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arXiv:quant-ph/0102079 · Zeitschrift für Naturforschung A

Verifying Atom Entanglement Schemes by Testing Bell's Inequality

Dimitris G. Angelakis, Almut Beigea, P. L. Knight, William J. Munro, Ben Tregenn

Published Feb 1, 2001• 0 citations
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Abstract

Abstract Recent experiments to test B ell's inequality using entangled photons and ions aimed at tests of basic quantum mechanical principles. Interesting results have been obtained and many loopholes could be closed. In this paper we want to point out that tests of Bell's inequality also play an important role in verifying atom entanglement schemes. We describe as an example a scheme to prepare arbitrary entangled states of N two-level atoms using a leaky optical cavity and a scheme to entangle atoms inside a photonic crystal. During the state preparation no photons are emitted, and observing a violation of B ell's inequality is the only way to test whether a scheme works with a high precision or not.

DOI
10.1515/zna-2001-0106

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Abstract Recent experiments to test B ell's inequality using entangled photons and ions aimed at tests of basic quantum mechanical principles. Interesting results have been obtained and many loopholes could be closed. In this paper we want to point out that tests of Bell's inequality also play an important role in verifying atom entanglement schemes. We describe as an example a scheme to prepare arbitrary entangled states of N two-level atoms using a leaky optical cavity and a scheme to entangle atoms inside a photonic crystal. During the state preparation no photons are emitted, and observing a violation of B ell's inequality is the only way to test whether a scheme works with a high precision or not.
Recent experiments to test Bell's inequality using entangled photons and ions aimed at tests of basic quantum mechanical principles. Interesting results have been obtained and many loopholes could be closed. In this paper we want to point out that tests of Bell's inequality also play an important role in verifying atom entanglement schemes. We describe as an example a scheme to prepare arbitrary entangled states of N two-level atoms using a leaky optical cavity and a scheme to entangle atoms inside a photonic crystal. During the state preparation no photons are emitted and observing a violation of Bell's inequality is the only way to test whether a scheme works with a high precision or not.
Previous work on Bell's inequality realized in the laboratory has used entangled photons. Here we describe how entangled atoms can violate Bell's inequality, and how these violations can be measured with a very high detection efficiency. We first discuss a simple scheme based on two-level atoms inside a cavity to prepare the entangled state. We then discuss a scheme using three-level atoms, which requires a parameter regime much easier to access experimentally using current technology. As opposed to other schemes, our proposal relies on the presence of finite decay rates and its implementation should therefore be much less demanding.
We study Bell-inequality tests with entanglement between a coherent-state field in a cavity and a two-level atom. In order to detect the cavity field for such a test, photon on-off measurements and photon number parity measurements, respectively, are investigated. When photon on-off measurements are used, at least 50% of detection efficiency is required to demonstrate violation of the Bell inequality. Photon number parity measurements for the cavity field can be effectively performed using ancillary atoms and an atomic detector, which leads to large degrees of Bell violations up to Cirel'son's bound. We also analyze decoherence effects in both field and atomic modes and discuss conditions required to perform a Bell inequality test free from the locality loophole.
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.
Experimental tests of Bell's inequality allow to distinguish quantum mechanics from local hidden variable theories. Such tests are performed by measuring correlations of two entangled particles (e.g. polarization of photons or spins of atoms). In order to constitute conclusive evidence, two conditions have to be satisfied. First, strict separation of the measurement events in the sense of special relativity is required ("locality loophole"). Second, almost all entangled pairs have to be detected (for particles in a maximally entangled state the required detector efficiency is 82.8%), which is hard to achieve experimentally ("detection loophole"). By using the recently demonstrated entanglement between single trapped atoms and single photons it becomes possible to entangle two atoms at a large distance via entanglement swapping. Combining the high detection efficiency achieved with atoms with the space-like separation of the atomic state detection events, both loopholes can be closed within the same experiment. In this paper we present estimations based on current experimental achievements which show that such an experiment is feasible in future.
In 1935 Einstein, Podolsky and Rosen used the assumption of local realism to conclude in a Gedankenexperiment with two entangled particles that quantum mechanics is not complete. For this reason EPR motivated an extension of quantum mechanics by so-called local hidden variables. Based on this idea in 1964 Bell constructed a mathematical inequality whereby experimental tests could distinguish between quantum mechanics and local-realistic theories. Many experiments have since been done that are consistent with quantum mechanics, disproving the concept of local realism. But all these tests suffered from loopholes allowing a local-realistic explanation of the experimental observations by exploiting either the low detector efficiency or the fact that the detected particles were not observed space-like separated. In this context, of special interest is entanglement between different quantum objects like atoms and photons, because it allows one to entangle distant atoms by the interference of photons. The resulting space-like separation together with the almost perfect detection efficiency of the atoms allows a first loophole-free test of Bell's inequality. The primary goal of the present thesis is the experimental realization of entanglement between a single localized atom and a single spontaneously emitted photon at a wavelength suitable for the transport over long distances. In the experiment a single optically trapped Rb87 atom is excited to a state which has two selected decay channels. In the following spontaneous decay a photon is emitted coherently with equal probability into both decay channels. This accounts for perfect correlations between the polarization state of the emitted photon and the Zeeman state of the atom after spontaneous decay. Because these decay channels are spectrally and in all other degrees of freedom indistinguishable, the spin state of the atom is entangled with the polarization state of the photon. To verify entanglement, appropriate correlation measurements in complementary bases of the photon polarization and the internal quantum state of the atom are performed. It is shown, that the generated atom-photon state yields an entanglement fidelity of 0.82. The experimental results of this work mark an important step towards the generation of entanglement between space-like separated atoms for a first loophole-free test of Bell's inequality. Furthermore entanglement between a single atom and a single photon is an important tool for new quantum communication and information applications, e.g. the remote state preparation of a single atom over large distances.