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Europhysics Letters (EPL)

Quantum billiard atom optics

Bernd Rohwedder

Published Nov 1, 2002• 5 citations
Publisher

Abstract

The phenomenon of fractional self-imaging can be used to implement atom-optical components in the interior of a rectangular quantum billiard. Their temporal concatenation may lead to complex "atom chips" operating in the time-domain. As an elementary example, we discuss a billiard internal Mach-Zehnder interferometer that can be transformed into an all-optical switch or controllable beam splitter for atoms. The inherent coherence and reversibility of its dynamics also provides a simple means to realize a Welcher Weg/Quantum erasure experiment. The whole concept is shown to be robust with respect to realistic wall-softness effects and feasible within the present state of the art.

DOI
10.1209/epl/i2002-00268-x

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The phenomenon of fractional self-imaging can be used to implement atom-optical components in the interior of a rectangular quantum billiard. Their temporal concatenation may lead to complex "atom chips" operating in the time-domain. As an elementary example, we discuss a billiard internal Mach-Zehnder interferometer that can be transformed into an all-optical switch or controllable beam splitter for atoms. The inherent coherence and reversibility of its dynamics also provides a simple means to realize a Welcher Weg/Quantum erasure experiment. The whole concept is shown to be robust with respect to realistic wall-softness effects and feasible within the present state of the art.
Certain classes of integrable quantum billiards provide a versatile arena for time-domain atom optics experiments. In order to learn how to fully exploit the fractional revival behavior that governs these kinds of systems, we here develop a convenient theoretical framework for their description. As an illustrative example, we present a billiard-internal realization of Grover's quantum search algorithm. The considered devices are scalable and could be used for the construction of quantum computers using trapped neutral atoms.
Summary form only given. The motion of a particle inside a closed area surrounded by reflecting walls can be integrable or chaotic, depending on the shape of the boundary. These billiards serve as a good and simple model to study chaotic dynamics both classically and quantum mechanically. Recently, we realized an "atom-optics billiard", where ultra-cold atoms are trapped inside a dark optical trap, whose shape can be varied to create different atom dynamics. In this work we describe how scattering and wall softness influence the dynamics of the atoms, and destroy or create stability.
A quantum mechanical description of a non-absorbing electromagnetic (em) beam splitter (BS) transformation is given by the use of momentum creation operators, which also include momentum shift operators operating on the BS. This BS transformation is used for analysing photon-statistics effects in the em Mach-Zehnder interferometer. Also the relation between this BS transformation and Welcher-Weg measurements is discussed. The analogy between em and atom interferometers is described with an emphasis on the use of high-order correlation functions. The entanglement between the interfering beams in these interferometers and the BS is taken into account in our analysis for treating special effects.
The 'collapse' of the wave function in a general measuring process is analyzed by a pure quantum mechanical (QM) approach. The problem of the delayed choice and Welcher-Weg (WW) experiments is analyzed for Mach-Zehnder (MZ) interferometer. The WW effect is related to complementarity principle and orthogonality of wavefunctions although it produces small momentum changes between the electromagnetic (EM) field and the beam-splitters (BS's). For QM states for which we have a superposition of states and interference effects there is no reality before measurement, but by excluding such effects the system gets a real meaning already before measurement.