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arXiv:1306.0642 · Physical Review A

Dephasing-assisted parameter estimation in the presence of dynamical decoupling

Qing-Shou Tan, Yixiao Huang, Le‐Man Kuang, Xiaoguang Wang

Published Jun 4, 2014• 24 citations
arXivHTMLPDF

Abstract

We study the dephasing-assisted parameter estimation precision (PEP) enhancement in an atom interferometer with dynamical decoupling (DD) pulses. Through calculating the spin squeezing (SS) and the quantum Fisher information, we find that dephasing noise can improve PEP by inducing SS, and the DD pulses can maximize the improvement. It is indicated that when using the DD pulse the dephasing-induced SS can reach the limit of ``one-axis twisting'' model ${\ensuremath{\xi}}^{2}\ensuremath{\simeq}{N}^{\ensuremath{-}2/3}$ with ${\ensuremath{\xi}}^{2}$ being the SS parameter and $N$ the number of atoms. In particular, we find that the DD pulses can amplify the dephasing-induced quantum Fisher information by a factor of $\ensuremath{\simeq}N/2$ compared with the noise-free case, which means that under the control of DD pulses, the dephasing noise can enhance the precision of parameter estimation to the scale of $\sqrt{2}/N$, the same scale of the Heisenberg limit ($1/N$).

DOI
10.1103/physreva.89.063604

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We study the dephasing-assisted parameter estimation precision (PEP) enhancement in an atom interferometer with dynamical decoupling (DD) pulses. Through calculating the spin squeezing (SS) and the quantum Fisher information, we find that dephasing noise can improve PEP by inducing SS, and the DD pulses can maximize the improvement. It is indicated that when using the DD pulse the dephasing-induced SS can reach the limit of ``one-axis twisting'' model \ensuremathξ2\ensuremath≃N\ensuremath−2/3{\ensuremath{\xi}}^{2}\ensuremath{\simeq}{N}^{\ensuremath{-}2/3}\ensuremathξ2\ensuremath≃N\ensuremath−2/3 with \ensuremathξ2{\ensuremath{\xi}}^{2}\ensuremathξ2 being the SS parameter and NNN the number of atoms. In particular, we find that the DD pulses can amplify the dephasing-induced quantum Fisher information by a factor of \ensuremath≃N/2\ensuremath{\simeq}N/2\ensuremath≃N/2 compared with the noise-free case, which means that under the control of DD pulses, the dephasing noise can enhance the precision of parameter estimation to the scale of 2/N\sqrt{2}/N2​/N, the same scale of the Heisenberg limit (1/N1/N1/N).
We investigate the dependence of the average parameter estimation precision (APEP), which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state |θ0, φ0〉 in a one-axis twisting model. Jin et al. [New J. Phys. 11 (2009) 073049] found that the spin squeezing sensitively depends on the polar angle θ0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ0 in the vicinity of π/2 and a near-Heisenberg limit ∝ 2/N in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ0 ∼ π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEP.
We investigate the dependence of the average parameter estimation precision (APEP), which is defined by the quantum Fisher information, on the polar angle of the initial coherent spin state |θ 0 , φ 0 〉 in a one-axis twisting model. Jin et al. [ New J. Phys. 11 (2009) 073049 ] found that the spin squeezing sensitively depends on the polar angle θ 0 of the initial coherent spin state. We show explicitly that the APEP is robust to the initial polar angle θ 0 in the vicinity of π/2 and a near-Heisenberg limit ∝ 2/ N in quantum single-parameter estimation may still be achieved for states created with the nonlinear evolution of the nonideal coherent spin states θ 0 ∼ π/2. Based on this model, we also consider the effects of the collective dephasing on spin squeezing and the APEP.
A detailed analysis of the quantum Fisher information (QFI) and spin squeezing (SS) of the non-Hermitian one-axis twisting model is conducted. The results show that the non-Hermitian model achieves significant entanglement in many-body systems, which is quite different from the Hermitian case, and achieves more SS than the optimal value of the Hermitian counterpart. Furthermore, we investigate the effect of dephasing, which is induced by external field fluctuations, and find out to what extent it weakens QFI and SS of the non-Hermitian one-axis twisting model.
Dephasing noise is a ubiquitous source of decoherence in current atomic sensors. We address the problem of entanglement-assisted frequency estimation subject to classical dephasing noise with full spatial correlations (collective) and arbitrary temporal correlations. Our contributions are threefold. (i) We derive rigorous, state-independent bounds on the achievable estimation precision, showing how they are entirely determined by the short-time behavior of the decoherence function. For temporally uncorrelated (Markovian) dephasing, precision is limited by a probe-independent constant. For temporally correlated stationary noise, the bound approaches the noiseless limit for classical states, precluding any asymptotic quantum advantage. (ii) We show that these scaling bounds are tight, by constructing generalized Ramsey protocols that saturate them. These optimal protocols use squeezing at the input and before readout, both of which are available in state-of-the-art atomic interferometers. Implementing a perfect-echo protocol, which reaches Heisenberg scaling in the absence of noise, remains optimal in this noisy setting, irrespective of the noise temporal correlations. (iii) We prove that arbitrary collective open-loop control cannot lift the no-go for super-classical precision scaling under either Markovian or colored stationary noise, highlighting the detrimental nature of full spatial correlations. In the latter case, temporal correlations may nonetheless enable constant-factor improvements over the standard quantum limit, which may still be important in practical metrological scenarios.
We present a scheme to enhance the precision of parameter estimation (PPE) in noisy systems by employing dynamical decoupling pulses. An exact analytical expression for the estimation precision of an unknown parameter is obtained by using the transfer matrix and time-dependent Kraus operators. We show that the PPE in noisy systems can be preserved in the Heisenberg limit by control of the dynamical decoupling pulses. It is found that a larger number of pulses and longer reservoir correlation time can greatly protect the PPE.
Realizing useful quantum operations with high fidelity is a two-task quantum control problem wherein decoherence is to be suppressed and desired unitary evolution is to be executed. The dynamical decoupling (DD) approach to decoherence suppression has been fruitful but synthesizing DD fields with certain quantum control fields may be experimentally demanding. In the context of spin squeezing, here we explore an unforeseen possibility that continuous DD fields may serve dual purposes at once. In particular, it is shown that a rather simple configuration of DD fields can suppress collective decoherence and yield a 1/N1/N1/N scaling of the squeezing performance (NNN is the number of spins), thus making spin squeezing more robust to noise and much closer to the so-called Heisenberg limit. The theoretical predictions should be within the reach of current spin squeezing experiments.