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Physical Review A

Cavity modified quantum beats

B. M. Garraway, P. L. Knight

Published Oct 1, 1996• 108 citations
Publisher

Abstract

The coupling of an atom to its environment can be strongly dependent on frequency when that atom is placed in, for example, a cavity. We consider here the exact dynamics of a three-level atom for a resonant form of the atom-environment coupling of the type found in a cavity. The three-level atom forms a quantum-beat V system in the general model that we consider. Without the use of perturbation theory, we derive a set of three coupled differential equations that describe the system. Results are compared to quantum beats in free space and an interpretation is provided in terms of the coupling of the three-level system to a pseudomode. The pseudomode is defined by the differential equations involving its amplitude and possesses the properties of a finite-Q cavity mode. The signal from a detector is formulated in terms of a resonant coupling between the detector and the cavity modes. Limits for a broadband and a narrow-band detector are considered. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.3592

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The coupling of an atom to its environment can be strongly dependent on frequency when that atom is placed in, for example, a cavity. We consider here the exact dynamics of a three-level atom for a resonant form of the atom-environment coupling of the type found in a cavity. The three-level atom forms a quantum-beat V system in the general model that we consider. Without the use of perturbation theory, we derive a set of three coupled differential equations that describe the system. Results are compared to quantum beats in free space and an interpretation is provided in terms of the coupling of the three-level system to a pseudomode. The pseudomode is defined by the differential equations involving its amplitude and possesses the properties of a finite-Q cavity mode. The signal from a detector is formulated in terms of a resonant coupling between the detector and the cavity modes. Limits for a broadband and a narrow-band detector are considered. \textcopyright{} 1996 The American Physical Society.
Atoms can nowadays be placed in increasingly exotic environments such as microscopic cavities and materials with photonic band gaps. High-Q cavities can now easily result in a strong coupling between an atom and its environment where perturbation theory should no longer be appropriate. The purpose of this paper is to describe the dynamics of a multilevel V-type atomic system (including the case of a two-level system) which interacts with a reservoir modeled by a generalized density of states. A theoretical construct, the pseudomode, is utilized to develop general methods for solution. Without using perturbation theory the equivalent master equation is developed and the relationship between the master equation, the pseudomodes, and the generalized density of states function is explored with examples. Utilizing a straightforward definition of the pseudomode, it is found that many functions for the density of states lead to problematic non-Lindblad master equations. Several examples are given, and it is shown how to convert the non-Lindblad master equations into a Lindblad form in these cases. The examples include a non-Lorentzian resonance and a simple model of a photonic band gap.
The generation of two-mode Gaussian-type entangled states of the cavity field is studied in a quantum beat laser, where three-level atoms of the VVV-type level configuration are coupled to two quantized modes of the cavity field and two upper levels of the atom are driven by a strongly classical field. According to Simon's criterion that is a necessary and sufficient condition for the inseparability of two-mode Gaussian states with a general form of covariance matrices, we analytically and numerically investigate the influence of phase and Rabi frequency of the classical driving field, cavity loss, and the purity and nonclassicality of the initial state of the cavity field on the entanglement property of the resulting two-mode Gaussian state. In the limit of weak cavity loss and strong driving, we show that the cavity field can be periodically into an ideal two-mode entangled Gaussian-type state.
We present the exact solution of the dynamics of N two-level atoms strongly driven by an external coherent field and equally coupled on resonance to a cavity mode, in the presence of both cavity dissipation and atomic decay. Analytical results are presented for system and subsystem dynamics, showing how environment-induced decoherence leads the system from pure to mixed states. In the limit of negligible atomic decay, where the system is known to exhibit decoherence-free subspaces, we present a detailed discussion of the decoherence function that can be monitored by atomic population measurements.
In this paper, the problem of a three-level atom interacting with a single mode of the quantized electromagnetic cavity field is considered. The considered theoretical model describes the distinct configurations of a three-level atom. Also, this model includes a detuning and arbitrary forms of both the field and the intensity-dependent atom-field coupling. We obtain the general forms for both the constants of motion and the wavefunction when the atom is initially prepared in one of its states. We use this model for computing a number of statistical aspects of the three-level system. As an illustration, we use the model for studying the time evolution of the second-order correlation function when the atom is initially in an upper state and the field is considered in a coherent state.
The dynamics of a three-level atom in a cascade configuration with both transitions coupled to a single structured reservoir of quantized field modes is treated using Laplace transform methods applied to the coupled amplitude equations. Results are also obtained from master equations by two different approaches, that is, involving either pseudomodes or quasimodes. Two different types of reservoir are considered, namely a high-Q cavity and a photonic band-gap system, in which the respective reservoir structure functions involve Lorentzians. Non-resonant transitions are included in the model. In all cases non-Markovian behaviour for the atomic system can be found, such as oscillatory decay for the high-Q cavity case and population trapping for the photonic band-gap case. In the master equation approaches, the atomic system is augmented by a small number of pseudomodes or quasimodes, which in the quasimode approach themselves undergo Markovian relaxation into a flat reservoir of continuum quasimodes. Results from these methods are found to be identical to those from the Laplace transform method including two-photon excitation of the reservoir with both emitting sequences. This shows that complicated non-Markovian decays of an atomic system into structured EM field reservoirs can be described by Markovian models for the atomic system coupled to a small number of pseudomodes or quasimodes.
Many transient signals from quantum systems result from beats among a large number of levels whose energies depend nonlinearly on the quantum number. Typical examples range from time-resolved laser femtochemistry to quantum optics of single atoms in cavities. Starting from rather general assumptions on the nature of the system, we derive approximate closed-form expressions, which describe such signals in the semiclassical limit. Our approach brings out in a most natural way the phenomenon of fractional revivals and full revivals and explains the oscillatory structures observed in recent experiments on atomic wave packets [Phys. Rev. Lett. 72, 3783 (1994)].