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Journal of Modern Optics

Non-local Interatomic Correlations in the Micromaser

Simon J. D. Phoenix, Stephen Mark Barnett

Published Jun 1, 1993• 71 citations
Publisher

Abstract

The interaction of an atom with the intracavity field of a micromaser will, in general leave the atom-field system in an entangled state. The long cavity lifetime means that the memory of this entanglement can persist and influence the interaction with subsequent atoms. We show how non-local correlations between successive atoms can be induced leading to a violation of Bell's inequality.

DOI
10.1080/09500349314551051

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The interaction of an atom with the intracavity field of a micromaser will, in general leave the atom-field system in an entangled state. The long cavity lifetime means that the memory of this entanglement can persist and influence the interaction with subsequent atoms. We show how non-local correlations between successive atoms can be induced leading to a violation of Bell's inequality.
We show that a micromaser can work as an effective source of highly correlated atoms. We consider a one-photon micromaser pumped by a Poissonian beam of atomic pairs. We show that the atoms forming the pairs leave the micromaser's cavity in entangled states and that they can violate the Bell inequality. We consider two aspects of the violation of the Bell inequality: we study the maximal value Bmax{\mathbf{B}}_{\mathrm{max}}Bmax​ of an expression appearing in the Bell inequality and we evaluate a vector-dependent $\mathbf{B}(\stackrel{\ensuremath{\rightarrow}}{a},{a}^{\ensuremath{'}},\stackrel{\ensuremath{\rightarrow}}{b},{b}^{\ensuremath{'}})$ depending upon experimental setup. We calculate the entanglement of the formation of states of the atomic pairs. We show that the pairs of atoms, which fly out from the micromaser cavity, are entangled for almost all values of control parameters characterizing the considered two-atom micromaser. This happens even if they do not violate the Bell inequality.
A pair of atoms interacting successively with the field of the same cavity and exchanging a single photon leave the cavity in an entangled state of Einstein-Podolsky-Rosen (EPR) type (see, for example, Phoenix S. J. D. and Barnett S. M., J. Mod. Opt. 40 (1993) 979). By implementing the model with the translational degrees of freedom, we show in this letter that the entanglement with the translational atomic variables can lead, under appropriate conditions, towards the separability of the internal variables of the two atoms. This implies that the translational dynamics can lead, in some cases, to difficulties in observing Bell's inequality violation for massive particles.
A micromaser in standard operation produces entangled two-level atoms. This entanglement can be investigated in the correlations of atoms leaving the micromaser cavity in the upper and lower maser levels. The correlations contribute to the stabilization of the photon number in the cavity and are thus vital for the generation of sub-Poissonian statistics in the maser field. We review how various statistical signatures for this entanglement are calculated in micromaser theory, and report recent measurements that demonstrate the case. Ways are described leading to an optimal entanglement for the atoms in the micromaser.
Rydberg atoms traversing a micromaser cavity one after the other can emerge in correlated states, and according to Copenhagen quantum mechanics this may lead to a violation of Bell's inequality, that is, to a Bell sum S>2. S is here calculated in various ideal physical situations including those with (1) different initial states of the atoms, (2) different free adjustable parameters, being either the phase or the turning angle of a classical radiation field put behind the cavity, and (3) either equal or different Rabi angles for successive atoms. The experiments are crucial for a realist interpretation which predicts S<2 or S=2 because particles of different kinds (photons and atoms) are involved.