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Chinese Physics Letters

Dynamical Behavior of an Atomic Beam Interacting with a Fock State Light Field

Ben Li, Jingbiao Chen

Published Jan 1, 2010• 0 citations
Publisher

Abstract

The collapse and revival of evolution with photon number of population inversion in the case of an atomic beam with velocity distribution interacting with a single-mode and Fock-state light field is investigated by full quantum theory. Compared to the previously reported coherent state case [Li B and Chen J B Chin. Phys. Lett. 26 (2009) 123203 ], which was induced by evolution with coupling strength of population inversion, in the case under consideration there exists Poisson distribution of photon numbers and atomic velocity distribution in the beam. Moreover, we prove that above, the collapse and revival have an analogy with conventional collapse and revival [Eberly J H et al. Phys. Rev. Lett. 44 (1980) 1323 ] in both the mathematical expression and physical significance.

DOI
10.1088/0256-307x/27/1/013201

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The collapse and revival of evolution with photon number of population inversion in the case of an atomic beam with velocity distribution interacting with a single-mode and Fock-state light field is investigated by full quantum theory. Compared to the previously reported coherent state case [Li B and Chen J B Chin. Phys. Lett. 26 (2009) 123203 ], which was induced by evolution with coupling strength of population inversion, in the case under consideration there exists Poisson distribution of photon numbers and atomic velocity distribution in the beam. Moreover, we prove that above, the collapse and revival have an analogy with conventional collapse and revival [Eberly J H et al. Phys. Rev. Lett. 44 (1980) 1323 ] in both the mathematical expression and physical significance.
We report on the phenomena of the periodic spontaneous collapse and revival in the dynamics of an atomic beam interacting with a single-mode and coherent-state light field. Conventional collapse and revival by Eberly et al. [ Phys. Rev. Lett. 44 (1980) 1323 ] are presented in the case of the evolution with time of the population inversion. Here, we study the evolution with coupling strength of population inversion. We define the collapse and revival coupling strengths as characteristic parameters to describe the above collapse and revival. Furthermore, we present the analytic formulas for the population inversion, the collapse and revival coupling strengths.
The collapse and revival of quantum states appear in diverse areas of physics. In quantum optics the occurrence of such a phenomena in the evolution of an atomic state, interacting with a light field initially in a coherent state, was predicted by using the Jaynes-Cummings model (JCM), and subsequently demonstrated experimentally. In this paper we revisit the JCM with the Monte-Carlo wave function approach and investigate the time evolution of the photon emission rate of the atom in a cavity. Analytical and numerical quantum trajectory calculations show that the cavity and the initial field statistics strongly influence the photon emission dynamics. A coherent field indeed gives rise to a collapse and revival behavior that mirrors atomic state evolution. However, there are differences between the two. The emission rate for a field in a Fock number state exhibits a sinusoidal oscillation, and there exists a quiescent period for a thermal field. These properties are quite different from those in free space. It is also shown that the fluctuation in photon emission is much less than that of the atomic population.
An extension of the standard Raman-coupled Jaynes-Cummings model has been made to include atomic external effects due to quantization of atomic motion. The collapse-and-revival phenomena in population inversion and in atomic motion, the velocity-selective population and their relation for a motion-quantized atom are given on the basis of a fundamental constant characterizing the interaction strength between the field modes and the atomic internal and external states. This study reveals how the initial statistics of atomic momentum affect the atomic internal dynamics and how those of the fields affect the atomic external dynamics through the atomic internal states. An exact expression for the time evolution of the density operator has been given for two fields and the center-of-mass motion initially in coherent states and in an arbitrary superposition of atomic momentum eigenstates. The statistics of atomic external and internal quantities such as the radiation force and the atomic momentum are given. \textcopyright{} 1996 The American Physical Society.
We investigate the atomic inversion dynamics that occur when an atom interacts with a two-mode quantized radiation field. Our work uses Schrodinger theory with the rotating wave approximation. We adiabatically eliminate all but two of the atomic states in order to obtain analytical and numerical results. By varying the width and average photon number of the field statistics, we have uncovered secondary revivals that arise because of the complicated double sum over the two field modes in the population inversion. The diagonal part of the sum (the part that contains commensurate frequencies) is closely related to the degenerate-mode work of Buck and Sukumar.1 The breaking of the exact periodicity with secondary revivals and eventual erratic behavior result from the off-diagonal terms. Use of Poisson statistics allows exact analytic results to be obtained and also allows comparisons with previous work to be made. However, because the width and mean are intimately related for Poisson statistics, we also use Gaussian statistics so that their effects may be separated. To investigate various possible initial field conditions, we use squeezed states (oscillatory in photon number), displaced number states, and generalized states. The latter interpolate between number states, coherent states, and thermal states.
Abstract We consider a two-level atom interacting with a quantized field in an optomechanical cavity and study the population inversion of the atom in this hybrid optomechanical system. Analytical solutions of the excited state population in the hybrid system are derived for various initial states of the cavity field and the mechanical mirror in the limit of weak single-photon coupling regime. Due to the mechanical mirror, the population inversion exhibits anomalous behavior, compared to the results predicted by the Jaynes–Cummings (JC) model. For an initial Fock state cavity field, we show that the atomic population inversion can undergo collapses and revivals induced by the mechanical mirror which is in a Fock state for the resonant atom-field interaction. When the cavity field is far-detuned from the atomic transition, the atom can couple to the mechanical mirror effectively via the JC interaction. In this case, the atomic population inversion can display either full Rabi oscillations or the collapse and revival behavior induced by a Fock state or a coherent state of the mechanical mirror, respectively. We also explore an experimentally more relevant situation when the mechanical mirror is initially in a mixed state. We derive an analytical expression of the excited state population via the unitary evolution for the density operator of the whole system. We find that the population inversion in this case exhibits slower collapse and smaller revival amplitude due to the initial mixture of the mechanical state. For an initial coherent state cavity field, we show that the predicted collapse regime in the original JC model can display nonzero oscillating values. Our analytical predications are further confirmed with numerical calculations in which the dissipation mechanism from the system is included.
The time-evolution of atomic population of a light-atoms interaction system,two atoms in Bell states Interacting with two-mode entangled coherent field,are investigated by means of quantum thoery and numerical method.The effect of the atomic initial state,mean photon numbers of field,the degree of the entanglment for the entangled coherent fields,and the coupling strength of dipole-dipole interaction between atoms on the atom's population are discussed by numerical calculation.The results show that the atomic population is time-independent provided that the atom is in |β11〉 state.For the other three Bell states,there will appear the periodical collapse-revival of the atomic population if the initial mean photon number reaches some special value.With the increase of the initial mean photon number,the oscillation frequency of the time-evolution of atomic population increases correspondingly,and the amplitude decreases.The revival period of the atomic population for the initial states |β00〉 and |β10〉 is twice of that for the initial state |β01〉.The degree of entanglement of the two-mode entangled coherent field and the intensity of two dipole-dipole interaction between atoms have no effects on the frequency of the Rabi oscillation,but have obvious effects on the amplitude of the oscillation.