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.
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.
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.
High precision interferometers are the building blocks of precision metrology and the ultimate interferometric sensitivity is limited by the quantum noise. Here, we propose and experimentally demonstrate a compact quantum interferometer involving two optical parametric amplifiers and the squeezed states generated within the interferometer are directly used for the phase-sensing quantum state. By both squeezing shot noise and amplifying phase-sensing intensity the sensitivity improvement of 4.86±0.24 dB beyond the standard quantum limit is deterministically realized and a minimum detectable phase smaller than that of all present interferometers under the same phase-sensing intensity is achieved. This interferometric system has significantly potential applications in a variety of measurements for tiny variances of physical quantities.
Quantum metrology harnesses nonclassical resources including squeezed states and quantum entanglement to overcome fundamental limitations imposed by the shot-noise limit (SNL). While conventional optical interferometers for phase detection typically operate in the MHz-frequency regime due to technical noise constraints at lower frequencies, numerous practical applications demand operation in the kHz regime or below. Here, we present a truncated SU(1,1) interferometric configuration that achieves enhanced phase sensitivity in the low-frequency (kHz) domain by exploiting quantum entanglement generated through two-mode squeezed states. Our approach incorporates quantum sideband control to achieve quantum correlations across multiple low-frequency bands while simultaneously suppressing technical noise. Through precise locking of optimal phase, we demonstrate a significant improvement in signal-to-noise ratio within the kHz range, with phase sensitivity surpassing the SNL by 2.0 ± 0.2 dB. These experimental results provide crucial validation for extending entanglement-enhanced optical interferometry into low-frequency metrological applications and establish novel methodologies for optical modulation and sideband-based quantum information processing and quantum sensing protocols.
We propose and experimentally demonstrate a quantum-enhanced fiber Mach-Zehnder interferometer for low-frequency phase measurement beyond the shot-noise limit using a high-frequency squeezing technique. The local oscillator field is amplitude-modulated in the MHz range and is then demodulated to avoid the technical noise that occurs at low frequencies. After measurement of the phase noise at a frequency of tens of kHz, an improvement of ∼2 dB relative to the shot-noise level is achieved. Additionally, the amplitude modulation depth has no significant effect on the phase noise improvement of the interferometer when deployed in our experimental configuration. The current scheme introduces a quantum technique into the fiber-based measurements, particularly for the low frequency range, and this scheme has potential applications in the high-precision fiber sensing of temperature, strain, and various other parameters.
An important part of optical sensing is interferometry, where direct or homodyne detection at the output of an interferometer yields information about small phase shifts. Classical interferometry operates at the shot-noise limit (SNL), caused by the photon structure of light and reached when an interferometer is fed with coherent light. The use of nonclassical light at the input of an interferometer enables overcoming the SNL. In particular, squeezed light is known to be less noisy than coherent light. An interferometer fed with strongly squeezed light can, in principle, provide the phase sensitivity at the Heisenberg limit, the ultimate limit allowed by the laws of physics. However, this supersensitive operation is strongly degraded by loss – both inside the interferometer and outside it, at the stage of detection. While the former (internal loss) seems to be inevitable, the latter (detection loss) can be overcome, and we demonstrate it in our recent experiment. The clue is to amplify light at the interferometer output using a phase-sensitive optical parametric amplifier. This device does not introduce additional noise, but it amplifies the fragile quantum signal and thus makes it tolerant to loss at the detection stage. In a proof-of-principle experiment, we build a polarization Mach-Zehnder interferometer and feed it with coherent light in one port and a squeezed vacuum in another port. At one output port, we amplify light with an optical parametric amplifier and measure a phase sensitivity of 13 mrad for 1500 photons in the interferometer. This result, achieved with 50% detection efficiency, overcomes the SNL by 3 dB. Moreover, by using stronger amplification, we can overcome the SNL under detection efficiency as low as 13%. Our results outline a way to use squeezed light for real-life sensing, where the detection efficiency cannot be very high, especially in spectral ranges like middle-infrared or terahertz.
Interferometric gravitational wave detectors (such as advanced LIGO) employ high-power solid-state lasers to maximize their detection sensitivity and hence their reach into the universe. These sophisticated light sources are ultra-stabilized with regard to output power, emission frequency and beam geometry; this is crucial to obtain low detector noise. However, even when all laser noise is reduced as far as technically possible, unavoidable quantum noise of the laser still remains. This is a consequence of the Heisenberg Uncertainty Principle, the basis of quantum mechanics: in this case, it is fundamentally impossible to simultaneously reduce both the phase noise and the amplitude noise of a laser to arbitrarily low levels. This fact manifests in the detector noise budget as two distinct noise sources—photon shot noise and quantum radiation pressure noise—which together form a lower boundary for current-day gravitational wave detector sensitivities, the standard quantum limit of interferometry. To overcome this limit, various techniques are being proposed, among them different uses of non-classical light and alternative interferometer topologies. This article explains how quantum noise enters and manifests in an interferometric gravitational wave detector, and gives an overview of some of the schemes proposed to overcome this seemingly fundamental limitation, all aimed at the goal of higher gravitational wave event detection rates. This article is part of a discussion meeting issue ‘The promises of gravitational-wave astronomy’.