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arXiv:quant-ph/0003010 · Fortschritte der Physik

On the Possibility of Quantum Computation Based on Photon Exchange Interactions

Tomáš Opatrný, Gershon Kurizki

Published Sep 1, 2000• 6 citations
arXivHTMLPDF

Abstract

We examine several proposed schemes by Franson et al. for quantum logic gates based on non-local exchange interactions between two photons in a medium. In these schemes the presence of a single photon in a given mode is supposed to induce a large phase shift on another photon propagating in the same medium. We conclude that the schemes proposed so far are not able to produce the required conditional phase shift, even though the proposals contain many stimulating and intriguing ideas.

DOI
10.1002/1521-3978(200009)48:9/11<1125::aid-prop1125>3.0.co;2-1

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We examine several proposed schemes by Franson et al. for quantum logic gates based on non-local exchange interactions between two photons in a medium. In these schemes the presence of a single photon in a given mode is supposed to induce a large phase shift on another photon propagating in the same medium. We conclude that the schemes proposed so far are not able to produce the required conditional phase shift, even though the proposals contain many stimulating and intriguing ideas.
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.
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.
The recently proposed idea to generate entanglement between photon states via exchange interactions in an ensemble of atoms (J.D. Franson and T.B. Pitman, Phys. Rev. A 60, 917 (1999) and J.D. Franson et al., (quant-ph/9912121)) is discussed using an S-matix approach. It is shown that if the nonlinear response of the atoms is negligible and no additional atom-atom interactions are present, exchange interactions cannot produce entanglement between photons states in a process that returns the atoms to their initial state. Entanglement generation requires the presence of a nonlinear atomic response or atom-atom interactions.
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.
Summary form only given. Nonlinear interactions between two photons are normally very weak because of the weak electric field associated with a single photon. We recently suggested that this difficulty could be avoided by relying on exchange interactions, which can have large effects even when there is no physical interaction at all between two particles. We consider two photons in well collimated beams that are incident upon an atomic vapor cell. The probability of there being two excited atoms in the medium is shown to be a factor of two larger in that case than if the two photons were incident upon two separate but otherwise identical media.