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arXiv:1509.00621

Weak measurement with a coherent state pointer and its implementation in optomechanical system

Gang Li, Ming-Yong Ye, Xiu‐Min Lin, He‐Shan Song

Published Sep 2, 2015• 0 citations
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Abstract

Weak measurement with a coherent state pointer and in combination with an orthogonal postselection can lead to a surprising amplification effect, and we give a fire-new physical mechanism about the weak measurement in order to understand this effect. Moreover, this physical mechanism is a general result and based on it, we present a scheme of optomechanical system to implement weak measurement amplification on an orthogonal postselection.

DOI
10.48550/arxiv.1509.00621

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Weak measurement with a coherent state pointer and in combination with an orthogonal postselection can lead to a surprising amplification effect, and we give a fire-new physical mechanism about the weak measurement in order to understand this effect. Moreover, this physical mechanism is a general result and based on it, we present a scheme of optomechanical system to implement weak measurement amplification on an orthogonal postselection.
Most studies for postselected weak measurement focus on using pure Gaussian state as a pointer, which can only give an amplification limit reaching the ground state fluctuation. In this paper we use the thermal state pointer. We find that its amplification limit can reach thermal fluctuations and we also give the amplification mechanism different from the one with pure Gaussian state pointer. To illustrate the results, we propose two schemes to implement room temperature amplification of the mechanical oscillator's displacement caused by one photon in optomechanical system. The two schemes can both enhance the original displacement by nearly seven orders of magnitude, attaining sensitivity to displacements of ~ 0.26 nm. Such amplification effect can be used to observe the impact of a single photon on a room temperature mechanical oscillator which is impossible to detect in traditional measurement.
Abstract Most studies for postselected weak measurement in optomechanical system focus on using a single photon as a measured system. However, we find that using weak coherent light instead of a single photon can also amplify the mirror’s position displacement of one photon. In the weak value amplification (WVA) regime, the weak value of one photon can lie outside the eigenvalue spectrum, proportional to the difference of the mirror’s position displacement between the successful and failed postselection and its successful postselection probability is dependent of the mean photon number of the coherent light and improved by adjusting it accordingly. Outside the WVA regime, the amplification limit can reach the level of the vacuum fluctuations, and when the mean photon number and the optomechanical coupling parameter are selected appropriately, its successful postselection probability becomes higher, which is beneficial to observe the maximum amplification value under the current experimental conditions. This result breaks the constraint that it is difficult to detect outside the WVA regime. This opens up a new regime for the study of a single photon nonlinearity in optomechanical system.
We revisit the scheme of single-photon weak-coupling optomechanics using postselection, proposed by Pepper, Ghobadi, Jeffrey, Simon, and Bouwmeester [Phys. Rev. Lett. 109, 023601 (2012)], by analyzing the exact solution of the dynamical evolution. Positive and negative amplification effects of the displacement of the mirror's position can be generated when the Kerr phase is considered. This effect occurs when the postselected state of the photon is orthogonal to the initial state, which cannot be explained by the usual weak measurement results. The amplification effect can be further modulated by a phase shifter, and the maximal displacement state can appear within a short evolution time.
Postselected weak measurement is a useful protocol for amplifying weak physical effects. However, there has recently been controversy over whether it gives any advantage in precision. While it is now clear that retaining failed postselections can yield more Fisher information than discarding them, the advantage of postselection measurement itself still remains to be clarified. In this Letter, we address this problem by studying two widely used estimation strategies: averaging measurement results, and maximum likelihood estimation, respectively. For the first strategy, we find a surprising result that squeezed coherent states of the pointer can give postselected weak measurements a higher signal-to-noise ratio than standard ones while all standard coherent states cannot, which suggests that raising the precision of weak measurements by postselection calls for the presence of "nonclassicality" in the pointer states. For the second strategy, we show that the quantum Fisher information of postselected weak measurements is generally larger than that of standard weak measurements, even without using the failed postselection events, but the gap can be closed with a proper choice of system state.
Abstract Most studies for postselected weak measurement focus on using the pure Gaussian state as a pointer, which can only give an amplification limit reaching the level of the ground state fluctuation. When the pointer is initialized in a thermal state, we find that the amplification limit after the postselection can reach the level of thermal fluctuation, indicating that the amplification effect achieving the level of thermal fluctuation is also increased with the temperature growth, and also that the amplification mechanism is different from that with pure Gaussian-state pointer. To illustrate these results, we propose two schemes to implement room temperature amplification of the mechanical oscillator’s displacement caused by a single photon in the optomechanical system. The two schemes both enhance the mechanical oscillator’s original displacement by nearly seven orders of magnitude, attaining sensitivity to displacements of ∼0.26 nm. Such amplification effect can be used to observe the impact of a single photon on a room temperature mechanical oscillator, which is hard to detect in traditional measurement.