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arXiv:2512.08638

Strain sensitivity enhancement in a Grover-Michelson interferometer

Anthony D. Manni, Christopher R. Schwarze, David S. Simon, Abdoulaye Ndao, Alexander V. Sergienko

quant-phphysics.opticsSubmitted Dec 9, 2025• Announced Dec 10, 2025
arXivHTMLPDF

Abstract

The Michelson interferometric phase detection resolution can be enhanced by replacing conventional beam splitters with novel directionally unbiased four-port scatterers, such as Grover coins. We present a quantitative analysis of the noise-to-signal ratio of sideband frequencies generated by gravitational wave-induced phase perturbations in a Grover-Michelson interferometer (GMI). We discuss the principles of GMI signal enhancement and demonstrate how combining this configuration with additional light-recycling arrangements further enhances the performance.

Journal reference
Phys. Rev. D, 112, 122002 (2025)
DOI
10.1103/8h71-w8tt
Comments
13 pages, 10 figures

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The Michelson interferometric phase detection resolution can be enhanced by replacing conventional beam splitters with novel directionally unbiased four-port scatterers, such as Grover coins. We present a quantitative analysis of the noise-to-signal ratio of sideband frequencies generated by gravitational wave-induced phase perturbations in a Grover-Michelson interferometer (GMI). We discuss the principles of GMI signal enhancement and demonstrate how combining this configuration with additional light-recycling arrangements further enhances the performance.
Power recycling techniques are usually used to improve the phase sensitivity of interferometers by reusing the input light energy, and can beat the shot noise level. Recent studies have demonstrated that the phase sensitivity of the interferometer is significantly improved via the addition of a recycling cavity, that is, coupling the interferometer with an external optical device. This study reviewed such types of interferometers named Grover-Michelson interferometers (GMI), and discusses their phase sensitivity with coherent states as inputs. Subsequently, a detailed comparison in terms of the scale of 1/ N and the standard quantum limit (SQL) is presented. The results demonstrate that the phase sensitivity of GMI improved owing to the power recycling and exceeded the value of 1/ N . Further, we proposed a modified Grover-Michelson interferometer (MGMI) with two input ports and examined its phase sensitivity with single photon or coherent states, respectively. Finally, in the presence of photon losses, we investigated the phase sensitivity of the four different interferometers, including MGMI, GMI, Mach-Zehnder interferometer (MZI), and SU(1,1) interferometer (SU(1,1)I), and conducted detailed comparisons. The results of this study indicated that the phase sensitivity of MGMI significantly improved owing to the increase in input energy, and MGMI exhibited the strongest robustness against photon number loss. These theoretical results are expected to facilitate improvements in interferometers and the detection of weak signals.
Here we introduce interferometric devices by combining optical feedback (cavities) with unbiased multiports, which, unlike traditional beam dividers, allow light to reflect back out of the port from which it originated. By replacing the traditional, directionally biased beam-splitter in a Michelson interferometer with an unbiased multiport, the functional dependence of the scattering amplitudes changes. As a result, the derivative of transmittance with respect to an external phase perturbation can be made substantially large. This significantly enhances the resolution of phase measurement and allows the phase response curves to be altered in real time by tuning an externally controllable phase shift.
We present a low-resource and robust optical implementation of the four-dimensional Grover coin, a four-port linear-optical scatterer that augments the low dimensionality of a regular beam-splitter. While prior realizations of the Grover coin required a potentially unstable ring cavity to be formed, this version of the scatterer does not exhibit any internal interference. When this Grover coin is placed in another system, it can be used for interferometry with a higher-dimensional set of optical field modes. In this case, we formed a Grover-Michelson interferometer, which results when the traditional beam-splitter of a Michelson interferometer is replaced with a four-port Grover coin. This replacement has been shown to remove a phase parameter redundancy in the original Michelson system, now allowing continuous tuning of the shape and slope of the interference pattern. We observed an intensity interferogram with 97% visibility and a phase sensitivity more than an order of magnitude larger than a regular Michelson interferometer. Because this device is readily formed with nearly the same number of optomechanical resources as a Michelson interferometer but can outperform it drastically in phase delay evaluation, it has a great potential to improve many interferometric sensing and control systems.
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.
We report on the experimental combination of three advanced interferometer techniques for gravitational wave detection, namely, power recycling, detuned signal recycling, and squeezed field injection. For the first time, we experimentally prove the compatibility of especially the latter two. To achieve a broadband nonclassical sensitivity improvement, we applied a filter cavity for compensation of quadrature rotation. The signal-to-noise ratio was improved by up to 2.8 dB beyond the coherent state's shot noise. The complete setup was stably locked for arbitrary times and characterized by injected single-sideband modulation fields.