Reflection of a particle from a quantum measurement

Jonathan B Mackrory; Kurt Jacobs; Daniel A Steck

doi:10.1088/1367-2630/12/11/113023

The following article is Open access

Reflection of a particle from a quantum measurement

Jonathan B Mackrory¹, Kurt Jacobs² and Daniel A Steck¹

Published 11 November 2010 • Published under licence by IOP Publishing Ltd
New Journal of Physics, Volume 12, November 2010 Citation Jonathan B Mackrory et al 2010 New J. Phys. 12 113023 DOI 10.1088/1367-2630/12/11/113023

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¹ Department of Physics and Oregon Center for Optics, 1274 University of Oregon, Eugene, OR 97403-1274, USA

² Department of Physics, University of Massachusetts at Boston, 100 Morrissey Blvd, Boston, MA 02125, USA

³ Author to whom any correspondence should be addressed.

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Received 24 July 2010
Published 11 November 2010

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Abstract

We present a generalization of continuous position measurements that accounts for a spatially inhomogeneous measurement strength. This describes many real measurement scenarios, in which the rate at which information is extracted about position has itself a spatial profile, and includes measurements that detect whether a particle has crossed from one region into another. We show that such measurements can be described, in their averaged behavior, as stochastically fluctuating potentials of vanishing time average. Reasonable constraints restrict the form of the measurement to have degenerate outcomes, which tend to drive the system to spatial superposition states. We present the results of quantum-trajectory simulations for measurements with a step-function profile (a 'which-way' measurement) and a Gaussian profile. We find that the particle can coherently reflect from the measurement region in both cases, despite the stochastic nature of the measurement back-action. In addition, we explore the connection to the quantum Zeno effect, where we find that the reflection probability tends to unity as the measurement strength increases. Finally, we discuss two physical realizations of a spatially varying position measurement using atoms.

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Movie 1 (figure 2). (0.5 MB, GIF) Wigner function animation for a particle incident on a static potential step, without a measurement. This animation corresponds to figure 2, which also has the parameters and axis labels.

Movie 2 (figure 3(a)). (1.0 MB, GIF) Wigner function animation for a single trajectory with particle reflecting from a step measurement, without a potential. This animation corresponds to figure 3(a), which also has the parameters and axis labels.

Movie 3 (figure 3(b)). (0.95 MB, GIF) Wigner function animation for a single trajectory with transmitting through a step measurement, without a potential. This animation corresponds to figure 3(b), which also has the parameters and axis labels.

Movie 4 (figure 3(c)). (0.94 MB, GIF) Wigner function animation for the ensemble average over measurement realizations for a step measurement, without a potential. This animation corresponds to figure 3(c), which also has the parameters and axis labels.

Movie 5 (figure 5). (0.12 MB, GIF) Wigner function animation for a particle incident on a static Gaussian potential, without a measurement. This animation corresponds to figure 5, which also has the parameters and axis labels.

Movie 6 (figure 6(a)). (0.73 MB, GIF) Wigner function animation for a single trajectory with particle mostly reflecting from a Gaussian measurement, without a potential. This animation corresponds to figure 6(a), which also has the parameters and axis labels.