An important feature of heterodyne laser Doppler vibrometer (LDV) is the possibility of measuring an optical path length oscillation at frequency f at a choosable frequency f_het-f, at which the photo-electric detector shows a sufficiently high dark noise clearance. The full squeezed light enhancement of a heterodyne LDV's signal to noise has not been achieved so far. Here we use a sideband spectrum that is squeezed around f_het=40 MHz and demonstrate the squeezing enhanced measurement of an optical path length vibration at f=1 MHz of about 3.5 dB while fully maintaining the signal power. The proof of principle we provide will enable the realization of ultra-precise LDVs over extended signal bandwidth for probes or environments that require low intensities.
An important feature of heterodyne laser Doppler vibrometer (LDV) is the possibility of measuring an optical path length oscillation at frequency f at a choosable frequency f_het-f, at which the photo-electric detector shows a sufficiently high dark noise clearance. The full squeezed light enhancement of a heterodyne LDV's signal to noise has not been achieved so far. Here we use a sideband spectrum that is squeezed around f_het=40 MHz and demonstrate the squeezing enhanced measurement of an optical path length vibration at f=1 MHz of about 3.5 dB while fully maintaining the signal power. The proof of principle we provide will enable the realization of ultra-precise LDVs over extended signal bandwidth for probes or environments that require low intensities.
In a recent paper, we experimentally realised a squeezed-light enhanced heterodyne Laser Doppler Vibrometer (LDV) for vibration measurements and demonstrated a phase-modulated signal with a carrier-to-noise ratio exceeding the shot noise limit.For this, we characterised the non-classical sensitivity enhancement with a spectrum analyser.However, to obtain the actual displacement values, the signal must be demodulated and digitised without adding significant noise.Here we show that clipping in combination with zero-crossing synchronous sampling can avoid quantisation noise during digital demodulation.For a signal with a frequency of 2 MHz, we improved the shot-noise limited resolution of a 50 𝜇W measurement beam from 10 fm/ √ Hz to 8 fm/ √ Hz.Our results show for the first time the effect of squeezed light enhancement in a demodulated signal of a heterodyne LDV.
Laser Doppler Vibrometry (LDV) is a high-precision, non-contact measurement technique that leverages optical interference between a reference beam and a Doppler-shifted measurement beam derived from coherent laser light. By detecting phase variations induced by surface vibrations, LDV has become a widely utilized tool in industrial environments for vibration analysis, structural diagnostics, and quality control. The detection sensitivity of the LDV is fundamentally constrained by the Poissonian statistics of photon arrivals. In heterodyne LDV systems, the enhancement of signal-to-noise ratio (SNR) and measurement resolution under shot-noise-limited conditions typically requires increasing the optical power of the measurement beam. However, this approach becomes infeasible in scenarios with strict constraints on thermal load or optical power. Recent studies have demonstrated that injecting squeezed vacuum states as non-classical light sources can suppress quantum noise while maintaining low optical power, thus surpassing the standard quantum limit. This thesis introduces the principle of the heterodyne LDV combined with squeezed light sources. The first scientific hypothesis proposed herein is that introducing laser light with squeezed quantum uncertainties into industrial heterodyne LDVs enables vibration measurements to exceed the physical resolution limits of traditional LDVs, achieving sub-shot-noise sensitivity. The thesis designed a squeezed-light-enhanced heterodyne LDV, achieving over 3 dB of squeezing within a 40 MHz measurement bandwidth and demonstrating a noise-equivalent displacement resolution reaching 8 fm/√Hz, thereby confirming the first hypothesis. Addressing the limitations imposed by the finite dynamic range of analog-to-digital converters (ADCs) on the SNR of digitally demodulated phase-modulated signals, the thesis proposes a clipping-based synchronous zero-crossing sampling technique and a corresponding second scientific hypothesis: that this sampling scheme enables heterodyne LDV to overcome the digital noise floor defined by the ADC's SNR. Experimental results demonstrate that this sampling and demodulation approach effectively reduces ADC quantization noise, allowing the digital resolution of the demodulated phase-modulated signal to surpass the ADC-imposed SNR limit while preserving the quantum noise-level squeezing, thereby validating the second hypothesis. Compared to previous work, this research constitutes the first experimental verification of squeezed-light-enhanced measurement feasibility in a classical heterodyne LDV operating at a 40 MHz difference frequency, advancing the application of quantum-enhanced precision metrology in industrial vibration testing.
Abstract Advanced industrial applications in nanotechnology, MEMS, and semiconductor manufacturing demand laser-Doppler vibrometers with femtometer displacement sensitivity. Conventional heterodyne interferometers provide high linearity and accuracy for industrial measurements but are fundamentally limited by quantum shot noise, whose disruptive influence effectively decreases with increasing measured light power. Although laser safety regulations permit a laser power of up to 10mW for a 1550nm measuring beam, temperature-sensitive structures often require lower light power. Note that a laser power of 10mW focused on 10 µm^2 corresponds to an irradiance of 1GWm^(−2). Highest resolution needs to be achieved at low laser powers of the measurement beam, which presents a challenge for shot-noise-limited measurements. In this work, we present a new resolution record for the demodulated displacement signal of our squeezedlight- enhanced heterodyne laser-Doppler vibrometer. Our system achieved a displacement sensitivity of 2.6 fm/√Hz with only 0.36 mW of measurement power. Our results demonstrate improved performance beyond the shot noise limit without increasing optical power, approaching sub-fm precision in vibration measurements.
A phase-sensitive (PS) heterodyne detector is intrinsically resistant to classical noises and useful in measurement of low-frequency signals below the shot noise. Despite the existence of image band vacuum, we show that the quantum-noise power level of this heterodyne detector sensing a coherent signal is exactly one light quantum per measurement time, i.e., twice the vacuum fluctuation power, which can be further reduced by use of squeezed light. We then report on an experiment on a PS heterodyne detector with a 10 Hz 1.0×10−18 W optical signal (1064 nm wavelength) at its input. The noise floor of the unmodulated coherent light is 2.2(±0.1)×10−19 W/Hz from 2 Hz to 20 Hz, and the signal-to-noise ratio is about 6.6 dB for the measured signal when the resolution bandwidth is 1 Hz. The quantum noise floor is reduced by 1.6(±0.3)dB when squeezed light is used, and the sub-shot-noise power spectral density is 1.6(±0.1)×10−19 W/Hz between 2 Hz and 20 Hz. This work should be an important advance towards squeezing-improved precision measurements of low-frequency signals with heterodyne detectors, including audio-band gravitational-wave detection.
Continuous variable (CV) audio-band frequency squeezed states at the fiber telecommunication wavelength is an important quantum resource for the practical applications based on optical fiber. As is well known, the optical power attenuation and phase diffusion effect of light at 1.3 μm in standard telecommunication fibres are low and small, respectively. The audio-band frequency squeezed light at 1.34 μm can be utilized to realize quantum precision measurement, such as quantum-enhanced sensing in the low-frequency range, laser interferometer for gravitational wave detection. In this paper, CV audio-band frequency vacuum squeezed states at 1.3 μm are experimentally generated by using a type-I degenerate optical parametric oscillator (DOPO) below the threshold. A home-made continuous-wave single-frequency dual-wavelength (671 nm and 1.34 μm) Nd:YVO4/LBO laser is used as a pump source for DOPO based on a type-I quasi-phase-matched periodically poled KTiOPO4 (PPKTP) crystal. Mode cleaners with a finesse of 400 and linewidth of 0.75 MHz are used to filter the noise of lasers at 671 nm and 1.34 μm, respectively. The intensity noises of the two lasers reach a shot noise level for analysis frequencies higher than 1.0 MHz and their phase noises reach shot noise level for analysis frequencies higher than 1.3 MHz, respectively. The low noise single-frequency 671 nm laser is utilized as a pump of the DOPO. The threshold power of the DOPO is 450 mW. In order to detect the audio-band frequency vacuum squeezed states, the power of local oscillator of a homodyne detector system is optimized to 60 μupW. Furthermore, the effect of common mode rejection ratio (CMRR) of detectors is discussed in detecting the audio-band frequency vacuum squeezed states. Improvement of CMRR of detectors is a good way to detect the audio-band frequency vacuum squeezed states effectively. When the phase matching temperature of PPKTP crystal is controlled at 53℃ by using a home-made temperature controller and the pump power is 95 mW, the vacuum squeezed states are generated at analysis frequency ranging from 8-100 kHz. A maximum measured squeeze of 5.0 dB is obtained at analysis frequency of 36 kHz. A 3.0 dB squeezed light is obtained at an audio-band frequency of 8 kHz.
Squeezing-based quantum metrology has been extensively applied in the field of precision measurement. Performance characteristics of squeezed light are obtained by a balanced homodyne detector. Here, we report a large dynamic range balanced homodyne detector with low-noise and high-signal-to-noise-ratio (SNR) for broadband squeezed light measurement. We perform a comprehensive theoretical analysis of the SNR in a wide bandwidth and experimentally analyze the important printed circuit board (PCB) layout and electronic components. Consequently, in the 100 MHz frequency band, the SNR and common mode rejection ratio (CMRR) rise over 12.6 dB and 55 dB, respectively, and the electronic noise is suppressed below -90 dB. The directly observed squeezing level at 1550 nm with the specified detector is 11.8 dB at 2 MHz and 3.1 dB at 100 MHz.