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Journal of the Optical Society of America B

Gravitational acceleration estimation with a nonlinear Mach–Zehnder interferometer

Leili Esmaeilifar, Timothy C. Ralph

Published Dec 15, 2021• 4 citations
Publisher

Abstract

We investigate the use of a nonlinear optical interferometer to estimate local gravitational acceleration. We study a Mach–Zehnder interferometer (MZI) in an optical fountain configuration where a Kerr nonlinear medium is placed in the arms of the interferometer. This configuration allows the parameter estimation to exceed the standard Heisenberg limit of a linear interferometer. Compared to previous studies, we argue that this interferometer configuration is better posed and achieves improved precision for similar scale and pump powers.

DOI
10.1364/josab.443339

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We investigate the use of a nonlinear optical interferometer to estimate local gravitational acceleration. We study a Mach–Zehnder interferometer (MZI) in an optical fountain configuration where a Kerr nonlinear medium is placed in the arms of the interferometer. This configuration allows the parameter estimation to exceed the standard Heisenberg limit of a linear interferometer. Compared to previous studies, we argue that this interferometer configuration is better posed and achieves improved precision for similar scale and pump powers.
The precise estimation of the gravitational acceleration is important for various disciplines. We consider making such an estimation using quantum optics. A Mach-Zehnder interferometer in an ``optical fountain'' type arrangement is considered and used to define a standard quantum limit for estimating the gravitational acceleration. We use an approach based on quantum field theory on a curved, Schwarzschild metric background to calculate the coupling between the gravitational field and the optical signal. The analysis is extended to include the injection of a squeezed vacuum to the Mach-Zehnder arrangement and also to consider an active, two-mode SU(1,1) interferometer in a similar arrangement. When detection loss is larger than 88%8, the SU(1,1) interferometer shows an advantage over the MZ interferometer with single-mode squeezing input. The proposed system is based on current technology and could be used to examine the intersection of quantum theory and general relativity as well as for possible applications.
We propose to exploit the quantum properties of nonlinear media to estimate the parameters of massless wormholes. The spacetime curvature produces a change in length with respect to Minkowski spacetime that can be estimated in principle with an interferometer. We use quantum metrology techniques to show that the sensitivity is improved with nonlinear media and propose a nonlinear Mach–Zehnder interferometer to estimate the parameters of massless wormholes that scales beyond the Heisenberg limit.
A nonlinear phase shift is introduced to a Mach-Zehnder interferometer (MZI), and we present a scheme for enhancing the phase sensitivity. In our scheme, one input port of a standard MZI is injected with a coherent state and the other input port is injected with one mode of a two-mode squeezed-vacuum state. The final interference output of the MZI is detected with the method of active correlation output readout. Based on the optimal splitting ratio of beam splitters, the phase sensitivity can beat the standard quantum limit and approach the quantum Cram\'er-Rao bound. The effects of photon loss on phase sensitivity are discussed. Our scheme can also provide some estimates for units of ${\ensuremath{\chi}}^{(3)}$, due to the relation between the nonlinear phase shift and the susceptibility ${\ensuremath{\chi}}^{(3)}$ of the Kerr medium.
Continuous-wave (CW) interferometry has stood at the frontier of precision measurement science since its inception, where it was used to search for the luminiferous ether, to the present day, where it forms the basis of interferometric gravitational-wave detection. Quantum theory predicts that this frontier can be expanded more rapidly by employing certain quantum resources, compared with the case of using only classical resources. In the quantum case, we can achieve ``Heisenberg scaling'', which manifests as a quadratic improvement over the best possible classical precision scaling. Although Heisenberg scaling has been demonstrated in pulsed operation, it has not been demonstrated for continuous operation. The challenge in doing so is two-fold: continuous measurements capable of Heisenberg scaling were previously unknown, and the requisite CW quantum states are fragile. Here we overcome these challenges and demonstrate the first CW interferometer exhibiting resource efficiency approaching Heisenberg scaling. Our scheme comprises a Mach-Zehnder interferometer illuminated with a pair of squeezed light sources, followed by a nonlinear estimator of the output homodyne record to estimate a differential phase modulation signal that drives the interferometer. We observe that this signal can be extracted with a precision that scales faster than what is allowed classically, and approaches the Heisenberg scaling limit.
We demonstrate a precision measurement of local gravity acceleration g in Wuhan by a compact cold atom interferometer. The atom interferometer is in vertical Mach—Zehnder configuration realized using a π/2 - π - π/2 Raman pulse sequence. Cold atoms were prepared in a magneto-optical trap, launched upward to form an atom fountain, and then coherently manipulated to interfere by stimulated Raman transition. Population signal vs Raman laser phase was recorded as interference fringes, and the local gravity was deduced from the interference signal. We have obtained a resolution of 7 × 10 −9 g after an integration time of 236s under the best vibrational environment conditions. The absolute g value was derived from the chirp rate with a difference of 1.5 × 10 −7 g compared to the gravity reference value. The tidal phenomenon was observed by continuously monitoring the local gravity over 123 h.
We study the problem of estimating the phase shift due to the general relativistic time dilation in the interference of photons using a nonlinear Mach-Zender interferometer setup. By introducing two nonlinear Kerr materials, one in the bottom and one in the top arm, we can measure the nonlinear phase ${\ensuremath{\phi}}_{\text{NL}}$ produced by the space-time curvature and achieve a scaling of the standard deviation with photon number (NNN) of $1/{N}^{\ensuremath{\beta}}$ where $\ensuremath{\beta}>1$, which exceeds the conventional Heisenberg limit of a linear interferometer (1/N1/N1/N). The nonlinear phase shift is an effect that is amplified by the intensity of the probe field. In a regime of high photon number, this effect can dominate over the linear phase shift.