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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum phase gate using single atom nonlinearlity

Shigeki Takeuchi, Hisaki Oka, Kunihiro Kojima, Holger Friedrich Hofmann, Keiji Sasaki

Published Aug 18, 2005• 0 citations
Publisher

Abstract

The nonlinear optical response obtained from a single two level atom in a one-sided cavity is studied using a model system, where a infinite atomic layer sits in front of a reflecting mirror. When the atomic layer is placed at the antinode of input field, the result given by finite difference time domain method coupled with the optical Bloch equations is consistent with previous analytical result [ H F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, J. Opt. B 5, 218 (2003) ] based on one-dimensional atom model.

DOI
10.1117/12.618045

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The nonlinear optical response obtained from a single two level atom in a one-sided cavity is studied using a model system, where a infinite atomic layer sits in front of a reflecting mirror. When the atomic layer is placed at the antinode of input field, the result given by finite difference time domain method coupled with the optical Bloch equations is consistent with previous analytical result [ H F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, J. Opt. B 5, 218 (2003) ] based on one-dimensional atom model.
The nonlinear optical response obtained from a model system of a quantum phase gate is investigated. The model system consists of a thin infinite atomic layer of two-level atoms placed in front of a perfect reflecting mirror. The optical response obtained from the model system is semiclassically analyzed using the finite difference time domain method with the optical Bloch equations. It is shown that a nonlinear phase shift of $\ensuremath{\pi}$ is achieved when the atomic layer is placed at an antinode of the input field. This result is consistent with the theoretical result obtained from a one-dimensional atom model [H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, J. Opt. B: Quantum Semiclassical Opt. 5, 218 (2003)]. The dependence of the nonlinear phase shift on the position of the atomic layer is also studied in detail.
We investigate the effects of decoherence on the nonlinear phase shift obtained from a one-dimensional atom implemented by a one-sided microcavity. The one-dimensional atom is realized by coupling a single atom confined in the cavity to the one-dimensional input-output fields of the cavity. The nonlinear optical response obtained from the one-dimensional atom can then be analyzed by using the optical Bloch equations. It is shown that the nonlinear phase shift depends on the coupling efficiency η, which is defined by the ratio of the coherent atom-field coupling rate and the total dipole relaxation rate. In particular, a maximal phase shift of π is obtained on resonance for coupling efficiencies η larger than one half, while the maximal phase shifts for coupling efficiencies η smaller than one half are obtained off resonance and are always smaller than π/2.
We propose a scheme for an optical quantum gate, i.e., a mirror in a quantum superposition state of total transmission and reflection. The model consists of a high-QQQ optical cavity strongly coupled to a single atom or ion in a quantum superposition state of two long lived internal states. By including spontaneous emission, dissipation, measurement back-action, and the time dependence of the atom-field coupling, we numerically simulate a system very close to experimental reality. The switching and quantum coherence properties are confirmed separately in two steps by using the gate directly and as an entrance beam splitter to an interferometer.
We propose to adapt the cellular automata approach as a tool for investigation of quantum optical systems. As an example we propose a model comprising a cavity filled with a one dimensional chain of identical two level atoms. To simulate the probabilistic character of a single atom evolution we use the Monte Carlo algorithm. We assume that the cavity is confined by mirrors of the reflectivity r. This fact allows simulation of the cavity losses. In this communication we shall show the influence of the probabilities of photon absorption by a single atom inside the cavity, on the system dynamics.
Within the framework of a two-dimensional microscopic, purely quantum mechanical model, we analyse the dynamics of single-photon wave packets interacting with optical elements (beam splitters, mirrors), modelled as systems of two-level atoms. That is, we utilize a two-dimensional cavity to simulate the quantum behaviour of simple optical components and networks made thereof. The field is quantized using the canonical procedure, and only the basis states with one unit of excitation are included. This, however, covers linear optical phenomena. The field is taken to interact with localized atoms through a dipole interaction. Using different configurations of atoms, and choosing their frequencies to be resonant or off-resonance, we can model mirrors, beam splitters, focusing devices and multicomponent systems. Thus we can model arbitrary linear networks of optical components. We show the time evolution of a photon wave packet in an interferometer as an example. As the state of the field is known at each instant, spectral properties and spatial coherence can immediately be obtained from the simulations. We also know the states of the two-level atoms constituting the components, which allows us to consider their quantum behaviour. Here the decay of an excited atom into the vacuum state of the electromagnetic field in the two-dimensional cavity is studied.
A quantum emitter interacting with photons in a single optical-mode constitutes a one-dimensional atom. A coherent and efficiently coupled one-dimensional atom provides a large nonlinearity, enabling photonic quantum gates. Achieving a high coupling efficiency (β factor) and low dephasing is challenging. Here, we use a semiconductor quantum dot in an open microcavity as an implementation of a one-dimensional atom. With a weak laser input, we achieve an extinction of 99.2% in transmission and a concomitant bunching in the photon statistics of g^{(2)}(0)=587, showcasing the reflection of the single-photon component and the transmission of the multi-photon components of the coherent input. The tunable nature of the microcavity allows β to be adjusted and gives control over the photon statistics-from strong bunching to antibunching-and the phase of the transmitted photons. We obtain excellent agreement between experiment and theory by going beyond the single-mode Jaynes-Cummings model. Our results pave the way towards the creation of exotic photonic states and two-photon phase gates.