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New Journal of Physics

Cavity-QED-based scheme for verification of the photon commutation relation

Jiyong Park, Su‐Yong Lee, Ho-Joon Kim, Hai-Woong Lee

Published Mar 12, 2010• 6 citations
Publisher

Abstract

We propose an experimental scheme to prove the photon commutation relation, [ a , a † ]=1. The scheme exploits interaction between a single-mode cavity field and three two-level atoms, two of which are prepared in an entangled state. The success of the scheme is subject to observation of the atoms in predetermined states after the interaction. We show, in particular, that a reasonably high success probability can be obtained with our scheme by preparing the cavity field in a superposition of two Fock states and choosing the interaction times appropriately.

DOI
10.1088/1367-2630/12/3/033019

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We propose an experimental scheme to prove the photon commutation relation, [ a , a † ]=1. The scheme exploits interaction between a single-mode cavity field and three two-level atoms, two of which are prepared in an entangled state. The success of the scheme is subject to observation of the atoms in predetermined states after the interaction. We show, in particular, that a reasonably high success probability can be obtained with our scheme by preparing the cavity field in a superposition of two Fock states and choosing the interaction times appropriately.
Theoretical analysis is given of an experimental scheme that can perform individual photon operations such as the photon annihilation operation a, creation operation a†, and commutation operation aa†−a†a, utilizing atom-cavity field interactions and conditional measurements. In order for the scheme to perform the desired photon operation, the atom-cavity field interaction times are generally required to be sufficiently short that photon annihilation and/or creation are dominated by the one-half Rabi cycle process. Such short interaction times, however, lead inevitably to a low success probability of the scheme. It is shown that this problem of low success probability can be overcome by preparing the cavity field in a superposition of a small number (two) of Fock states and choosing the interaction times appropriately.
A single two-level atom can be used to prepare an arbitrary photon number state (Fock state) in a high Q cavity . The atom undergoes a controlled succession of interactions with two cavity modes. One of them contains a coherent field. The atom transfers photons one by one from this field to the initially empty second mode. The scheme can be extended to prepare a quantum superposition of the vacuum with a Fock state, a highly non-classical situation. We discuss the feasibility of the experiment with our present Rydberg-atom cavity QED set-up.