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arXiv:quant-ph/9902080 · American Journal of Physics

Photon polarization measurements without the quantum Zeno effect

V. Kidambi, A. Widom, C. Lerner, Y. N. Srivastava

Published May 1, 2000• 4 citations
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Abstract

We consider a photon beam incident on a stack of polarizers as an example of a von Neumann projective measurement, theoretically leading to the quantum Zeno effect. The Maxwell theory (which is equivalent to the single-photon Schrödinger equation) describes measured polarization phenomena, but without recourse to the notion of a projective measurement.

DOI
10.1119/1.19462

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We consider a photon beam incident on a stack of polarizers as an example of a von Neumann projective measurement, theoretically leading to the quantum Zeno effect. The Maxwell theory (which is equivalent to the single-photon Schrödinger equation) describes measured polarization phenomena, but without recourse to the notion of a projective measurement.
Abstract Quantum Zeno effect concerns deterministic dynamics of a quantum system induced by a series of projective quantum measurements. Applying this effect in optics, one can achieve an arbitrary lossless transformation of linear polarization of light with help of linear polarizers. However, to demonstrate this effect in practice, we have to take into account unavoidable losses in each polarizer that limits probability of successful transformations. In this work, we theoretically study a realistic quantum Zeno effect with an optimal discrete set of polarizers and find the maximum success probability
We describe a version of the Zeno effect where the monitored physical property cannot be represented by a standard operator in the system space and the evolution to be prevented by observation is not unitary. This is the case of quantum-state purity of a spin-1/2 system, which is equivalent to the degree of polarization of a single photon. By a suitable embedding of the system (say, a single photon) in an enlarged space of a pair of photons, pure and fully mixed components lead to orthogonal subspaces, with lack of purity becoming equivalent to entanglement. By imposing desirable properties the representation of the system in the enlarged space is unique. We show that the Zeno effect is possible, and experimentally feasible, in the enlarged space. The peculiarity that photons in identical polarization states are involved in pairs to observe the dynamics of each photon allows us to refer it as the self-Zeno effect or Narcissus effect.
The usual, "static" version of the quantum Zeno effect consists in the hindrance of the evolution of a quantum systems due to repeated measurements. There is however a "dynamic" version of the same phenomenon, first discussed by von Neumann in 1932 and subsequently explored by Aharonov and Anandan, in which a system is forced to follow a given trajectory. A Berry phase appears if such a trajectory is a closed loop in the projective Hilbert space. A specific example involving neutron spin is considered and a similar situation with photon polarization is investigated.