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Physical Review A

Dynamics of the four-level Λ system in a two-mode cavity

Maciej Janowicz, J. M. A. Ashbourn

Published Mar 1, 1997• 18 citations
Publisher

Abstract

In this paper we investigate the properties of a four-level atomic system interacting with two modes of the electromagnetic field in a cavity. By linearization of the Hamiltonian we show that the corresponding mathematical model is exactly solvable. To obtain simpler effective Hamiltonians the method of multiple scales is applied. It is shown that under some special values of the detunings and coupling constants, exactly predictable collapses and revivals in the atomic populations appear. Also, due to the specific interactions of the atom with the cavity modes and the ensuing measurement of energy or angular momentum and energy, two-mode Schr\"odinger-cat states arise in the cavity. Finally, the stabilization and trapping properties of the system are demonstrated in a lossy cavity within the Wigner-Weisskopf approximation. The existence of stationary states is shown and it is also shown that interference effects can cause cancellation of one line in both transmitted light and spontaneous emission spectra.

DOI
10.1103/physreva.55.2348

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We study the non-resonant interaction of a moving four-level N -type atom with cavity fields in the presence of a nonlinear Kerr-like medium. The exact solutions of the considered models are obtained when the atom is initially in an upper state, while the field is in a coherent state. We derive an expression for the occupation numbers of the photon state. Also, the momentum increment of the atomic system is obtained. The influence of the detuning parameters or the Kerr medium on the evolution time of the momentum increment is examined numerically. The existence of the detuning parameters leads to the retraction of the revivals for the three atomic systems. On the other hand, the presence of the Kerr medium is conducive to increasing the regularity and periodicity of the collapse–revival phenomenon for the one- and two-mode systems, while chaotic behaviour occurs for the three-mode system.

Journal of Physics B Atomic Molecular and Optical Physics•May 6, 2008•31 citations
In this paper we investigate the properties of a four-level atomic system interacting with two modes of the electromagnetic field in a cavity. By linearization of the Hamiltonian we show that the corresponding mathematical model is exactly solvable. To obtain simpler effective Hamiltonians the method of multiple scales is applied. It is shown that under some special values of the detunings and coupling constants, exactly predictable collapses and revivals in the atomic populations appear. Also, due to the specific interactions of the atom with the cavity modes and the ensuing measurement of energy or angular momentum and energy, two-mode Schr"odinger-cat states arise in the cavity. Finally, the stabilization and trapping properties of the system are demonstrated in a lossy cavity within the Wigner-Weisskopf approximation. The existence of stationary states is shown and it is also shown that interference effects can cause cancellation of one line in both transmitted light and spontaneous emission spectra.
The Hamiltonian is derived for the interaction of a Λ-type three-level atom with a two-mode quantum cavity field from the general interaction Hamiltonian between a multi-level atom and a multi-mode radiation field, and it is reduced to an effective two-mode Raman-coupled model under a large detuning condition. We propose a modified effective Hamiltonian for the two-mode Raman-coupled model, find the time-dependent state vectors, and present the validity conditions for the involved interaction Hamiltonians. It is shown that in the study of the two-mode Raman-coupled model it is not enough to retain only the usually used effective Hamiltonian, one must also take into account the ac Stark shift of the atomic levels (at least one of the levels). Finally, we study the atomic dynamics in the interaction of a Λ-type three-level atom with a two-mode quantum cavity field and in the two-mode Raman-coupled model. We find that the number of collapse-revivals, the collapse time and the revival time show new characteristics.
Abstract The dynamics of an atom of three levels in Λ configuration interacting with a quantized field of two modes in a cavity is studied within the rotating wave approximation by considering experimental values of accessible hyperfine levels of alkali atoms. The Hamiltonian model is constructed on the basis of the direct product of the atomic states with Fock states of light. This simplified basis allows us to generalize the state of light to any quantum field. The interaction term of the Hamiltonian restricts the system to a 3D Hilbert space. The system’s time evolution results show some similarities with the effective two-level system, such as the presence of collapses and revivals and the atom-field entanglement. By an analysis of the statistics of the photons, we show that when the three-level atom is interacting with a coherent field of two modes, it is possible to control experimentally the statistics of the field to be super-Poissonian or sub-Poissonian by the choice of the initial atomic state.
We describe the dynamics of an exactly solvable Raman coupled model interacting with two modes of a quantized cavity electromagnetic field. The model consists of a three-level atom in the \ensuremath{\Lambda} configuration whose excited state is considered to be far off resonance and is adiabatically eliminated. The effective Hamiltonian for this system contains products of the transition operators between the two ground-state levels and a field annihilation operator from one mode and a creation operator from the other. This Hamiltonian provides an example of a zero-photon process. We study the atomic inversion and investigate the production of nonclassical effects such as antibunched light, violations of the Cauchy-Schwartz inequality, and squeezing.
An analytical expression of the emission and absorption spectra, for a Λ-type three-level cavity-bound atom interacting with a two-mode cavity field, is given using the dressed states of the system. We take explicitly into account the existence of forms of nonlinearities of both the field and the intensity-dependent atom–field coupling. The characteristics of the emission and absorption spectra for binomial and squeezed coherent states of the modes are exhibited. The effects of the mean number of photons, detuning and the nonlinearity forms on the spectra are analysed.
In this paper, the effects of the field damping and Kerr-like medium on a system of a four-level atom in the [Formula: see text]-type interacting nonlinearly with a two-mode field are studied. Analytical solution of the system of differential equations resulting from the Schrödinger equation is obtained. The effects of detuning parameters, Kerr-like parameter, coupling function and damping rate are discussed for atomic population inversion, the second-order correlation function, Shannon information entropy, and linear entropy. Under justifiable all conditions, extreme entanglement states may appear periodically with the evolution of time. The arrival of the quantum system to a pure state can be controlled by variations of the Kerr medium and the damping parameters. The results also exhibit that the periods of strong and weak entanglement between the parts of the system are achieved during the periods of collapses and revivals of the atomic population inversion. Moreover, the photon distribution changes from non-classical to classical by increasing the damping rate.
We study the non-resonant interaction of a moving four-level N -type atom with cavity fields in the presence of a nonlinear Kerr-like medium. The exact solutions of the considered models are obtained when the atom is initially in an upper state, while the field is in a coherent state. We derive an expression for the occupation numbers of the photon state. Also, the momentum increment of the atomic system is obtained. The influence of the detuning parameters or the Kerr medium on the evolution time of the momentum increment is examined numerically. The existence of the detuning parameters leads to the retraction of the revivals for the three atomic systems. On the other hand, the presence of the Kerr medium is conducive to increasing the regularity and periodicity of the collapse–revival phenomenon for the one- and two-mode systems, while chaotic behaviour occurs for the three-mode system.