Quantum interferometers offer phase measurement capabilities that surpass the standard quantum limit (SQL), with phase sensitivity and quantum enhancement factor serving as key performance metrics. However, practical implementations face severe degradation of both metrics due to unavoidable losses, representing the foremost challenge in advancing quantum interferometry toward real-world applications. To address this challenge, we propose a coherent-amplifier-empowered quantum interferometer. The coherent amplifier dramatically suppresses the decay of both sensitivity and quantum enhancement under high-loss conditions, maintaining phase sensitivity beyond the original SQL even for losses exceeding 90%. Using an injected 4.2 dB squeezed-vacuum state in experimental demonstration, our scheme reduces the quantum enhancement degradation under 90% loss from 3.7 dB in a conventional quantum interferometer (CQI) to only 1.5 dB. More importantly, the phase sensitivity degradation under the same loss is limited to 4.0 dB, markedly outperforming the 11.2 dB degradation observed in a CQI. This improvement is enabled by the coherent amplifier's phase-sensitive photon amplification and its protection of the quantum state. This breakthrough in amplifier-empowered quantum interferometry overcomes the critical barrier to practical deployment, enabling robust quantum-enhanced measurements in lossy environments.
Quantum interferometers offer phase measurement capabilities that surpass the standard quantum limit (SQL), with phase sensitivity and quantum enhancement factor serving as key performance metrics. However, practical implementations face severe degradation of both metrics due to unavoidable losses, representing the foremost challenge in advancing quantum interferometry toward real-world applications. To address this challenge, we propose a coherent-amplifier-empowered quantum interferometer. The coherent amplifier dramatically suppresses the decay of both sensitivity and quantum enhancement under high-loss conditions, maintaining phase sensitivity beyond the original SQL even for losses exceeding 90%. Using an injected 4.2 dB squeezed-vacuum state in experimental demonstration, our scheme reduces the quantum enhancement degradation under 90% loss from 3.7 dB in a conventional quantum interferometer (CQI) to only 1.5 dB. More importantly, the phase sensitivity degradation under the same loss is limited to 4.0 dB, markedly outperforming the 11.2 dB degradation observed in a CQI. This improvement is enabled by the coherent amplifier's phase-sensitive photon amplification and its protection of the quantum state. This breakthrough in amplifier-empowered quantum interferometry overcomes the critical barrier to practical deployment, enabling robust quantum-enhanced measurements in lossy environments.
Optical interferometers, as precision measurement tools, inevitably experience optical path losses in practical applications, which introduce unavoidable vacuum noise and reduce the sensitivity in the phase estimation. To mitigate the effects of losses on sensitivity, we propose an enhanced interferometer scheme that integrates a Raman amplifier. This amplifier is strategically positioned within the lossy interference arm to counteract the reduction in phase sensitivity caused by losses. Our research highlights the crucial role of amplifier positioning, revealing that pre-amplification (PRA, placing the amplifier before the lossy section) significantly outperforms post-amplification (POA, placing the amplifier after the lossy section). PRA effectively enhances sensitivity by increasing the number of phase-sensitive particles and minimizing noise amplification. As the loss increases, the superiority of PRA in mitigating loss effects becomes increasingly evident. To validate our approach, we conducted experimental demonstrations. When the losses reach 90%, PRA experimentally achieves a sensitivity improvement of 4.6 dB compared with the case of only loss without the amplifier, equivalent to increasing the input laser power by over 8 times. PRA can effectively improve the robustness against losses for the practical application solely through the use of a coherent amplifier, with a simple technical implementation yet remarkable enhancement effects. We believe that current PRA-enhanced interferometry facilitates the practical implementation of phase measurement in environments characterized by significant loss.
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.
Interferometers are crucial for precision measurements, including gravitational waves, laser ranging, radar, and imaging. The phase sensitivity, the core parameter, can be quantum-enhanced to break the standard quantum limit (SQL) using quantum states. However, quantum states are highly fragile and quickly degrade with losses. We design and demonstrate a quantum interferometer utilizing a beam splitter with a variable splitting ratio to protect the quantum resource against environmental impacts. The optimal phase sensitivity can reach the quantum Cramér-Rao bound of the system. This quantum interferometer can greatly reduce the quantum source requirements in quantum measurements. In theory, with a 66.6% loss rate, the sensitivity can break the SQL using only a 6.0 dB squeezed quantum resource with the current interferometer rather than a 24 dB squeezed quantum resource with a conventional squeezing-vacuum-injected Mach-Zehnder interferometer. In experiments, when using a 2.0 dB squeezed vacuum state, the sensitivity enhancement remains at ∼1.6 dB via optimizing the first splitting ratio when the loss rate changes from 0% to 90%, indicating that the quantum resource is excellently protected with the existence of losses in practical applications. This strategy could open a way to retain quantum advantages for quantum information processing and quantum precision measurement in lossy environments.
Correlated interferometry offers various advantages in precision measurements, such as sub-shot noise sensitivity, high resolution, and prevention of detector saturation benefiting from dark output. In certain practical scenarios, e.g. absorptive measurement, there is usually unbalanced loss between the probe and reference beams, which destroys the correlation and remains a significant obstacle in the efficient application of entanglements. Here, we study the performance of a nonlinear interferometer whose arms experience unbalanced loss and demonstrate the use of a phase-sensitive amplifier in the sensing or reference arms to amplify or squeeze the light field, which can both reduce the degradation of quantum enhancement from unbalanced absorption in a lossy environment. We find that the loss after amplification, i.e. from imperfect interferometry and detection, can be mitigated when the phase-sensitive amplifier is placed at the sensing arm and functions as a noiseless amplifier. Our approach may be helpful to the practical application of quantum-enhanced absorptive measurement.
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.
Squeezing-assisted interferometers achieve sub-shot-noise sensitivity to phase shifts, but losses can strongly degrade their performance. Here we present the first experimental demonstration of detection-loss tolerance for this class of interferometers employing degenerate optical parametric amplification at one output port. For 50% detection efficiency, the phase sensitivity of any interferometer with coherent and squeezed vacuum inputs would not overcome the shot-noise limit, but in our case the output amplification gives 6 dB sub-shot-noise sensitivity. We further demonstrate that robustness increases with higher gain of the output amplifier: sub-shot-noise sensitivity is achieved for detection efficiency as low as 13%. We believe that overcoming detection inefficiency will become crucial to take full advantage of quantum metrology, for example in gravitational-wave detection, quantum sensing and imaging.