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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Theory of two-photon nonlinearity by a realistic matter system with many degrees of freedom in a cavity

Akira Ishikawa, Toshiro Isu, Hajime Ishihara

Published Jun 1, 2007• 1 citation
Publisher

Abstract

Two-photon nonlinearity (TPN) has been investigated in the context of realization of a quantum logic gate, where the cavity QED system has been considered to realize a sufficiently strong TPN.
DOI
10.1109/cleoe-iqec.2007.4386950

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We propose a new scheme for strong two-photon nonlinearity (TPN) by cavity QED systems with many three-level atoms, although the TPN due to the saturation effect of two-level atoms generally declines with an increase in the number of atoms. The reduction in anharmonicity by the increase in the number of atoms can be overcome if the system satisfies particular criteria. The new scheme is significant for realizing TPN devices using solid-state materials because it is generally difficult to control the number of atoms, which are few, introduced in the device.
We have investigated two-photon nonlinearity in general cavity QED systems, which cover both weak- and strong-coupling regimes and include the radiative loss from an atom. One- and two-photon propagators are obtained in analytical forms. By surveying both coupling regimes, we have revealed the conditions on a photonic pulse for yielding large nonlinear effects, depending on the cavity QQQ value. We also discuss the effects of radiative loss on nonlinearity.
Exploiting the field-amplification effect of a cavity, the possibility of optical nonlinearity by only two photons was indicated experimentally. In the present article, we review our recent analysis of the two-photon dynamics in a cavity quantum electrodynamics (QED) system. Since a cavity-QED system is highly dispersive around its resonances, the shapes of photonic pulses are significantly deformed through interaction with the system. Thus, the present analysis is based on a formalism beyond single-mode approximations. The external photon field is treated rigorously as a continuum, which enables us to handle the two-photon wavefunction in the space representation. The degree of optical nonlinearity in a two-photon state is quantified by comparing the output wavefunction with the linear output wavefunction. It is revealed that the semiclassical optical response theory can be applied for evaluation of the two-photon optical nonlinearity. The two-photon nonlinearity appears not purely as a phase shift in the output wavefunction. The degradation of the fidelity between the output wavefunction and the linear output wavefunction always occurs, which hinders the application of this nonlinear effect as a quantum phase gate. The optimum condition for maximizing the two-photon nonlinearity is clarified, suggesting that pulse shape control is more essential than the Q-value control of the cavity QED system.
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.