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arXiv:1012.0896 · New Journal of Physics

Weak measurement of photon polarization by back-action-induced path interference

M. Iinuma, Yutaro Suzuki, Gen Taguchi, Yutaka Kadoya, Holger F Hofmann

Published Mar 31, 2011• 41 citations
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Abstract

An essential feature of weak measurements on quantum systems is the reduction of measurement back-action to negligible levels. To observe the non-classical features of weak measurements, it is therefore more important to avoid additional back-action errors than it is to avoid errors in the actual measurement outcome. In this paper, it is shown how an optical weak measurement of diagonal (PM) polarization can be realized by path interference between the horizontal (H) and vertical (V) polarization components of the input beam. The measurement strength can then be controlled by rotating the H and V polarizations towards each other. This well-controlled operation effectively generates the back-action without additional decoherence, while the visibility of the interference between the two beams only limits the measurement resolution. As the experimental results confirm, we can obtain extremely high weak values, even at rather low visibilities. Our method therefore provides a realization of weak measurements that is extremely robust against experimental imperfections.

DOI
10.1088/1367-2630/13/3/033041

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An essential feature of weak measurements on quantum systems is the reduction of measurement back-action to negligible levels. To observe the non-classical features of weak measurements, it is therefore more important to avoid additional back-action errors than it is to avoid errors in the actual measurement outcome. In this paper, it is shown how an optical weak measurement of diagonal (PM) polarization can be realized by path interference between the horizontal (H) and vertical (V) polarization components of the input beam. The measurement strength can then be controlled by rotating the H and V polarizations towards each other. This well-controlled operation effectively generates the back-action without additional decoherence, while the visibility of the interference between the two beams only limits the measurement resolution. As the experimental results confirm, we can obtain extremely high weak values, even at rather low visibilities. Our method therefore provides a realization of weak measurements that is extremely robust against experimental imperfections.
We realize a minimum back‐action quantum non‐demolition measurement of variable strength on photon polarization in the diagonal(PM) basis by two‐mode path interference. This method uses the phase difference between the positive (P) and negative (M) superpositions in the interference between the horizontal (H) and vertical (V) polarized paths in the input beam. Although the interference can not occur when the H and V polarizations are distinguishable, a well‐controlled amount of interference is induced by erasing the H and V information using a coherent rotation of polarization toward a common diagonal polarization. This method is particularly suitable for the realization of weak measurements, where the control of the back‐action is essential.
A sequential measurement of two non-commuting quantum observables results in a joint probability distribution for all output combinations that can be explained in terms of an initial joint quasi-probability of the non-commuting observables, modified by the resolution errors and back-action of the initial measurement. Here, we show that the error statistics of a sequential measurement of photon polarization performed at different measurement strengths can be described consistently by an imaginary correlation between the statistics of resolution and back-action. The experimental setup was designed to realize variable strength measurements with well-controlled imaginary correlation between the statistical errors caused by the initial measurement of diagonal polarizations, followed by a precise measurement of the horizontal/vertical polarization. We perform the experimental characterization of an elliptically polarized input state and show that the same complex joint probability distribution is obtained at any measurement strength.
Quantum mechanics violates Leggett–Garg inequalities because the operator formalism predicts correlations between different spin components that would correspond to negative joint probabilities for the outcomes of joint measurements. However, the uncertainty principle ensures that such joint measurements cannot be implemented without errors. In a sequential measurement of the spin components, the resolution and back-action errors of the intermediate measurement can be described by random spin flips acting on an intrinsic joint probability. If the error rates are known, the intrinsic joint probability can be reconstructed from the noisy statistics of the actual measurement outcomes. In this paper, we use the spin-flip model of measurement errors to analyze experimental data on photon polarization obtained with an interferometric setup that allows us to vary the measurement strength and hence the balance between resolution and back-action errors. We confirm that the intrinsic joint probability obtained from the experimental data is independent of measurement strength, and show that the same violation of the Leggett–Garg inequality can be obtained for any combination of measurement resolution and back-action.
Quantum weak measurements became extremely popular in classical optics to amplify small optical signals for fundamental interests and potential applications. Later, a more general extension, joint weak measurement has been proposed to extract weak value from a joint quantum measurement. However, the detection of joint weak value in the realm of classical optics remains less explored. Here, using the polarization-dependent longitudinal and transverse optical beam shift as a platform, we experimentally realize the quantum joint weak measurement in a classical optical setting. Polarization states are cleverly pre and post-selected, and different single and joint canonical position-momentum observables of the beam are experimentally extracted and subsequently analyzed for successful detection of complex joint weak value. We envision that this work will find usefulness for gaining fundamental insights on quantum measurements and to tackle analogous problems in optics.