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Annual Meeting Optical Society of America

Test of Bell’s Inequalities using Rydberg atoms

Brian J. Oliver, Carlos R. Stroud

Published Jan 1, 1986• 0 citations
Publisher

Abstract

An experimental test of Bell’s inequalities using two-level atoms is proposed. The test is analogous to that proposed by Bohm but, instead of using spins and Stern-Gerlach magnets, two-level atoms and resonant pulses are used. Two atoms excited to a common Rydberg state, but traveling in different directions, are introduced into a microwave cavity. The microwave field resonantly couples two Rydberg states and excites the atoms into a correlated state. The atoms then pass out of the cavity and into separate interaction regions where resonant microwave fields rotate their Bloch vectors through angles directly corresponding to the angles of orientation of the Stern-Gerlach magnets in the spin experiment. State selective ionization is then used to determine whether each atom is in the upper or lower Rydberg state. State selective ionization of Rydberg states has been demonstrated with an efficiency approaching 100% so that tests of Bell’s inequalities which are even more stringent than those using cascade photon polarization may be possible.

DOI
10.1364/oam.1986.thj9

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arXiv:quant-ph/9811042•Nov 17, 1998•0 citations
An experimental test of Bell’s inequalities using two-level atoms is proposed. The test is analogous to that proposed by Bohm but, instead of using spins and Stern-Gerlach magnets, two-level atoms and resonant pulses are used. Two atoms excited to a common Rydberg state, but traveling in different directions, are introduced into a microwave cavity. The microwave field resonantly couples two Rydberg states and excites the atoms into a correlated state. The atoms then pass out of the cavity and into separate interaction regions where resonant microwave fields rotate their Bloch vectors through angles directly corresponding to the angles of orientation of the Stern-Gerlach magnets in the spin experiment. State selective ionization is then used to determine whether each atom is in the upper or lower Rydberg state. State selective ionization of Rydberg states has been demonstrated with an efficiency approaching 100% so that tests of Bell’s inequalities which are even more stringent than those using cascade photon polarization may be possible.
The analogy between two-level atoms and spins is used to show that Rydberg atoms provide a new medium through which Bell’s inequalities may be studied. The low-efficiency particle detectors that have been used in experiments to test Bell’s inequalities are replaced by nearly 100% efficient state-selective ionizers in Rydberg-atom experiments. Two methods for producing correlated states of pairs of atoms are discussed. Each method can be used to create correlated states of more than two atoms. A Bell inequality for a three-atom system is considered and compared with quantum-mechanical predictions. A violation of the inequality for the three-particle system is predicted.
The tests of Bell's inequality to date have failed to be definitive because of the ``detection loophole,'' due to the inefficiency of photodetectors. An idealized experiment using pairs of two-level Rydberg atoms, correlated with the help of a quantized cavity field, was proposed by Oliver and Stroud [J. Opt. Soc. Am. B 4, 1426 (1987)] for the purpose of blocking this loophole. We develop their proposal by removing their idealizations. We carefully define the ensemble of atom pairs by imposing conditions on arrival times at the analyzers of the atoms. We take into account the spread of velocities of the atoms, which implies that the ensemble must be described quantum mechanically by a statistical operator rather than a pure state, and we show that with detector efficiencies of 0.9 or better, quantum mechanics implies a strong violation of Bell's inequality in the ensemble. Upper and lower bounds on ensemble averages can be inferred from experimental averages, thereby permitting an experimental test of Bell's inequality in the ensemble. \textcopyright{} 1996 The American Physical Society.
It is well known that Bell’s inequality may be violated for special quantum states, e.g., an entangled state for a pair of particles. The entangled state is generalized here into a polyentangled state. Specifically, instead of only two possible states for each individual particle of the pair, several states are possible in an entangled way. An experimental realization for the polyentangled state is presented. It is the state for a pair of atoms in their Zeeman sublevels, in which the atoms are produced from dissociation of a homonuclear (I = 1/2) paradimer that is initially in a J = even rotational state of the singlet electron state. The three possible angular momentum components (M2 = 0,±1) in a specific direction can be determined because the different Zeeman sublevels can be selectively excited by polarized lasers, and then subsequently detected by photoionization. Because of the high detection efficiency (>90%) and fast responsivity (<10 ns) for these processes, the two main loopholes in previous LHV experiments using optical photons can be blocked.
Most experimental tests of Bell inequalities have involved measurements of correlations between two photons. One of the first definitive experiments involved the linear polarization correlation between two photons in an atomic cascade of 200 Hg. That experiment is discussed in depth in this paper. The form of the initial state density matrix was a critical part of that experiment; and the experimental and theoretical determination of the density matrix, including finite solid-angle effects is discussed. However, all Bell inequality experiments to date have two widely recognized loopholes, detector efficiency and locality. This paper concludes with a very brief description of an experiment that will close both of these loopholes. In contrast to existing experiments with photons, this new test involves spin correlations between the nuclei of two 199 Hg atoms; it is an exact experimental realization of Bohm's version of the Einstein-Podolsky-Rosen gedankenexperiment.
There have been studies on the formation of quantum-nonlocal states in two spatially separate cavities. We suggest a nonlocal test for a field prepared in two cavities. We couple classical driving fields with cavities where a nonlocal state is prepared. Two independent two-level atoms are then sent through respective cavities to interact off-resonantly with the cavity fields. The atomic states are measured after the interaction. Bell's inequality can be tested by the joint probabilities of the two-level atoms being in their excited or ground states. We find that a violation of Bell's inequality can also be tested using a single atom sequentially interacting with the two cavities. Potential experimental errors are also considered. We show that with the present experimental condition of 5% error in the atomic velocity distribution, the violation of Bell's inequality can be measured.
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.