Quantum logic using photon-exchange interactions

María Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini +1 more

J. D. Franson, T. B. Pittman

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.

Philip John Walther, Anton Zeilinger

Michael Fleischhauer

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.

Tomáš Opatrný, Gershon Kurizki

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.

George Svetlichny