The shot-noise-limited sensitivity for detecting audio-frequency phase signals has garnered significant interest in both research and practical applications. This work presents a novel experimental setup that generates frequency-synthesized light with suppressed carrier and enhanced sidebands using an electro-optic intensity modulator (EOIM). When injected into a Mach-Zehnder interferometer (MZI), the EOIM-generated light not only enables phase-sensitive heterodyne locking to stabilize the relative phase of the MZI but also functions as a balanced heterodyne detector for audio-frequency phase measurements. By integrating these three key techniques into the MZI, phase detection sensitivity reaches the shot-noise limit across the audio-frequency band. This advancement holds promise for applications in gravitational wave detection, vacuum magnetic birefringence studies, spin-orbital interactions, material characterization, polarization microscopy, atomic magnetometry, and biomedical optics.
The shot-noise-limited sensitivity for detecting audio-frequency phase signals has garnered significant interest in both research and practical applications. This work presents a novel experimental setup that generates frequency-synthesized light with suppressed carrier and enhanced sidebands using an electro-optic intensity modulator (EOIM). When injected into a Mach-Zehnder interferometer (MZI), the EOIM-generated light not only enables phase-sensitive heterodyne locking to stabilize the relative phase of the MZI but also functions as a balanced heterodyne detector for audio-frequency phase measurements. By integrating these three key techniques into the MZI, phase detection sensitivity reaches the shot-noise limit across the audio-frequency band. This advancement holds promise for applications in gravitational wave detection, vacuum magnetic birefringence studies, spin-orbital interactions, material characterization, polarization microscopy, atomic magnetometry, and biomedical optics.
Traditional locking techniques, such as PDH (Pound-Drever-Hall), HC (Hansh-Couillaud), spatial mode interference technique, offset sideband locking technique, quantum noise locking, etc., have been widely applied to laser frequency stabilization and precision optical interferometry measurement. Here, a new technique, which we call phase-sensitive heterodyne locking (PSHL), is investigated by use of frequency-synthesized light to obtain a phase-sensitive high-frequency photoelectric readout to lock the phase of a squeezed light. Comparing with above techniques, there are several kinds of advantages for PSHL to be advocated. Frequency-synthesized light, which allows arbitrary control of the amplitudes and phases of the modulation sidebands relative to the carrier, is derived by the AOM (acousto-optic modulator), not the EOM (electro-optic modulator). Interferometic signals coming from a balanced heterodyne detector are high-frequency AC photoelectric current which can easily get rid of low-frequency classical noise and lead to reach or break through the shot noise limit. A theoretical derivation of the PSHL error signal and the associated stability of the squeezed and anti-squeezed lock points will be carried out in this work.
Measurement of audio signal plays a significant role in many applications, such as gravitational wave detection, bio-particle imaging and magnetometer. In this paper, low-frequency squeezed light is generated by a non-degenerate optical parametric amplifier. In order to avoid the effect of injected light on low-frequency squeezing, an auxiliary laser is used to lock the length of non-degenerate optical parametric amplifier and a method of locking quantum noise is employed to lock the phase between the local light and the squeezed light. By isolating the vibration noises at low-frequency and reducing back action of parasitic interference, the squeezing of (7.1±0.1) dB takes place at 19 kHz. Then the squeezed light is injected into the Mach-Zehnder interferometer to measure an audio signal which drives a piezoelectric transducer to generate a small phase variation between two arms of Mach-Zehnder interferometer. According to the low-frequency squeezing, we realize experimentally the measurement of phase signal at audio frequency which exceeds the shot-noise limit of (3.0±0.4) dB. The experiment provides technical supports for the generation of low-frequency squeezed light and the measurement of audio signal. Furthermore it can be extended to other quantum measurements, such as high-precision magnetometer and measurement of small-displacement.
Quantum noise limited interferometry for subhertz phase measurement is of essence in precision metrology applications, such as gravitational wave detection. However, suppression of subhertz classical noises below the shot-noise level is very challenging in practice. Two-frequency interferometry has been previously proposed to avoid low-frequency noises and may be useful for squeezing-enhanced high-precision phase measurement. Here we experimentally demonstrate a subhertz interferometer at the standard quantum noise (shot-noise) limit, by use of dual-frequency coherent probe light at the input and phase-sensitive heterodyne detection to measure the output interfered light. When the interferometer is locked at a dark fringe, the noise floor of the phase variance in the interferometer reaches the shot-noise level down to Fourier frequencies below 1 Hz. This work should pave a way for a realization of subhertz interferometry beyond the shot-noise limit.
The advent of stable, highly squeezed states of light has generated great interest in the gravitational wave community as a means for improving the quantumnoise- limited performance of advanced interferometric detectors. To confidently measure these squeezed states, it is first necessary to measure the shot-noise across the frequency band of interest. Technical noise, such as non-stationary events, beam pointing, and parasitic interference, can corrupt shot-noise measurements at low Fourier frequencies, below tens of kilo-Hertz. In this paper we present a qualitative investigation into all of the relevant noise sources and the methods by which they can be identified and mitigated in order to achieve quantum noise limited balanced homodyne detection. Using these techniques, flat shot-noise down to Fourier frequencies below 0.5 Hz is produced. This enables the direct observation of large magnitudes of squeezing across the entire audio-band, of particular interest for ground-based interferometric gravitational wave detectors. 11.6 dB of shot-noise suppression is directly observed, with more than 10 dB down to 10 Hz.
The advent of stable, highly squeezed states of light has generated great interest in the gravitational wave community as a means for improving the quantumnoise- limited performance of advanced interferometric detectors. To confidently measure these squeezed states, it is first necessary to measure the shot-noise across the frequency band of interest. Technical noise, such as non-stationary events, beam pointing, and parasitic interference, can corrupt shot-noise measurements at low Fourier frequencies, below tens of kilo-Hertz. In this paper we present a qualitative investigation into all of the relevant noise sources and the methods by which they can be identified and mitigated in order to achieve quantum noise limited balanced homodyne detection. Using these techniques, flat shot-noise down to Fourier frequencies below 0.5 Hz is produced. This enables the direct observation of large magnitudes of squeezing across the entire audio-band, of particular interest for ground-based interferometric gravitational wave detectors. 11.6 dB of shot-noise suppression is directly observed, with more than 10 dB down to 10 Hz.
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.