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Journal of Modern Optics

Cavity QED analog of spin

Christopher C. Gerry

Published Nov 1, 1997• 9 citations
Publisher

Abstract

Using the even and odd coherent states, we show that a single mode cavity field, prepared in a coherent state by a classical source and manipulated by both dispersive and resonant interactions with atoms, is analogous to a spin one-half particle interacting with Stern–Gerlach magnets where the parity of the field is the analog of spin. Because the number of photons in the cavity may be large, the system we describe can exhibit quantum effects on at least a mesoscopic scale. We show that entangled two and three cavity systems can be generated. The three cavity case can be used to demonstrate the contradiction between local realistic theories and quantum mechanics in the manner proposed by Greenberger, Horne and Zeilinger in 1989 [13].

DOI
10.1080/09500349708231876

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Using the even and odd coherent states, we show that a single mode cavity field, prepared in a coherent state by a classical source and manipulated by both dispersive and resonant interactions with atoms, is analogous to a spin one-half particle interacting with Stern–Gerlach magnets where the parity of the field is the analog of spin. Because the number of photons in the cavity may be large, the system we describe can exhibit quantum effects on at least a mesoscopic scale. We show that entangled two and three cavity systems can be generated. The three cavity case can be used to demonstrate the contradiction between local realistic theories and quantum mechanics in the manner proposed by Greenberger, Horne and Zeilinger in 1989 [13].
A proposal is made for obtaining a mesoscopic realization of the Greenberger-Horne-Zeilinger (GHZ) "all or nothing" contradiction between quantum mechanics and local realism in the context of cavity QED. The proposed experiment involves three separated micromaser cavities, each initially prepared in a coherent state, which are then entangled by dispersive atom-field interactions followed by selective ionization of a single atom that has passed through all three cavities. The cavities are then probed individually by single atoms manipulated to obtain a measurement of the parity of the cavity fields. Using an isomorphism between coherent-state cavity fields and a spin-\textonehalf{} system, we show how this experiment gives rise to violations of local realism in the manner of GHZ.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ‘‘meter’’ measuring the other. We have performed a ‘‘quantum nondemolition’’ measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (‘‘Schrodinger cat’’) gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schrodinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
After they have interacted, quantum particles generally behave as a single nonseparable entangled system. The concept of entanglement plays an essential role in quantum physics. We have performed entanglement experiments with Rydberg atoms and microwave photons in a cavity and tested quantum mechanics in situations of increasing complexity. Entanglement resulted either from a resonant exchange of energy between atoms and the cavity field or from dispersive energy shifts affecting atoms and photons when they were not resonant. With two entangled particles (two atoms or one atom and a photon), we have realized new versions of the Einstein-Podolsky-Rosen situation. The detection of one particle projected the other, at a distance, in a correlated state. This process could be viewed as an elementary measurement, one particle being a ``meter'' measuring the other. We have performed a ``quantum nondemolition'' measurement of a single photon, which we detected repeatedly without destroying it. Entanglement is also essential to understand decoherence, the process accounting for the classical appearance of the macroscopic world. A mesoscopic superposition of states (``Schr\"odinger cat'') gets rapidly entangled with its environment, losing its quantum coherence. We have prepared a Schr\"odinger cat made of a few photons and studied the dynamics of its decoherence, in an experiment which constitutes a glimpse at the quantum/classical boundary. We have also investigated entanglement as a resource for the processing of quantum information. By using quantum two-state systems (qubits) instead of classical bits of information, one can perform logical operations exploiting quantum interferences and taking advantage of the properties of entanglement. Manipulating as qubits atoms and photons in a cavity, we have operated a quantum gate and applied it to the generation of a complex three-particle entangled state. We finally discuss the perspectives opened by these experiments for further fundamental studies.
We demonstrate how a new exactly soluble cavity QED model can be used to test local realism associated with three-particle entangled states, as proposed by Mermin. These states embody the correlations described by Greenberger, Horne, and Zeilinger (GHZ) and provide a stronger refutation of local hidden variable theories than is possible with Bell inequalities. It is shown that two photons distributed in the model’s four cavity modes coupled with a two-level atom can effectively produce three independent spin-1/2 particle states. We discuss preparation of the desired perfectly correlated GHZ state and a method to perform measurement on various field modes and atomic level correlations equivalent to a spin component along any direction.