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Physical Review A

Experimental demonstration of a method to realize weak measurement of the arrival time of a single photon

Qin Wang, Fang‐Wen Sun, Yong-Sheng Zhang, Jianli, Yun‐Feng Huang, Guang‐Can Guo

Published Feb 17, 2006• 47 citations
Publisher

Abstract

We present a realization of weak measurement for the arrival time of a single photon in virtue of the simultaneous characteristic of biphotons. Our experimental setup is based on a Hong-Ou-Mandel interferometer. A birefringent crystal is used to perform weak measurement between a preselected and a postselected measurement by two polarizers. The extreme weak values lie well outside of the eigenvalues of the observable.

DOI
10.1103/physreva.73.023814

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We present a realization of weak measurement for the arrival time of a single photon in virtue of the simultaneous characteristic of biphotons. Our experimental setup is based on a Hong-Ou-Mandel interferometer. A birefringent crystal is used to perform weak measurement between a preselected and a postselected measurement by two polarizers. The extreme weak values lie well outside of the eigenvalues of the observable.
We experimentally determine weak values for a single photon's polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave theory, due to the two-photon entanglement. We observe the variation in the size of the weak value with measurement strength, obtaining an average measurement of the S1 Stokes parameter more than an order of magnitude outside of the operator's spectrum for the smallest measurement strengths.
We show that a weak projective measurement of photon arrival time can be realized by controllable two-photon interferences with photons from short-time reference pulses at a polarization beam splitter. The weak value of the projector on the arrival time defined by the reference pulse can be obtained from the coincidence rates conditioned by a specific output measurement. If the weak measurement is followed by a measurement of frequency, the coincidence counts reveal the complete temporal coherence of the single-photon wave function. Significantly, the weak values of the input state can also be obtained at higher measurement strengths, so that correlations between weak measurements on separate photons can be observed and evaluated without difficulty. The method can thus be used to directly observe the nonclassical statistics of time-energy entangled photons.
In this paper we propose a setup for the weak measurement of photon arrival time. It is found that the weak values of this arrival time can lie far away from the expectation value, and in principle also in regions forbidden by special relativity. We discuss in brief the implications of these results as well as their reconciliation with the principle of causality. Furthermore, an analysis of the weak arrival times of a pair of photons in a Bell state shows that these weak arrival times are correlated.
We report an experimental realization of the quantum paradox of the separation of a single photon from one of its properties (the so-called "quantum Cheshire cat"). We use a modified Sagnac interferometer with displaced paths to produce appropriately pre- and postselected states of heralded single photons. Weak measurements of photon presence and circular polarization are performed in each arm of the interferometer by introducing weak absorbers and small polarization rotations and analyzing changes in the postselected signal. The absorber is found to have an appreciable effect only in one arm of the interferometer, while the polarization rotation significantly affects the signal only when performed in the other arm. We carry out both sequential and simultaneous weak measurements and find good agreement between measured and predicted weak values. In the language of Aharonov et al. and in the sense of the ensemble averages described by weak values, the experiment establishes the separation of a particle from one its properties during the passage through the interferometer.
The first experimental realization of a measurement of the weak value of a variable, a concept recently introduced by Aharonov, Albert and Vaidman, is presented. Weak measurements (measurements of a weak value) address the situation in which the separation of the eigenvalues caused by a weakly interacting measurement device is small compared to the width of the distribution of the individual eigenvalues. By appropriate choice of the pre- and post-selected state it is possible that the overlapping eigenvalues will interfere producing a value outside the range of eigenvalues. We demonstrate that the weak value is a practical method of amplifying and resolving the separation between overlapping eigenvalues in an optical experiment proposed by Duck, Stevenson and Sudarshan. In this experiment a birefringent crystal spatially separates two linear polarization components of a Gaussian laser beam by a distance much smaller than the beam waist.
We provide a tool for measuring the Stokes parameters and the degree of polarization of single photons by employing second-order interference, namely, the Hong-Ou-Mandel (HOM) interferometer. It is shown that the technique is able to distinguish a partially polarized photon where the polarization state is coupled to an internal degree of freedom, such as time of arrival, from partial polarization due to external entanglement with the environment. The method does not directly resort to any kind of polarization-selective components and therefore is not limited by the extinction ratio of polarizers. Moreover, the technique can be generalized to any two-level encoding of quantum information in single photons, such as time-bin or orbital angular momentum qubits.