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Chinese Physics B

Super-sensitive phase estimation with coherent boosted light using parity measurements

Lan Xu, Qing-Shou Tan

Published Jan 1, 2018• 1 citation
Publisher

Abstract

We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach–Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer–Rao bound than the pure active (e.g., SU(1,1)) interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves [ Phys. Rev. D 23 1693 (1981)], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves’ scheme.

DOI
10.1088/1674-1056/27/1/014203

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We consider a passive and active hybrid interferometer for phase estimation, which can reach the sub-shot-noise limit in phase sensitivity with only the cheapest coherent sources. This scheme is formed by adding an optical parametric amplifier before a Mach–Zehnder interferometer. It is shown that our hybrid protocol can obtain a better quantum Cramer–Rao bound than the pure active (e.g., SU(1,1)) interferometer, and this precision can be reached by implementing the parity measurements. Furthermore, we also draw a detailed comparison between our scheme and the scheme suggested by Caves [ Phys. Rev. D 23 1693 (1981)], and it is found that the optimal phase sensitivity gain obtained in our scheme is always larger than that in Caves’ scheme.
Abstract We have theoretically investigated the phase sensitivity of the hybrid interferometer with two coherent beams using the method of balance homodyne detection. The measurement device is a nonlinear–linear hybrid interferometer consisting of an optical parametric amplifier and a beam splitter. We prove that the phase sensitivity can beat the shot noise limit in the optimal conditions. Furthermore, we derive the quantum Cramér–Rao bound of the hybrid interferometer. The effects of transmission loss and detection loss on the measurement accuracy are discussed. The detection accuracy of this scheme is compared with that of the conventional SU (1,1) interferometer. Our results show that this scheme outperforms the conventional SU (1,1) interferometer scheme at high parametric strength. This scheme can be implemented with existing experimental techniques and will have important applications in quantum precision measurements.
We theoretically study the phase estimation based on a Mach-Zehnder interferometer (MZI) with a two-mode squeezed coherent state. By maximizing the quantum Fisher information, we find that the quantum Cramér-Rao bounds (QCRB) can reach sub-Heisenberg limit under the phase-matched condition. The optimal phase sensitivity can reach the sub-shot noise limit (SNL) and approach the QCRB by employing the intensity difference detection. Meanwhile, compared with the MZI fed with a coherent plus a single-mode squeezed vacuum state, this scheme can have better performance by adjusting the squeezing parameter and the mean photon number. With the same parameter, our scheme shows more sensitive phase measurement than the SU(1,1) interferometer with a coherent plus a vacuum state. We also show that the phase sensitivity of our proposal can still reach the SNL when the loss of the photon is 36%. This scheme can provide potential applications in optical sensors.
How to find the specific measurement scheme to approach the quantum Cramér-Rao bound (QCRB) is an important issue in quantum metrology, especially for the continuous-variable optical interferometers input with non-classical states. In the ideal situation (i.e., without any photon loss), this can be usually achieved by using the parity measurement, which, however, does not work well when the photon loss occur. Alternatively, in this work we find that the coincidence measurements are more robust to the photon loss than the parity measurement. Importantly, in certain cases, the sensitivity with the coincidence measurement can even approach very closely to the QCRB despite of the photon loss. Though the results are obtained based on the analysis with the typical two-photon twin-Fock state, it might be also generalized for the other input ones. Thus, our work may provide an effective measurement scheme for beating the shot-noise limit in practical experiments.
As the simplest phase estimation protocol, the inversion estimator has been widely adopted in the quantum metrology, since its performance can be simply quantified by the error-propagation formula. For a general binary-outcome measurement, we show that both the inversion estimator and the maximum likelihood estimator are the same and can asymptotically saturate the Cramér-Rao lower bound. These observations are applied to the parity detection and the zero-nonzero photon counting that have achieved super-resolved phase measurement near the shot-noise phase sensitivity in a coherent-state light Mach–Zehnder interferometer. We numerically show that the phase uncertainty almost follows the theoretical prediction of the lower bound. At the optimal working point, the best sensitivities also reach their associated analytic results for the two binary-outcome measurement schemes.
Abstract A scheme is proposed based on a Mach–Zehnder interferometer with high phase sensitivity, utilizing a two-mode squeezed coherent state, generated by four-wave mixing, as input. The phase sensitivity of this scheme easily surpasses the Heisenberg limit when intensity difference detection is applied. Under phase-matching conditions, the quantum Cramér–Rao bound significantly exceeds the Heisenberg limit. Additionally, the scheme exhibits robustness against photon loss. When compared with the modified SU(1,1) interferometer with two coherent state inputs, this approach demonstrates superior measurement sensitivity, evaluated through various detection methods and the quantum Cramér–Rao bound. This work holds potential applications in quantum metrology.