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Physical Review Letters

Cooperative Enhancement of Optical Quantum Gates

J. D. Franson

Published May 19, 1997• 25 citations
Publisher

Abstract

Nonlinear phase shifts at the two-photon level can be greatly enhanced by a cooperative effect involving pairs of atoms, which can give a phase shift proportional to the square of the number of atoms in a medium. This is a nonlocal quantum effect that does not exist for classical states of light. Cooperative effects of this kind may have practical applications in quantum computing.

DOI
10.1103/physrevlett.78.3852

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Nonlinear phase shifts at the two-photon level can be greatly enhanced by a cooperative effect involving pairs of atoms, which can give a phase shift proportional to the square of the number of atoms in a medium. This is a nonlocal quantum effect that does not exist for classical states of light. Cooperative effects of this kind may have practical applications in quantum computing.
Summary form only given.Nonlinear optical effects are normally limited to high-intensity fields containing a large number of photons because the electric field associated with a single photon is usually very weak. Nonlinear phase shifts at the two-photon level previously have been observed using high-Q cavities and atomic beams. The authors recently predicted that nonlocal effects involving pairs of atoms in a medium could enhance the nonlinear interaction between two photons to the point that nonlinear phase shifts could be obtained in an ordinary medium without the use of resonant cavities.
The operation of a quantum computer is inherently nonlocal due to the entanglement of separated quantum gates. This paper is concerned instead with the use of nonlocal effects to construct the quantum gates themselves. A nonlocal interaction in which pairs of atoms exchange two photons is expected to produce a large nonlinear phase shift. An interesting feature of this effect is that energy is not conserved at the location of an individual atom but it is conserved overall. The preliminary results from a series of experiments in a sodium vapor cell are in apparent agreement with the predictions of the theory. These nonlinear phase shifts can be used to construct quantum logic gates, such as a Controlled-NOT.
Nonlinear interactions between two photons would have many potential applications, including the implementation of quantum logic gates for use in quantum computing. We are investigating a new mechanism for nonlinear optics at the two-photon level that is based on the exchange of photons by pairs of atoms in a medium, such as an atomic vapor. The effect can be understood as being due to a factor of two increase in the probability of having two excited atoms in the medium compared to the case in which the two photons propagate in two separate media. These effects are expected to be sufficiently large that cavities and traps should not be required, which may eventually allow the construction of large numbers of simple quantum logic gates. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Nonlinear interactions between two photons are required for the construction of optical quantum logic gates, but those interactions are normally very weak due to the small magnitude of the electric field associated with a single photon. We note that exchange interactions can have a large effect even when there is no physical interaction between two particles, and we exploit this property for the construction of optical quantum logic gates. We show that the probability of there being two virtually-excited atoms in a medium can be a factor of 2 larger when two nonresonant photons propagate through the same medium as compared to the case in which they propagate through two separate media, in analogy with photon bunching. As a result, the application of one or more laser pulses will produce a nonlinear phase shift that can be used to construct an XOR quantum logic gate. This provides an example of a quantum control process in which one photon can control the state of another photon even when there is no sequence of physical interactions linking the two photons. From a classical point of view, it is not possible to identify a path for the flow of information or a specific cause for the outcome of the control process.