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

A cavity with two level atoms: simulations and cellular automata method

W. Leoński, M. Walczak, Adam Miranowicz

Published Nov 21, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.545174

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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.
The absorption of a single photon by a single two-level system (TLS) in free space is a fundamental physical process. In this contribution, we present the experimental realization of a model system to simulate the dynamics of such an absorption experiment: Comparing the absorption process of a single photon by a single TLS and the incoupling dynamics of an optical resonator, one finds an analogy between the energy stored inside the resonator and the probability of the photon to be absorbed by the TLS [1]. Both systems, resonators and TLS, respond in an equivalent way to the temporal profile of the incident light pulse. The energy storage in a resonator as well as the absorption of a single photon by a TLS can reach an unit efficiency under idealized conditions. Such an optimized process is achieved by an exponentially rising incident light field with a time constant which matches the lifetime of the system [2]. For such a perfect coupling, the end mirror of the resonator needs to have a reflectivity of unity. This corresponds to the excitation of a TLS from the complete solid angle. For a smaller reflectivity of the end mirror, the cavity simulates the absorption dynamics in the case of excitation from only a part of the solid angle. However, using real mirrors, a good analogy with excitation from a large solid angle can still be obtained by using a strongly asymmetric resonator, i.e. an incoupling mirror which has a significantly lower reflectivity than the end mirror of the cavity.
The absorption and the emission of photons by an atom involves quantum jumps between states. We investigate the quantum jump statistics for the system of a two-level atom and a single-mode cavity field. We use the Jaynes-Cummings model for this problem, perform Monte Carlo numerical simulations, and give a detailed exact analysis on these simulations. These studies reveal that the waiting-time distribution (WTD) for photon absorptions (emissions) has a unique novel statistic, and that the photon absorption (emission) rate is not uniform, but counter-intuitively depends on the position in the Rabi cycle. The effects of the nonclassical nature of the field on the WTD is discussed.
We study single-photon transport in an array of coupled microcavities where two two-level atomic systems are embedded in two separate cavities of the array. We find that a single photon can be totally reflected by a single two-level system. However, two separate two-level systems can also create, between them, single-photon quasibound states. Therefore, a single two-level system in the cavity array can act as a mirror while a different type of cavity can be formed by using two two-level systems, acting as tunable ``mirrors,'' inside two separate cavities in the array. In analogy with superlattices in solid state physics, we call this ``cavity inside a coupled-cavity array'' a supercavity. This supercavity is the quantum analog of Fabry-Perot interferometers. Moreover, we show that the physical properties of this quantum supercavity can be adjusted by changing the frequencies of these two-level systems.