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arXiv:quant-ph/0502065 · Physical Review A

Quantum erasure within the optical Stern-Gerlach model

M. Chianello, Michele Tumminello, Alessandro Vaglica, G. Vetri

Published May 7, 2004• 9 citations
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Abstract

In the optical Stern-Gerlach effect the two branches in which the incoming atomic packet splits up can display interference pattern outside the cavity when a field measurement is made which erases the which-way information on the quantum paths the system can follow. On the contrary, the mere possibility to acquire this information causes a decoherence effect which cancels out the interference pattern. A phase-space analysis is also carried out to investigate on the negativity of the Wigner function and on the connection between its covariance matrix and the distinguishability of the quantum paths.

DOI
10.1103/physreva.69.053403

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In the optical Stern-Gerlach effect the two branches in which the incoming atomic packet splits up can display interference pattern outside the cavity when a field measurement is made which erases the which-way information on the quantum paths the system can follow. On the contrary, the mere possibility to acquire this information causes a decoherence effect which cancels out the interference pattern. A phase-space analysis is also carried out to investigate on the negativity of the Wigner function and on the connection between its covariance matrix and the distinguishability of the quantum paths.
In the optical Stern-Gerlach effect the interaction of a two-level atom with an optical-field gradient causes a state-selective deflection that leads to a splitting of the atomic trajectory. The semiclassical approach to this problem actually predicts a splitting of the atomic beam into two paths, similar to the well-known magnetic Stern-Gerlach effect for spin 1/2. Here we study a model in which the quantum nature of the field is taken into account and we show, in particular, that for an initial coherent state of the cavity light the optical Stern-Gerlach effect manifests itself as a splitting of the atomic beam into two groups containing, however, many spots. \textcopyright{} 1996 The American Physical Society.
Abstract Quantum erasure probes the dynamic nature of quantum coherence. It allows quantum systems to exhibit interference effects by recovering coherence that was previously lost through entanglement with another system. In this paper we examine the concept of a quantum eraser which creates and then erases path information through repeated use of the Stern–Gerlach effect. We explore the degree to which this eraser can recover quantum coherence. We find that the recovered coherence depends on the spin of the objects passing through the eraser and on the relative angle between the orientations of the eraser’s two magnets. We determine that full coherence can always be recovered for spin-1/2 objects independent of the value of the spin projection but cannot always be recovered for objects with larger spin values. We then discuss how the quantum coherence could be experimentally measured in this setup. Finally, we comment on the limitations of this Stern–Gerlach eraser and similar erasure schemes.
We analyze the Stern-Gerlach experiment in phase space with the help of the matrix Wigner function, which includes the spin degree of freedom. Such analysis allows for an intuitive visualization of the quantum dynamics of the device. We include the interaction with the environment, as described by the Caldeira-Leggett model. The diagonal terms of the matrix provide us with information about the two components of the state that arise from interaction with the magnetic field gradient. In particular, from the marginals of these components, we obtain an analytical formula for the position and momentum probability distributions in the presence of decoherence that shows a diffusive behavior for large values of the decoherence parameter. These features limit the dynamics of the present model. We also observe the decay of the nondiagonal terms with time and use this fact to quantify the amount of decoherence from the norm of those terms in phase space. From here, we can define a decoherence time scale, which differs from previous results that make use of the same model. We analyze a typical experiment and show that, for that setup, the decoherence time is much smaller than the characteristic time scale for the separation of the two beams, implying that they can be described as an incoherent mixture of atoms traveling in the up and down directions with opposite values of the spin projection. Therefore, entanglement is quickly destroyed in the setup we analyzed.
In the optical Stern-Gerlach effect, the interaction of a traveling two-level atom with the electromagnetic field of an optical cavity causes a splitting of the atomic trajectory. One may ask if it is possible to single out particular initial configurations of the system that will lead to selective scattering, in which the atoms follow only one trajectory. We show that these configurations consist of a coherent superposition of the atomic internal states, and of a field phase state or a field coherent state, with a precise phase relation between the two subsystems: The same configurations which produce the so-called atomic coherent trapping in the Jaynes-Cummings model.