Nonlinear interferometers offer a robust platform for quantum sensing beyond the standard quantum limit. Specifically, the generation of high-quality intensity-difference-squeezed (IDS) states provides a distinct advantage by circumventing the need for complex phase-coherent local oscillators. However, practical imperfections such as asymmetric inter-stage transmission and unbalanced detection losses severely degrade the generation of these states. In this work, we analyze IDS state generation within fiber nonlinear interferometers utilizing cascaded parametric amplifiers. Using a single-mode theoretical framework and experimental demonstration, we derive an optimal electronic gain ratio for differential detection to compensate for asymmetric detection-induced noise mismatches, extending achievable squeezing into the high-gain regime. We further analyze system tolerance to inter-stage losses and path delays. Experiments demonstrate that while higher initial parametric gain improves quantum correlations, it amplifies intensity noise and accelerates gain saturation, resulting in optimal squeezing at balanced low-gain configurations. These findings establish a robust framework for the design and optimization of all-fiber quantum sensors.
Nonlinear interferometers offer a robust platform for quantum sensing beyond the standard quantum limit. Specifically, the generation of high-quality intensity-difference-squeezed (IDS) states provides a distinct advantage by circumventing the need for complex phase-coherent local oscillators. However, practical imperfections such as asymmetric inter-stage transmission and unbalanced detection losses severely degrade the generation of these states. In this work, we analyze IDS state generation within fiber nonlinear interferometers utilizing cascaded parametric amplifiers. Using a single-mode theoretical framework and experimental demonstration, we derive an optimal electronic gain ratio for differential detection to compensate for asymmetric detection-induced noise mismatches, extending achievable squeezing into the high-gain regime. We further analyze system tolerance to inter-stage losses and path delays. Experiments demonstrate that while higher initial parametric gain improves quantum correlations, it amplifies intensity noise and accelerates gain saturation, resulting in optimal squeezing at balanced low-gain configurations. These findings establish a robust framework for the design and optimization of all-fiber quantum sensors.
A nonlinear interferometer uses nonlinear elements as beam splitters to split and to recombine optical waves for interference. As a result, the interference fringe size has a nonlinear dependence on the intensity of the field for phase sensing and leads to an enhanced phase signal. In this paper, a practical scheme of nonlinear interferometry for precision phase measurement is analyzed with parametric amplifiers as the nonlinear beam splitters. It is found that the signal due to phase shift is enhanced by a factor of the amplification gain as compared to a linear interferometer with the same phase-sensing light intensity while the quantum noise is kept at the vacuum level, thus, effectively increasing the signal-to-noise ratio (SNR) beyond the standard quantum limit. Furthermore, the scheme is not as sensitive to the detection loss as the linear scheme with a squeezed state for noise reduction. However, losses inside the interferometer limit the enhancement factor in SNR. We apply the concept to a Michelson interferometer but with parametric amplifiers involved for gravitational-wave detection. We find that effective power is increased by the gain of the amplifiers without actually increasing the cycling power inside the interferometer. Furthermore, the full benefits with squeezed input and variational output or the combination of a quantum nondemolition interferometer for sensitivity beyond the standard quantum limit apply here with even better results. Such a nonlinear interferometer will find wide applications in precision measurements.
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.
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.
Over the past decade, several schemes for imaging and sensing based on nonlinear interferometers have been proposed and demonstrated experimentally. These interferometers exhibit two main advantages. First, they enable probing a sample at a chosen wavelength while detecting light at a different wavelength with high efficiency (bicolor quantum imaging and sensing with undetected light). Second, they can show quantum-enhanced sensitivities below the shot-noise limit, potentially reaching Heisenberg-limited precision in parameter estimation. Here, we compare three quantum-imaging configurations using only easily accessible intensity-based measurements for phase estimation: a Yurke-type SU(1,1) interferometer, a Mandel-type induced-coherence interferometer, and a hybrid scheme that continuously interpolates between them. While an ideal Yurke interferometer can exhibit Heisenberg scaling, this advantage is known to be fragile under realistic detection constraints and in the presence of loss. We demonstrate that differential intensity detection in the Mandel interferometer provides the highest and most robust phase sensitivity among the considered schemes, reaching but not surpassing the shot-noise limit, even in the presence of loss. Intensity measurements in a Yurke-type configuration can achieve genuine sub-shot-noise sensitivity under balanced losses and moderate gain; however, their performance degrades in realistic high-gain regimes. Consequently, in this regime, the Mandel configuration with differential detection outperforms the Yurke-type setup and constitutes the most robust approach for phase estimation.
The intensity-difference squeezed state is an important concept in quantum optics, which is not only of great significance for fundamental research in quantum physics, but also an important quantum resource in the fields of quantum communication, quantum computing, and quantum precision measurement. The optical parametric amplifier based on atomic four-wave mixing is one of the most effective means to achieve intensity-difference squeezed light. However, due to the absorption loss of atomic vapor in the light field, the output squeezing still needs improving. By feeding the non-classical optical field from the optical parametric amplifier back to the input port, the quantum characteristics of its output optical field can be enhanced. However, the intensity-difference squeezing enhancement from a phase-insensitive amplifier is experimentally realized based on coherent feedback control. The intensity-difference squeezing enhancement of the phase-sensitive amplifier has not been discussed. In this work, a two-port coherent feedback-controlled phase-sensitive amplifier is analyzed theoretically. The dependence of the intensity-difference squeezing, respectively, on the feedback intensity, the intensity gain of the optical parametric amplifier, and the losses of the system are investigated. For the ideal case in which the losses of the system are ignored, infinite squeezing can be achieved by adjusting the strength and phase of feedback. Considering the actual atomic absorption losses, squeezing enhancement can also be achieved over a wide range of intensity gains within a certain feedback intensity range. In addition, the squeezing enhancement is quite efficient for the medium intensity gain range. The intensity-difference squeezing enhancement strongly depends on the absorption loss of atomic vapor. The smaller the absorption loss, the more significant the squeezing enhancement effect is. Furthermore, the experimental feasibility of this scheme is also considered in detail. Our research can provide useful references for achieving high-quality non classical light fields in experiment, which may find applications in quantum information processing and quantum precise measurement.
Bicolor quantum imaging can reach, in principle, phase supersensitivity approaching the Heisenberg limit using squeezed light from high-gain parametric down-conversion, but established quantum-imaging setups typically operate in the low-gain, spontaneous regime, where such scaling is inaccessible. Here, we show experimentally and theoretically that a symmetric nonlinear interferometer, even in the spontaneous regime, retains a phase-sensitivity advantage over configurations where entanglement is not exploited as a quantum-metrological resource, although the achievable phase sensitivity remains shot-noise-limited. This advantage appears as a shift of the optimal working point toward the dark fringe, the low-gain signature of the mechanism underlying high-gain supersensitivity. We derive design choices for phase-optimized nonlinear interferometers accordingly, favoring configurations that exploit entanglement as a metrological resource and specifying their optimal operating point.