and so on and can provide the working state (working frequency, damping and so on) of resonators (or sensors). In particular, the drive signal drives the nonlinear device and/or system 1 to stay on-resonance or around on-resonance (and provide a squeezing state for enhancing the signal).

[0064] When the nonlinear device and/or system 1 needs to be optimized to have the lowest noise floor, a pulse of test or probe signal is sent into the system in addition to the drive signal. For example, the types of the test or probe signal can be low-frequency multi-tones (particularly with equal amplitudes) or low-frequency white noise with small bandwidth or any other non-sinusoidal wave function having multiple low frequencies and a small bandwidth (particularly a wave function which does not represent just a single tone or harmonics). It can be either continuously send the device and/or system 1 or can be performed while requested by a command of requesting the squeezing factor from a processor.

[0065] In particular, the frequency of the test signal is lower than that of drive signal, for instance, only 1% of the drive frequency. Then, the vibration of the nonlinear system is captured by a read-out method, for example by a capacitance detection, electromagnetic induction, optical interferometry, etc., and converted into an electrical signal. The captured electrical signal is further processed by applying a real-time FFT to the electrical signal around the working frequency after the control unit 70 and/or the command unit 90 requests the squeezing factor. The real-time FFT can be done, for example, by a field programmable gate array (FPGA) or any other suitable logical circuit.

[0066] The signal capture and FFT can be done, for example, continuously or time to time on demand. Subsequent to the real-time FFT, the anti-resonance sideband shape can be obtained, and the antiresonance frequency can be read out. Optionally, the squeezing factor can be calculated by the control unit 70 in real-time (providing the information of how the noise has been suppressed by squeezing effects), and the control unit 70 determines, if the working status of the nonlinear device and/or system 1 needs to be adjusted as well as how it feeds back to the nonlinear device and/or system 1. This feedback technique itself is well known to the skilled person and thus not further described within the present invention. In particular, as it is known from publication [3], by adjusting the drive power and/or drive frequency (detuning), the squeezing and the antiresonance effect can be controlled (see FIG. 3 and the corresponding description in publication [3]).

[0067] Optionally, the antiresonance frequency can also be used directly to determine if the current working status has the lowest noise floor. For example, the on-resonance states provide the best squeezing state for enhancing the signal in some nonlinear system and the antiresonance frequency of the on-resonance states is close to zero. Therefore, the processor (e.g. the control unit 70) can compare the obtained antiresonance frequency with zero and then determine how to feed back to the nonlinear system 1.

[0068] Since it is unnecessary to integrate the captured signal, the frequency of the request and feedback can be relatively high by using the present invention, especially for a nonlinear system with high working frequency and/or high Q-factor. For example, if the working frequency of a nonlinear system is at 200 MHz and the Q-factor is 10⁵, the test signal can be multi-tones with a basic frequency of 100 Hz, and the frequency of a squeezing request can be as high as the basic frequency of the multi-tones. For example, the multi-tones may have frequencies of 100 Hz, 150 Hz, 200 Hz, etc. Then, the frequency of the squeezing request can be as high as 100 Hz.

[0069] After lowering the noise floor of the nonlinear device and/or system 1 by reading the antiresonance frequency, the in-phase signal of the working mass (that is the noise suppressed signal) can be extracted, and a good quality of the output signal with suppressed noise can be achieved. It is noted that the extraction of the in-phase signal can be done either before or after the real-time FFT.

[0070] In particular, by the present invention, a real-time monitoring of squeezing effects of nonlinear oscillators or resonators working in a wide range of conditions can be achieved. The invention avoids the harsh requirements of phase-space. Rather, it only needs easy post analysis and thus makes the dynamic feedback of the squeezing factor easier. In particular, the present invention provides a method and system for monitoring the noise squeezing factor of nonlinear resonators in real-time and thus reducing the noise of resonators. More particularly, it provides a method and system for real-time monitoring the intensity of in-phase noise of nonlinear resonators and feeding back to the drive source to adjust the working conditions of resonators, for example drive frequency and power level. More particularly, it provides a method and system for real-time monitoring the in-phase noise by measuring the antiresonance frequency in the real-time frequency spectrum obtained by frequency modulation of low-frequency signals. For example, the present invention enables the realization of noise squeezed nonlinear resonators, for instance NEMS/MEMS resonating detectors. In applications, the present invention enables, for example, an improved detection and/or signal transmission. Thus, the present invention particularly enables real-time monitoring of squeezing effects of resonators working in the nonlinear state to improve detector performance: suppressing noise, enhancing sensitivity and stability, fast response, robust applicational scenarios (e.g. large signal-to-noise-ratio), large operational frequency range, and/or real time characterization.

List of Reference Numerals

[0071] 

1

nonlinear device and/or system

3

input of the nonlinear device and/or system

4

detection contact / detection pad

5

output of the nonlinear device and/or system

7

pre-amplifier

8

measuring device (spectrum analyzer / oscilloscope / lock-in amplifier)

10

drive signal source

20

probe signal source

30

signal capturing unit

32

signal acquisition unit

34

in-phase signal processing unit

40

frequency spectrum determination unit

50

antiresonance frequency determination unit

60

calculation unit

70

controlling unit

80

feedback unit

90

command unit

100

real-time monitoring system

Claims

1. A method for real-time monitoring noise squeezing effects of a nonlinear device and/or system (1), comprising the following steps:

- applying a drive signal S_d having a drive frequency f_d to an input (3) of the nonlinear device and/or system (1) for driving the nonlinear device and/or system (1) in a nonlinear state

- applying an additional probe signal S_p to the input of the nonlinear device and/or system (1);

- capturing an output signal S_out of the nonlinear device and/or system (1);

- determining, based on the captured output signal S_out, a frequency spectrum of the output signal S_out;

- determining, based on the frequency spectrum of the output signal S_out, an antiresonance frequency f_ar, the antiresonance frequency f_ar being a measure for the noise squeezing effects of the nonlinear device and/or system (1);
characterized in that:

the additional probe signal S_p comprises a multi-tone signal having a plurality of different probe frequencies, and/or

the additional probe signal S_p comprises white noise having a frequency bandwidth that is smaller than the drive frequency f_d.

2. The method of claim 1,
wherein the multi-tone signal is defined as follows:

or

wherein:

V_k denotes amplitudes, t denotes the time, ϕ_k denotes arbitrary phases, n is an integer with n ≥ 2, m is an integer with m ≥ 3, a_k is equal to 1 for at least two different values of k, and a_k is equal to 0 for at least one further different value of k; and

wherein ω₁ is preferably below 100·2π Hz, more preferably below 50·2π Hz, and particularly about 10·2π Hz.

3. The method of claim 1 or 2, wherein
the frequency bandwidth BD of the white noise is below 0.1 of the drive frequency, preferably below 0.05 of the drive frequency, and more preferably equal to or below 0.02 of the drive frequency.

4. The method of any one of the preceding claims, wherein the additional probe signal S_p, which is applied to the input (3) of the nonlinear device and/or system (1), is not changed for determining the antiresonance frequency f_ar.

5. The method of one of the preceding claims, wherein the antiresonance frequency f_ar is determined by using a fast-fitting process.

6. The method of any one of the preceding claims, wherein the steps of capturing an output signal S_out of the nonlinear device and/or system, determining a frequency spectrum of the output signal, and determining an antiresonance frequency f_ar, are repeated, in the given order, continuously and/or based on a request.

7. The method of any one of the preceding claims, further comprising:

- determining a squeezing factor of the nonlinear device and/or system (1) based on the determined antiresonance frequency f_ar.

8. The method of any one of the preceding claims, wherein the method serves for reducing noise of the nonlinear device and/or system (1) in real-time and further comprises:

- adjusting the drive signal S_d applied to the input (3) of the nonlinear device and/or system (1), particularly the drive frequency f_d and/or a drive power of the drive signal S_d, based on the determined antiresonance frequency f_ar.

9. A real-time monitoring system (100) for real-time monitoring noise squeezing effects of a nonlinear device and/or system (1), comprising:

- a drive signal source (10) configured to apply a drive signal S_d having a drive frequency f_d to an input (3) of the nonlinear device and/or system (1) for driving the nonlinear device and/or system (1) in a nonlinear state;

- a probe signal source (20) configured to apply an additional probe signal S_p to the input (3) of the nonlinear device and/or system (1);

- a signal capturing unit (30) for capturing an output signal S_out of the nonlinear device and/or system (1);

- a frequency spectrum determination unit (40) being coupled with the signal capturing unit (30) and configured to determine, based on the captured output signal S_out, a frequency spectrum of the output signal S_out;

- an antiresonance frequency determination unit (50) being configured to determine, based on the frequency spectrum of the output signal S_out, an antiresonance frequency f_ar, the antiresonance frequency f_ar being a measure for the noise squeezing effects of the nonlinear device and/or system (1);
wherein:

the additional probe signal S_p comprises a multi-tone signal having a plurality of different probe frequencies, and/or

the additional probe signal S_p comprises white noise having a frequency bandwidth that is smaller than the drive frequency f_d.

10. The system (100) of claim 9, further comprising:

- a calculation unit (60) being coupled with the antiresonance frequency determination unit (50) and configured to determine a squeezing factor of the nonlinear device and/or system (1) based on the determined antiresonance frequency f_ar.

11. The system (100) of claim 9 or 10, further comprising:

- a signal acquisition unit (32) being coupled with the signal capturing unit (30) and configured to acquire, based on the captured output signal S_out, an in-phase signal of the nonlinear device and/or system (1).

12. The system (100) of claim 11, further comprising:

- an in-phase signal processing unit (34) being coupled with the signal acquisition unit (32) and configured to process and/or analyze the in-phase signal of the nonlinear device and/or system (1).

13. The system (100) of any one of claims 9 to 12, further comprising:

- a feedback unit (80) being coupled with the drive signal unit (10) and configured to adjust, based on the determined antiresonance frequency f_ar, the drive signal S_d applied to the input (3) of the nonlinear device and/or system (1), wherein the feedback unit (80) is preferably controlled by a controlling unit (70).

14. The system (100) of any one of claims 9 to 13, further comprising:

- a command unit (90) for requesting the determination of the antiresonance frequency f_ar, wherein the command unit (90) is preferably controlled by a controlling unit (70).

Drawing