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arXiv:1303.1903 · Physical Review A

Reinterpretations of an experiment on the backaction in a weak measurement

Kouji Nakamura, M. Iinuma

Published Oct 9, 2013• 2 citations

Abstract

Interpretations of an experiment on the backaction in a weak measurement in [Iinuma et al., New J. Phys. 13, 033041 (2011)] are revisited. We show two different but essentially equivalent interpretations for this experiment along the original scenario of weak measurements proposed by Aharonov, Albert, and Vaidman [Phys. Rev. Lett. 60, 1351 (1988)]. To do this, we introduce the notion of extended weak values, which is associated not only with the states of the system but also the state of the measuring device. We also evaluate fluctuations in this experiment, and found that an optimal measurement strength exists for a fixed polarization angle prepared as an initial state, at which fluctuations in measurement results vanish. The consistency of this evaluation with the experimental results is discussed.

DOI: 10.1103/physreva.88.042106

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Interpretations of an experiment on the backaction in a weak measurement in [Iinuma et al., New J. Phys. 13, 033041 (2011)] are revisited. We show two different but essentially equivalent interpretations for this experiment along the original scenario of weak measurements proposed by Aharonov, Albert, and Vaidman [Phys. Rev. Lett. 60, 1351 (1988)]. To do this, we introduce the notion of extended weak values, which is associated not only with the states of the system but also the state of the measuring device. We also evaluate fluctuations in this experiment, and found that an optimal measurement strength exists for a fixed polarization angle prepared as an initial state, at which fluctuations in measurement results vanish. The consistency of this evaluation with the experimental results is discussed.

We extend the idea of weak measurements to the general case, provide a complete treatment and obtain results for both the regime when the 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. We also find interesting quantities, the orthogonal weak values, which play the role of weak values for the case when the PPS are exactly orthogonal.

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.

The contribution of the detector dynamics to the weak measurement is analyzed. According to the usual theory [Y. Aharonov, D. Z. Albert, and L. Vaidman, Phys. Rev. Lett. 60, 1351 (1988)] the outcome of a weak measurement with preselection and postselection can be expressed as the real part of a complex number: the weak value. By accounting for the Hamiltonian evolution of the detector, here we find that there is a contribution proportional to the imaginary part of the weak value to the outcome of the weak measurement. This is due to the coherence of the probe being essential for the concept of complex weak value to be meaningful. As a particular example, we consider the measurement of a spin component and find that the contribution of the imaginary part of the weak value is sizable.

We give a critical discussion of a recent Letter of Aharonov, Albert, and Vaidman. Although their work contains several flaws, their main point is valid: namely, that there is a sense in which a certain "weak measurement" procedure yields values outside the eigenvalue spectrum. Our analysis requires no approximations and helps to clarify the physics behind the effect. We describe an optical analog of the experiment and discuss the conditions necessary to realize the effect experimentally.

The notion of the weak value of a quantum mechanical observable has recently been introduced by Aharonov et al. (Phys. Rev A 41,11 (1990)), hereafter referred to as AAV. We have performed an experiment similar to one proposed by Knight et al. (1990) and demonstrated that weak values can be observed and that they exhibit the properties described by AAV within the regime of validity. We suggest that preselection and postselection measurement techniques could be useful for study of physical phenomena that might be otherwise unobservable.

We present the first realization of a measurement of a ``weak value,'' a concept recently introduced by Aharonov, Albert, and Vaidman (AAV). Our experiment uses a birefringent crystal to separate the two linear-polarization components of a laser beam by a distance small compared to the laser-beam waist. This ``weak measurement'' is followed by a strong measurement which translates the centroid of the beam by a distance far larger than the birefringence-induced separation. In addition, we present data corresponding to orthogonal initial and final states, for which the weak value is not defined. This interference effect may have application in the amplification and detection of weak effects.