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Physical Review A

Heisenberg-limited estimation of the coupling rate in an optomechanical system with a two-level system

Guolong Li, Xiaoguang Wang

Published Jul 3, 2018• 8 citations
Publisher

Abstract

We theoretically investigate the high-precision estimation of the coupling rate, which can reflect an actual observable, in a hybrid optomechanical system (OMS). In our scheme, apart from an optical cavity, the mechanical vibrator is also coupled to a two-level system (TLS) via a direct dispersive coupling. As for the initial state, we take into account coherent states for both optical and mechanical modes. After evolving a period of the vibrator, the final state then carries the information about the estimated coupling rate. We find that through measuring the internal state of the TLS, the precision can achieve a Heisenberg limit that indicates remarkable improvement of estimation in quantum metrology. This result is obviously shown in a simple analytical expression under the approximate condition, and further analysis demonstrates that the Heisenberg limit can be attained indeed. Moreover, we also study the dependence of the precision on the estimated parameter to reveal the appropriate measurement ranges.

DOI
10.1103/physreva.98.013803

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We theoretically investigate the high-precision estimation of the coupling rate, which can reflect an actual observable, in a hybrid optomechanical system (OMS). In our scheme, apart from an optical cavity, the mechanical vibrator is also coupled to a two-level system (TLS) via a direct dispersive coupling. As for the initial state, we take into account coherent states for both optical and mechanical modes. After evolving a period of the vibrator, the final state then carries the information about the estimated coupling rate. We find that through measuring the internal state of the TLS, the precision can achieve a Heisenberg limit that indicates remarkable improvement of estimation in quantum metrology. This result is obviously shown in a simple analytical expression under the approximate condition, and further analysis demonstrates that the Heisenberg limit can be attained indeed. Moreover, we also study the dependence of the precision on the estimated parameter to reveal the appropriate measurement ranges.
Multiparameter quantum estimation has emerged as a central task in quantum metrology. In this work, we investigate multiparameter quantum estimation in a hybrid exciton--optomechanical (EOM) system. The system consists of a semiconductor quantum well embedded inside a driven optomechanical microcavity, where the excitonic, optical, and mechanical modes interact coherently through exciton--photon and radiation-pressure couplings. Using the Gaussian-state formalism, we derive the covariance matrix of the steady-state quantum fluctuations and employ both the symmetric logarithmic derivative (SLD) and right logarithmic derivative (RLD) approaches to evaluate the quantum Fisher information matrix associated with the simultaneous estimation of the exciton--photon coupling strength ggg and the excitonic decay rate kxk_xkx​. We analyze the corresponding quantum Cramér--Rao bounds and determine the most informative precision limit governing the attainable estimation accuracy. The influence of several experimentally relevant parameters, including temperature, driving power, optomechanical coupling strength, and dissipation rates, is investigated in detail. Our results show that strong hybrid interactions and low-temperature regimes significantly enhance the estimation precision, whereas thermal fluctuations and dissipation processes deteriorate the metrological performance. Furthermore, we compare the ultimate quantum limits with experimentally feasible Gaussian measurement strategies based on homodyne and heterodyne detection. We show that heterodyne detection provides better estimation performance than homodyne schemes and can approach the optimal quantum precision limit in suitable parameter regimes.
We propose a scheme to implement a supersensitive estimation of the coupling strength in a hybrid optomechanical system which consists of a cavity-Bose-Einstein condensate system coupled to an impurity. This method can dramatically improve the estimation precision even when the involved photon number is small. The quantum Fisher information indicates that the Heisenberg scale sensitivity of the coupling rate could be obtained when the photon loss rate is smaller than the corresponding critical value in the input of either coherent state or squeezed state. The critical photon decay rate for the coherent state is larger than that of the squeezed state, and the coherent state input case is more robust against the photon loss than the squeezed state case. We also present the measurement scheme which can saturate the quantum Cramér-Rao bound.
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We propose a scheme to implement Heisenberg-limited spin squeezing in a hybrid cavity optomechanical-spin system. In our system, NNN two-level systems are coupled via Tavis-Cummings interactions to a mechanical resonator (MR) in a standard optomechanical setup. Within the dispersive coupling regime, adiabatic elimination of the optical mode induces a squeezing effect on the MR, which, in the squeezed representation, effectively transforms the collective spin operators into a Bogoliubov form. Under large detuning conditions, the phonon mode mediates interactions among the Bogoliubov collective spins, thereby enabling a two-axis twisting squeezing protocol through appropriate parameter tuning. Both theoretical analysis and numerical simulations show that in the presence of dephasing and phonon dissipation, the maximum squeezing degree asymptotically converges to a constant as NNN increases, which implies the metrological precision asymptotically approaches the standard quantum limit without parameter optimization. Nevertheless, in parameter optimization we extract a scaling relation of the optimal squeezing which surpasses existing schemes in the literature. Moreover, the optimization also leads to a considerable reduction of the preparation time for the optimal squeezing. Our work may provide insights into dissipation effects in spin squeezing and offer a potential route for high-precision quantum metrology in many-body systems.
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