Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Interaction of a three-level atom with an SU(2) coherent state

W. K. Lai, V. Buek, P. L. Knight

Published Aug 1, 1991• 25 citations
Publisher

Abstract

In this paper we investigate the sensitivity of coupled atomic transitions to correlations between field modes. In particular, we show that a three-level atom interacting with a cavity field supporting two quantized modes can be highly sensitive to the nature of the correlations between the modes. Correlated two-mode states include the two-mode squeezed state, whereas the SU(2) coherent state is an example of an anticorrelated state. We study in detail the dynamics of a three-level atom in the \ensuremath{\lambda} configuration, interacting with the two modes of an SU(2) coherent state. We show that for certain choices of the atom-field coupling constants, the generalized two-photon Rabi frequency for the system becomes independent of the photon number, leading to a purely periodic behavior in time of the atomic population probabilities; for other choices of the atom-field coupling constants, we observe the usual collapse and revival of the Rabi oscillations. We study also the dynamics of the field, in particular the correlations between the modes. Finally, for comparison purposes, we present a parallel study of the case in which the field modes are initially uncorrelated.

DOI
10.1103/physreva.44.2003

Related papers

Dynamics of a three-level atom in a two-mode squeezed vacuum

W. K. Lai, V. Buek, P. L. Knight

In this paper we study the dynamics of a three-level atom interacting with a two-mode squeezed vacuum, a highly correlated state in which each mode contains the same number of quanta yet exhibits a thermal photon distribution. Under exact resonance, the Rabi oscillations exhibit an irregular behavior reminiscent of those in the thermal-state Jaynes-Cummings model. If the individual field modes are sufficiently detuned from the intermediate atomic level, the Rabi oscillations become quasiperiodic. The three-level system in this case reduces to an effective two-level system in which two-photon processes dominate. The times of revivals of the Rabi oscillations in this limit depend only on the atom-field coupling constants and the detuning. For comparison, we present a parallel study of the case in which the initial field is prepared in an uncorrelated two-mode state, such as a two-mode thermal state or a two-mode coherent state. Under the full resonance condition, the former leads to an irregular evolution of the Rabi oscillations, while the latter leads to the usual collapse and revival phenomena. If the individual modes are sufficiently detuned from the intermediate atomic level, we observe the same quasiperiodicity of the Rabi oscillations as in the case of the two-mode squeezed vacuum but with a doubling of revival times (for equal atom-field coupling constants). Whereas the two-mode squeezed vacuum and the two-mode thermal-state transition dynamics lead to correlation between the field modes, the two-mode coherent state leads to anticorrelation (when sufficiently detuned from the intermediate atomic level).

Physical Review A•Nov 1, 1991•53 citations

Nonclassical properties of a two-mode SU(2) coherent field resonantly interacting with a three-level Λ-type atom

Zheng Nai-qing, 宁德师范高等专科学校物理与电气工程系,宁德 352100

Nonclassical properties of a two-mode field initially in an SU(2) coherent state resonantly interacting with a three-level Λ-type atom are investigated by means of the quantum theory and numerical calculations. The dependence of the nonclassical properties on the total photon number of the two-mode, the partition parameter and the coupling constant is discussed for three cases: (1) no state-selective atomic measurement; (2) direct state-selective atomic measurement; and (3) state-selective atomic measurement after the application of a classical field. The results indicate that when the total photon number of the two-mode is increased or the state-selective measurement is performed on the atom, the difference squeezing of two-mode is distinctly enhanced; and when the partition parameter is decreased or the state-selective measurement is performed on the atom after the application of a classical field, the average intensity of the sub-Poisson statistic distribution of mode a is reduced and that of mode b is enhanced; when the total photon number of the two modes is increased or the direct state-selective measurement is performed on the atom, the anti-correlation character between the two modes is preserved, but the average intensity of the anti-correlation is reduced; and when the direct state-selective measurement is performed on the atom, the Cauchy-Schwartz inequality is violated.

Acta Physica Sinica•Jan 1, 2010•0 citations

Unitary transformation and the dynamics of a three-level atom interacting with two quantized field modes

Moorad Alexanian, Subir K. Bose

Starting from a three-level atom coupled to two modes of radiation field, we derive a Raman-coupled Hamiltonian by a unitary transformation, evaluated perturbatively in coupling constants. The Rabi oscillation frequency and the collapse and revival times of the atomic coherence are found to have strikingly different photon-intensity dependence than those found previously.

Physical Review A•Sep 1, 1995•100 citations

New Quantum Effects in the Dynamics of a Two-mode Field Coupled to a Two-level Atom

G. Benivegna, ANTONINO MESSINA

The dynamics of a degenerate two-mode electromagnetic field coupled to a single two-level atom is investigated both analytically and numerically. New quantum effects are discussed concerning the time dependence of the photon number and of its fluctuations, assuming that at t = 0 one of the modes is coherent and the other is empty. The field dynamics are dominated by oscillatory net exchanges of a large number of photons between the two modes, displaying amplitude decay. Over a longer time scale, revivals and collapses in the field populations take place. The time scales of these phenomena are much larger than those of the atomic Rabi oscillations decay. Moreover, the system attains a highly non-classical regime in which the field intensity in each mode is subjected to strong fluctuations even for a large initial number of photons in the coherent mode. Various correlations between atomic and field dynamics are pointed out, and the physical origin of the new quantum effects is briefly discussed. Finally, using our fully quantized calculations, we comment on the validity of the atomic homodyne detection proposed by Wilkens and Meystre.

Journal of Modern Optics•May 1, 1994•29 citations

Entanglement of a three-level atom interacting with two-modes field in a cavity

Alejandra del Río‐Lima, Freddy Jackson Poveda-Cuevas, Octavio Castaños

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.

arXiv:2401.04892•Journal of Physics B Atomic Molecular and Optical Physics•Aug 22, 2024•4 citations

Characteristics of Rabi oscillations in the two-mode squeezed state of the field

Amitabh Joshi, Ravinder Rupchand Puri

The phenomenon of collapses and revivals of Rabi oscillations is studied for a two-level atom undergoing either one- or two-photon transitions in the two-mode squeezed state field inside a lossless cavity. The qualitative behavior of this phenomenon is found to be different as compared with corresponding coherent-state fields. Analytic expressions for excitation probabilities are obtained. Also, the statistical aspect of the field in terms of intensity-intensity correlations is discussed.

Physical Review A•Oct 1, 1990•49 citations
In this paper we investigate the sensitivity of coupled atomic transitions to correlations between field modes. In particular, we show that a three-level atom interacting with a cavity field supporting two quantized modes can be highly sensitive to the nature of the correlations between the modes. Correlated two-mode states include the two-mode squeezed state, whereas the SU(2) coherent state is an example of an anticorrelated state. We study in detail the dynamics of a three-level atom in the \ensuremath{\lambda} configuration, interacting with the two modes of an SU(2) coherent state. We show that for certain choices of the atom-field coupling constants, the generalized two-photon Rabi frequency for the system becomes independent of the photon number, leading to a purely periodic behavior in time of the atomic population probabilities; for other choices of the atom-field coupling constants, we observe the usual collapse and revival of the Rabi oscillations. We study also the dynamics of the field, in particular the correlations between the modes. Finally, for comparison purposes, we present a parallel study of the case in which the field modes are initially uncorrelated.
In this paper we study the dynamics of a three-level atom interacting with a two-mode squeezed vacuum, a highly correlated state in which each mode contains the same number of quanta yet exhibits a thermal photon distribution. Under exact resonance, the Rabi oscillations exhibit an irregular behavior reminiscent of those in the thermal-state Jaynes-Cummings model. If the individual field modes are sufficiently detuned from the intermediate atomic level, the Rabi oscillations become quasiperiodic. The three-level system in this case reduces to an effective two-level system in which two-photon processes dominate. The times of revivals of the Rabi oscillations in this limit depend only on the atom-field coupling constants and the detuning. For comparison, we present a parallel study of the case in which the initial field is prepared in an uncorrelated two-mode state, such as a two-mode thermal state or a two-mode coherent state. Under the full resonance condition, the former leads to an irregular evolution of the Rabi oscillations, while the latter leads to the usual collapse and revival phenomena. If the individual modes are sufficiently detuned from the intermediate atomic level, we observe the same quasiperiodicity of the Rabi oscillations as in the case of the two-mode squeezed vacuum but with a doubling of revival times (for equal atom-field coupling constants). Whereas the two-mode squeezed vacuum and the two-mode thermal-state transition dynamics lead to correlation between the field modes, the two-mode coherent state leads to anticorrelation (when sufficiently detuned from the intermediate atomic level).
Nonclassical properties of a two-mode field initially in an SU(2) coherent state resonantly interacting with a three-level Λ-type atom are investigated by means of the quantum theory and numerical calculations. The dependence of the nonclassical properties on the total photon number of the two-mode, the partition parameter and the coupling constant is discussed for three cases: (1) no state-selective atomic measurement; (2) direct state-selective atomic measurement; and (3) state-selective atomic measurement after the application of a classical field. The results indicate that when the total photon number of the two-mode is increased or the state-selective measurement is performed on the atom, the difference squeezing of two-mode is distinctly enhanced; and when the partition parameter is decreased or the state-selective measurement is performed on the atom after the application of a classical field, the average intensity of the sub-Poisson statistic distribution of mode a is reduced and that of mode b is enhanced; when the total photon number of the two modes is increased or the direct state-selective measurement is performed on the atom, the anti-correlation character between the two modes is preserved, but the average intensity of the anti-correlation is reduced; and when the direct state-selective measurement is performed on the atom, the Cauchy-Schwartz inequality is violated.
The dynamics of a degenerate two-mode electromagnetic field coupled to a single two-level atom is investigated both analytically and numerically. New quantum effects are discussed concerning the time dependence of the photon number and of its fluctuations, assuming that at t = 0 one of the modes is coherent and the other is empty. The field dynamics are dominated by oscillatory net exchanges of a large number of photons between the two modes, displaying amplitude decay. Over a longer time scale, revivals and collapses in the field populations take place. The time scales of these phenomena are much larger than those of the atomic Rabi oscillations decay. Moreover, the system attains a highly non-classical regime in which the field intensity in each mode is subjected to strong fluctuations even for a large initial number of photons in the coherent mode. Various correlations between atomic and field dynamics are pointed out, and the physical origin of the new quantum effects is briefly discussed. Finally, using our fully quantized calculations, we comment on the validity of the atomic homodyne detection proposed by Wilkens and Meystre.
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.