© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Journal of Modern Optics

Dressed states and exact dynamics of intensity-dependent two-mode two-photon Jaynes-Cummings models

Anna Napoli, ANTONINO MESSINA

Published Apr 1, 1996• 39 citations

Abstract

We study the two-photon interaction of a two-level atom with a quantized bimodal field of a loss-free cavity. We assume that both the coupling strength and the atom-field detuning may depend on the populations of the two modes. We show that this general nonlinear model is exactly solvable in terms of a dressing unitary operator. Exact expressions for the eigenstates as well as for the Rabi frequencies of the coupled system are given as explicit functions of the nonlinearity terms present in the model. Exploiting the flexibility of these results, we investigate the atomic inversion supposing that at t=0 one mode is coherent, the other is in a Fock state and the atom is excited. We compare the dynamical behaviour of various particular nonlinear models. A common feature is the presence of collapses and revivals of the Rabi oscillations. We find that the atomic inversion manifests exact periodicity when only one specific type of intensity-dependent term (coupling strength or detuning) is present. Such behaviour is physically interpreted in the framework of the dressed atom representation. The simulataneous presence of both nonlinear contributions in the model breaks such regular behaviour in the long-time atomic evolution, in which case competition effects occur which qualitatively modify the quantum dynamics of the system. Other quantum manifestations are brought to light. Their relevance, in connection with the possibility of preparing a cavity mode in an arbitrary Fock state, is briefly discussed.

DOI: 10.1080/09500349608232773

Related papers

Dynamics of entanglement in a two-mode nonlinear Jaynes-Cummings mode

A. B. M. Ahmed, S. Sivakumar

Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.

arXiv:0907.2992•Jul 17, 2009•2 citations

Single dressed-atom laser: lasing out of a driven Jaynes-Cummings system

Young-Tak Chough, Jung Bog Kim, Kyungwon An

A variant Jaynes-Cummings model (JCM) where the two-state atom coupled to the cavity mode is driven by a strong external field reveals many interesting behaviors. On resonance, a large scale oscillatory behavior of the mean cavity photon number is predicted. It varies sinusoidally with the amplitude of 2(/spl epsi//g)/sup 2/, centered at the same value, where /spl epsi/ is the (real) driving field amplitude and g the vacuum Rabi frequency. The period of the oscillation was found to be exactly twice the "revival time" of the atomic inversion, i.e., T/sub 0/=(4/spl pi//g)(/spl epsi//g). Furthermore, the oscillation then shows another kind of "collapse-and-revival" type behavior as time proceeds. It is very similar to that of the atomic inversion, but the size of oscillation and the time scales are fundamentally different. The "revival" time of the oscillation, for instance, is found to be exactly one half of the so-called "fractional revival" time of the atomic inversion. Our current interest is directed to the radiative behavior of the driven JCM in a more general situation where dissipation as well as detuning is introduced.

Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR)•Jan 20, 2003•0 citations

The Jaynes-Cummings Model with Modulated Field-atom Coupling in Resonator Quantum Electrodynamics

Sergey V. Prants, L.S. Yacoupova

We extend the standard Jaynes-Cummings model to include transient effects due to a modulation of the atom-field coupling. The exact solution for such a generalized model is found in terms of Bessel functions for the atom-cavity mode interaction modulated by the exponential function. This function is incorporated into the basic Hamiltonian phenomenologically for modelling the processes of adiabatic switching on or switching off the interaction of a two-level atom (at rest) with a quantized mode. The dynamical behaviour of the atomic inversion for such processes is plotted and compared with the atomic dynamics for the standard model. If we take into account that, in micromaser experiments, Rydberg atoms move through a cavity with a spatially inhomogenous field, we deal with the Jaynes-Cummings model with a spatial modulation the form of which is defined by the mode-shape function depending, in turn, on the geometrical form of resonator. In the cases of a rectangular and a spherical cavity the analytical solutions for atomic inversion are found in the explicit form in the weak-coupling limit. We consider in detail the time evolution of the atomic inversion while the atom passes through a rectangular cavity. Contrary to the standard model the initial inversion can be exactly restored during the atomic transit depending on the relation between the detuning, the atomic velocity and the number of half-wavelengths of the chosen mode. The numerical solutions of the basic equations are also obtained and plotted for rectangular and spherical resonators.

Journal of Modern Optics•May 1, 1992•27 citations

Dynamical evolution of the two-photon Jaynes-Cummings model in a Kerr-like medium

Amitabh Joshi, Ravinder Rupchand Puri

The collapse-and-revival phenomenon in the population inversion and the time evolution of the quasiprobability Q function of an atom undergoing a two-photon process are investigated when the cavity is supposed to be filled with a Kerr-like medium. An exact expression for the atomic population inversion has been given for a field initially in the coherent state. The closed form of this expression as well as that of the Q function are obtained under the high-field approximation. Also, the tendency toward inhibited decay of the excited state has been explicitly shown. This study reveals how the simultaneous occurrence of two nonlinear processes affects the atomic dynamics.

Physical Review A•Apr 1, 1992•115 citations

Dynamics for a two-atom two-mode intensity-dependent Raman coupled model

Sudha Singh, Karuna Gilhare

We study the quantum dynamics of a two-atom Raman coupled model interacting with a quantized bimodal field with intensity-dependent coupling terms in a lossless cavity. The unitary transformation method used to solve the time-dependent problem also gives the eigensolutions of the interaction Hamiltonian. We study the atomic-population dynamics and dynamics of the photon statistics in the two cavity modes, and present evidence of cooperative effects in the production of antibunching and anticorrelations between the modes. We also investigate the effect of detuning on the evolution of second-order correlation functions and observe that the oscillations become more rapid for large detuning.

Journal of Experimental and Theoretical Physics•Jun 1, 2016•4 citations

Quantum Rabi oscillations of a qubit strongly coupled to a one-dimensional waveguide

Ya. S. Greenberg, A. A. Shtygashev, O. A. Chuikin +2 more

We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.

quant-pharXiv:2608.16077•Aug 18, 2026•0 citations

We study the two-photon interaction of a two-level atom with a quantized bimodal field of a loss-free cavity. We assume that both the coupling strength and the atom-field detuning may depend on the populations of the two modes. We show that this general nonlinear model is exactly solvable in terms of a dressing unitary operator. Exact expressions for the eigenstates as well as for the Rabi frequencies of the coupled system are given as explicit functions of the nonlinearity terms present in the model. Exploiting the flexibility of these results, we investigate the atomic inversion supposing that at t=0 one mode is coherent, the other is in a Fock state and the atom is excited. We compare the dynamical behaviour of various particular nonlinear models. A common feature is the presence of collapses and revivals of the Rabi oscillations. We find that the atomic inversion manifests exact periodicity when only one specific type of intensity-dependent term (coupling strength or detuning) is present. Such behaviour is physically interpreted in the framework of the dressed atom representation. The simulataneous presence of both nonlinear contributions in the model breaks such regular behaviour in the long-time atomic evolution, in which case competition effects occur which qualitatively modify the quantum dynamics of the system. Other quantum manifestations are brought to light. Their relevance, in connection with the possibility of preparing a cavity mode in an arbitrary Fock state, is briefly discussed.

Dynamics of entanglement due to intensity-dependent interaction between a two-level atom and a single-mode electromagnetic field in a Kerr medium is studied. The form of the interaction is such that the Hamiltonian evolution is exactly solvable. The Hamiltonian is shown to be a deformed Jaynes-Cummings model admitting a closed, symmetric algebra. Dynamics of population inversion and atom-field entanglement are studied taking the initial state of the field to be either a coherent state or a squeezed vacuum. Analysis is extended to the case of a two-mode cavity field interacting with a two-level atom. For the two-mode case, the initial field is a pair coherent state or a two-mode squeezed vacuum. Effects due to nonlinearity, intensity-dependent interaction and detuning on the dynamics are discussed and compared with those of the single-mode case.

A variant Jaynes-Cummings model (JCM) where the two-state atom coupled to the cavity mode is driven by a strong external field reveals many interesting behaviors. On resonance, a large scale oscillatory behavior of the mean cavity photon number is predicted. It varies sinusoidally with the amplitude of 2(/spl epsi//g)/sup 2/, centered at the same value, where /spl epsi/ is the (real) driving field amplitude and g the vacuum Rabi frequency. The period of the oscillation was found to be exactly twice the "revival time" of the atomic inversion, i.e., T/sub 0/=(4/spl pi//g)(/spl epsi//g). Furthermore, the oscillation then shows another kind of "collapse-and-revival" type behavior as time proceeds. It is very similar to that of the atomic inversion, but the size of oscillation and the time scales are fundamentally different. The "revival" time of the oscillation, for instance, is found to be exactly one half of the so-called "fractional revival" time of the atomic inversion. Our current interest is directed to the radiative behavior of the driven JCM in a more general situation where dissipation as well as detuning is introduced.

We extend the standard Jaynes-Cummings model to include transient effects due to a modulation of the atom-field coupling. The exact solution for such a generalized model is found in terms of Bessel functions for the atom-cavity mode interaction modulated by the exponential function. This function is incorporated into the basic Hamiltonian phenomenologically for modelling the processes of adiabatic switching on or switching off the interaction of a two-level atom (at rest) with a quantized mode. The dynamical behaviour of the atomic inversion for such processes is plotted and compared with the atomic dynamics for the standard model. If we take into account that, in micromaser experiments, Rydberg atoms move through a cavity with a spatially inhomogenous field, we deal with the Jaynes-Cummings model with a spatial modulation the form of which is defined by the mode-shape function depending, in turn, on the geometrical form of resonator. In the cases of a rectangular and a spherical cavity the analytical solutions for atomic inversion are found in the explicit form in the weak-coupling limit. We consider in detail the time evolution of the atomic inversion while the atom passes through a rectangular cavity. Contrary to the standard model the initial inversion can be exactly restored during the atomic transit depending on the relation between the detuning, the atomic velocity and the number of half-wavelengths of the chosen mode. The numerical solutions of the basic equations are also obtained and plotted for rectangular and spherical resonators.

The collapse-and-revival phenomenon in the population inversion and the time evolution of the quasiprobability Q function of an atom undergoing a two-photon process are investigated when the cavity is supposed to be filled with a Kerr-like medium. An exact expression for the atomic population inversion has been given for a field initially in the coherent state. The closed form of this expression as well as that of the Q function are obtained under the high-field approximation. Also, the tendency toward inhibited decay of the excited state has been explicitly shown. This study reveals how the simultaneous occurrence of two nonlinear processes affects the atomic dynamics.

We study the quantum dynamics of a two-atom Raman coupled model interacting with a quantized bimodal field with intensity-dependent coupling terms in a lossless cavity. The unitary transformation method used to solve the time-dependent problem also gives the eigensolutions of the interaction Hamiltonian. We study the atomic-population dynamics and dynamics of the photon statistics in the two cavity modes, and present evidence of cooperative effects in the production of antibunching and anticorrelations between the modes. We also investigate the effect of detuning on the evolution of second-order correlation functions and observe that the oscillations become more rapid for large detuning.

We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.