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arXiv:1510.00157

Classicality and amplification in postselected weak measurement

Tao Wang, Rui Zhang, Gang Li, Su, Xue-Mei

Published Oct 1, 2015• 0 citations
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Abstract

Nearly thirty years ago the possibility of anomalous weak amplfication (AWA) was revealed by Aharonov, Albert and Vaidman [1]. Recently two papers presents two AWA schemes which are beyond the traditional proposal given by them [14, 15]. At the first glance the two papers seems very different. Ref. [14] discusses the thermal light cross-Kerr effect and finds only postselection can give the amplification effect without interference of the postselected meter states, and Ref. [15] shows that only weak interaction itself can give the amplification effect without postselection. Here the relationships between the two papers are pointed out and a generalized framework for AWA via postselecting a pair of orthogonal final states is shown.

DOI
10.48550/arxiv.1510.00157

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Nearly thirty years ago the possibility of anomalous weak amplfication (AWA) was revealed by Aharonov, Albert and Vaidman [1]. Recently two papers presents two AWA schemes which are beyond the traditional proposal given by them [14, 15]. At the first glance the two papers seems very different. Ref. [14] discusses the thermal light cross-Kerr effect and finds only postselection can give the amplification effect without interference of the postselected meter states, and Ref. [15] shows that only weak interaction itself can give the amplification effect without postselection. Here the relationships between the two papers are pointed out and a generalized framework for AWA via postselecting a pair of orthogonal final states is shown.
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We extend the idea of weak measurements to the general case, provide a complete treatment, and obtain results for both the regime when the preselected and postselected states (PPS) are almost orthogonal and the regime when they are exactly orthogonal. We surprisingly find that for a fixed interaction strength, there may exist a maximum signal amplification and a corresponding optimum overlap of PPS to achieve it. For weak measurements in the orthogonal regime, we find interesting quantities that play the same role that weak values play in the nonorthogonal regime.
In common sense, postselected weak amplification must be related to destructive interference effect of the meter system, and a single photon exerts no effect on thermal field via cross-phasemodulation (XPM) interaction. In this Letter we present, for the first time, a thermal light cross-Kerr effect. Through analysis, we reveal two unexpected results: i) postselection and weak amplification can be explained at a classical level without destructive interference, and ii) weak amplification and weak value are not one thing. After postselection a new mixed light can be generated which is nonclassical. This scheme can be realized via electromagnetically-induced transparency.
A measurement of an observable A performed on a quantum system that is initially prepared in a state ρi, followed by a probabilistic procedure that leaves the system in a final state ρf, a process often referred as state postselection (or filtering process), can yield, on average, anomalous measurement results, i.e., values that may exceed the eigenvalue range of the observable being measured or be complex numbers. There is, therefore, an amplification effect of the average measurement result, i.e., the effect of the system on the measurement device is increased. When the coupling between the system and the measurement device satisfies some weakness conditions, the amplification effect occurs due to the weak value of the operator A. In this article, the amplification effect due to the postselection process is reviewed, and theoretical proposals and experiments published in the recent literature on the field are commented on. The emphasis is made on interactions occurring in optical nonlinear media and opto-mechanical and spin-mechanical systems, in which the amplification of number operators takes place.
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.