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

Journal of Modern Optics

The Damped-vacuum-field Jaynes-Cummings Model

Gui-Yu Hu, E. Irwin, P. K. Aravind

Published Feb 1, 1995• 2 citations
Publisher

Abstract

We study the dynamics of a two-level atom interacting with a single mode of a damped cavity at 0 K when the cavity is initially in the vacuum state and the atom enters it in an arbitrary (pure or mixed) state. A complete analytical solution of this simple model is presented. On the basis of this solution we firstly investigate the pseudo-spin dynamics of the atom and the cavity field, secondly give an illustration of the Araki-Lieb theorem concerning the von Neumann entropies of interacting quantum systems and thirdly demonstrate the generation of entangled states of the atom and cavity field that are of interest in connection with the Bell inequalities.

DOI
10.1080/09500349514550331

Related papers

The damped Jaynes–Cummings model

Stephen Mark Barnett, John Jeffers

The dynamics of the much studied Jaynes–Cummings model, of a single two-level atom interacting with a single quantized field mode, is simple to solve for because the number of quanta in the system is strictly conserved. Including the effects of cavity damping makes the model significantly more difficult to treat. Here we present a simple derivation of the evolution of the atomic inversion in the presence of cavity damping. This will enable us to explain the physical meaning of the solution, first derived more than 20 years ago, and also to show that it is valid for much stronger damping than was appreciated at that time.

Journal of Modern Optics•Sep 10, 2007•18 citations

MAXIMUM ENTANGLEMENT IN A JAYNES-CUMMINGS SYSTEM WITH STRONGLY DRIVEN ATOMS

Federico Casagrande, ALFREDO LULLI

We describe the entanglement of a Jaynes-Cummings system, where a two-level atom is also strongly driven by an external coherent field while it crosses a resonant cavity prepared in a coherent state. First we consider the atom-cavity field entanglement, described by the Von Neumann entropy. We find that it depends only on the interaction time and the initial atomic state. The entropy vanishes in the case of maximally polarized atom, independent of the interaction time, whereas it reaches its maximum value for atom in the upper or lower state and for long enough interaction times. Then we investigate the entanglement between two consecutive strongly driven atoms interacting with the cavity mode assumed in the vacuum state, showing that they never entangle in spite of the existence of atom-atom correlations.

International Journal of Modern Physics B•May 20, 2006•4 citations

Dynamical symmetries of the vacuum field Jaynes–Cummings model

Gui-Yu Hu, P. K. Aravind

We examine the dynamics of the Jaynes–Cummings model when it is restricted to the following initial conditions: atom in an arbitrary (pure or mixed) state and field in the vacuum state. It is shown that the model exhibits two dynamical symmetries that are characterized by the Lie algebras SU(2) × SU(2) and SU(3). A pair of interacting spins in a magnetic field also possesses the former symmetry, whereas the latter symmetry naturally describes a three-level atom driven by two laser fields; thus close correspondences with these systems are established. A pseudospin treatment of the model is devised and used to carry out a systematic investigation of its dynamics. On the basis of this treatment we (a) obtain the constants of motion of the problem, (b) establish bounds on the atomic and field inversions for arbitrary model conditions, (c) expose a striking symmetry between field and atomic (i.e., dipole) squeezing, and (d) discuss the occurrence of nonclassical correlations between the atom and the cavity field.

Journal of the Optical Society of America B•Sep 1, 1989•20 citations

Entropy and entanglement in the Jaynes–Cummings model with effects of cavity damping

A.‐S. F. Obada, H. A. Hessian, A.‐B. A. Mohamed

The temporal evolution of entanglement for a single-mode field interacting with a two-level atom via intensity-dependent coupling in the off-resonant case has been studied, where the leakage of photon through the cavity is taken into account. The effects of cavity damping on the coherence properties of the atom and the field are studied. The amount of entanglement is compared with the total correlations. It is found that the atom–field system is inhibited from going into a pure state in the off-resonant case.

Journal of Physics B Atomic Molecular and Optical Physics•Jun 23, 2008•12 citations

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

Adiabatic entanglement in two-atom cavity QED

Constantinos Lazarou, B. M. Garraway

We analyze the problem of a single mode field interacting with a pair of two level atoms. The atoms enter and exit the cavity at different times. Instead of using constant coupling, we use time-dependent couplings which represent the spatial dependence of the mode. Although the system evolution is adiabatic for most of the time, a previously unstudied energy crossing plays a key role in the system dynamics when the atoms have a time delay. We show that conditional atom-cavity entanglement can be generated, while for large photon numbers the entangled system has a behavior which can be mapped onto the single atom Jaynes-Cummings model. Exploring the main features of this system we propose simple and fairly robust methods for entangling atoms independently of the cavity, for quantum state mapping, and for implementing SWAP and controlled-NOT (CNOT) gates with atomic qubits.

arXiv:0810.0640•Physical Review A•Feb 19, 2008•19 citations
We study the dynamics of a two-level atom interacting with a single mode of a damped cavity at 0 K when the cavity is initially in the vacuum state and the atom enters it in an arbitrary (pure or mixed) state. A complete analytical solution of this simple model is presented. On the basis of this solution we firstly investigate the pseudo-spin dynamics of the atom and the cavity field, secondly give an illustration of the Araki-Lieb theorem concerning the von Neumann entropies of interacting quantum systems and thirdly demonstrate the generation of entangled states of the atom and cavity field that are of interest in connection with the Bell inequalities.
The dynamics of the much studied Jaynes–Cummings model, of a single two-level atom interacting with a single quantized field mode, is simple to solve for because the number of quanta in the system is strictly conserved. Including the effects of cavity damping makes the model significantly more difficult to treat. Here we present a simple derivation of the evolution of the atomic inversion in the presence of cavity damping. This will enable us to explain the physical meaning of the solution, first derived more than 20 years ago, and also to show that it is valid for much stronger damping than was appreciated at that time.
We describe the entanglement of a Jaynes-Cummings system, where a two-level atom is also strongly driven by an external coherent field while it crosses a resonant cavity prepared in a coherent state. First we consider the atom-cavity field entanglement, described by the Von Neumann entropy. We find that it depends only on the interaction time and the initial atomic state. The entropy vanishes in the case of maximally polarized atom, independent of the interaction time, whereas it reaches its maximum value for atom in the upper or lower state and for long enough interaction times. Then we investigate the entanglement between two consecutive strongly driven atoms interacting with the cavity mode assumed in the vacuum state, showing that they never entangle in spite of the existence of atom-atom correlations.
We examine the dynamics of the Jaynes–Cummings model when it is restricted to the following initial conditions: atom in an arbitrary (pure or mixed) state and field in the vacuum state. It is shown that the model exhibits two dynamical symmetries that are characterized by the Lie algebras SU(2) × SU(2) and SU(3). A pair of interacting spins in a magnetic field also possesses the former symmetry, whereas the latter symmetry naturally describes a three-level atom driven by two laser fields; thus close correspondences with these systems are established. A pseudospin treatment of the model is devised and used to carry out a systematic investigation of its dynamics. On the basis of this treatment we (a) obtain the constants of motion of the problem, (b) establish bounds on the atomic and field inversions for arbitrary model conditions, (c) expose a striking symmetry between field and atomic (i.e., dipole) squeezing, and (d) discuss the occurrence of nonclassical correlations between the atom and the cavity field.
The temporal evolution of entanglement for a single-mode field interacting with a two-level atom via intensity-dependent coupling in the off-resonant case has been studied, where the leakage of photon through the cavity is taken into account. The effects of cavity damping on the coherence properties of the atom and the field are studied. The amount of entanglement is compared with the total correlations. It is found that the atom–field system is inhibited from going into a pure state in the off-resonant case.
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.
We analyze the problem of a single mode field interacting with a pair of two level atoms. The atoms enter and exit the cavity at different times. Instead of using constant coupling, we use time-dependent couplings which represent the spatial dependence of the mode. Although the system evolution is adiabatic for most of the time, a previously unstudied energy crossing plays a key role in the system dynamics when the atoms have a time delay. We show that conditional atom-cavity entanglement can be generated, while for large photon numbers the entangled system has a behavior which can be mapped onto the single atom Jaynes-Cummings model. Exploring the main features of this system we propose simple and fairly robust methods for entangling atoms independently of the cavity, for quantum state mapping, and for implementing SWAP and controlled-NOT (CNOT) gates with atomic qubits.