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Quantum-enhanced laser-Doppler vibrometer with 2.6 fm/√Hz sensitivity in the broadband demodulated signal

Christian Rembe, Mengwei Yu, P. Gewecke, Roman Schnabel

Published Jan 9, 2026• 1 citation
Publisher

Abstract

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.

DOI
10.21203/rs.3.rs-8288663/v1

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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.
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 Quantum technologies that exploit quantum-correlated resources offer advantages over quantum technologies that just exploit coherent states. Here we propose and demonstrate the exploitation of squeezed light to enhance laser interferometers being at the sensitivity limit of eye-safe optical powers into a new regime otherwise impossible without sacrificing eye-safety. We realised a homodyne Mach–Zehnder interferometer that in its arms used an eye-safe combined optical power of only 10 mW at the wavelength of 1550 nm, and nevertheless achieved a displacement noise spectral density of as low as 0.26 fm Hz−1/2. This value is more than a factor of 10 below what is possible with 10 mW in ideal coherent states at 1550 nm and slightly lower than what is possible with 100 mW at the same wavelength. We envision a new user application for squeezed light in avoiding costs for laser safety measures.
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.
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.
The optical shot-noise limit of a laser beam represents the classical limit in precision and signal to noise ratio achievable in optical sensors and imaging systems. It is known that quantum states of light, such as squeezed light and quantum correlated twin beams can be used to enhance precision and signal to noise ratio to beyond this limit. This promises optical sensors with fundamentally superior performance to the state of the art. While quantum-enhanced signal to noise ratio has been demonstrated with macroscopic powers of squeezed probe beam, demonstrations of quantum enhanced precision have remained at extremely low powers of light (femto-Watts). Here we will give examples where increasing SNR with quantum light is not sufficient to increase precision and we will review proof of principle experiments that have demonstrated sub shot noise precision, including for absorption spectroscopy and imaging. We will also report our efforts to achieve this sub-shot-noise precision performance for transmission measurement with ~0.1mW of average probe power, equating to ~10W peak power in a pulsed experiment. Time permitting, we will discuss how integrated optics and integrated electronics enables 10s GHz bandwidth in the detection of squeezed light, for integrated quantum sensor technology.