Известия Российской академии наук Серия физическая

Multiparameter quantum metrology with bright solitons

A. P. Alodjants, Dmitriy V. Tsarev, S. G. Osipov, Mikhail S. Podoshvedov, S. P. Kulik

Published Jun 15, 2024• 0 citations

Abstract

We consider the problem of quantum metrology with simultaneous measurement of several phase parameters in the framework of current tendencies of development of alternative navigation. The fundamental limits of linear and nonlinear metrology are studied. The effect of losses on the accuracy of quantum metrology for several parameters is revealed. A realistic scenario for preparing three-mode NooN states using atomic bright solitons is proposed.

DOI: 10.31857/s0367676524060022

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Известия Российской академии наук Серия физическая

Multiparameter quantum metrology with bright solitons

A. P. Alodjants, Dmitriy V. Tsarev, S. G. Osipov, Mikhail S. Podoshvedov, S. P. Kulik

Published Jun 15, 2024• 0 citations

Publisher

Abstract

DOI: 10.31857/s0367676524060022

Related papers

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Bulletin of the Russian Academy of Sciences PhysicsJun 1, 20240 citations

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Quantum metrology allows the enhanced precision on estimating phase shifts in an optical interferometer to reach the $\ensuremath{\propto}1/N$ scaling of precision ( $N$ is the mean photon number of the light field). But when $N$ is very large, the nonlinear optical effects may be nonnegligible. Here we investigate theoretically the quantum uncertainty bounds for simultaneously detecting the linear and nonlinear phase shifts. Focusing our attentions only on the linear and the nonlinear Kerr phase shifts, we find the NOON states can not be used to measure the two phase parameters. Using the entangled coherent states, the estimation precision is limited by the $1/{N}^{1/2}$ ( $1/{N}^{3/2}$ ) scaling for the linear (nonlinear) phase. To increase the precisions and beat the standard quantum limit, we show that the entangled Schr\"odinger-cat states can be used to reach the $1/N$ scaling for the linear phase and $1/{N}^{2}$ scaling for the nonlinear phase.Quantum metrology allows the enhanced precision on estimating phase shifts in an optical interferometer to reach the $\ensuremath{\propto}1/N$ scaling of precision ($N$ is the mean photon number of the light field). But when $N$ is very large, the nonlinear optical effects may be nonnegligible. Here we investigate theoretically the quantum uncertainty bounds for simultaneously detecting the linear and nonlinear phase shifts. Focusing our attentions only on the linear and the nonlinear Kerr phase shifts, we find the NOON states can not be used to measure the two phase parameters. Using the entangled coherent states, the estimation precision is limited by the $1/{N}^{1/2}$ ($1/{N}^{3/2}$) scaling for the linear (nonlinear) phase. To increase the precisions and beat the standard quantum limit, we show that the entangled Schr\"odinger-cat states can be used to reach the $1/N$ scaling for the linear phase and $1/{N}^{2}$ scaling for the nonlinear phase.

Physical Review ADec 29, 201424 citations

k=1

) and nonlinear (

k=3

) quantum metrology approaches to solitons. We examine multipartite NOON states specially prepared for the improvement of multiparameter estimation protocols. As a particular example of producing such states, we propose a three-mode soliton Josephson-junction (TMSJJ) model as a three-mode extension for the soliton Josephson-junction bosonic model, which we previously proposed. The energy spectrum of the TMSJJ exhibits sharp phase transition peculiarities for the TMSJJ ground state. The transition occurs from a Gaussian-like (coherent) state to the superposition of entangled Fock states, which rapidly approach the three-mode NOON state. We show that in the presence of weak losses the TMSJJ enables saturation scaling relevant to the optimal state limit close to the GHL. Our findings open prospects for quantum network sensorics with atomtronic circuits.

1/N

) and super-Heisenberg (up to

1/{N}^{3}

) scaling levels in the framework of the linear and nonlinear metrology approaches, respectively. The heart of our setup is a soliton Josephson junction (SJJ) system, which provides the formation of the quantum probe, the entangled Fock (NOON-like) state, beyond the superfluid-Mott insulator quantum phase transition point. We illustrate that such states are close to the optimal ones even with moderate losses. The enhancement of phase estimation accuracy remains feasible for both the linear and nonlinear metrologies with the SJJs and allows further improvement for the current experiments performed with atomic condensate solitons with a mesoscopic number of particles.

Quantum metrology allows the enhanced precision on estimating phase shifts in an optical interferometer to reach the $\ensuremath{\propto}1/N$ scaling of precision (

N

is the mean photon number of the light field). But when

N

is very large, the nonlinear optical effects may be nonnegligible. Here we investigate theoretically the quantum uncertainty bounds for simultaneously detecting the linear and nonlinear phase shifts. Focusing our attentions only on the linear and the nonlinear Kerr phase shifts, we find the NOON states can not be used to measure the two phase parameters. Using the entangled coherent states, the estimation precision is limited by the

1/{N}^{1/2}

(

1/{N}^{3/2}

) scaling for the linear (nonlinear) phase. To increase the precisions and beat the standard quantum limit, we show that the entangled Schr\"odinger-cat states can be used to reach the

1/N

scaling for the linear phase and

1/{N}^{2}

scaling for the nonlinear phase.