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

Optics and Spectroscopy

Squeezed states of the Jaynes-Cummings model and their excitation in parametric processes

É. M. Verlan, Margarita A. Razumova

Published Oct 1, 2002• 0 citations
Publisher

Abstract

Squeezed states of the Jaynes-Cummings (JC) model are constructed and the statistical properties of the field oscillator in these states are studied. The presence of interaction between the field oscillator and the atom results in the appearance of slow temporal variations in the average values of the dynamic quantities. Two cases essentially differ: When only one of two modes of the JC model is excited, the variations in time, in particular, of the average value of the coordinate are governed by the mode anharmonicity. In the case when both modes of the JC model with close frequencies are excited, the temporal variations represent collapse and revival of oscillations with the frequency $$2k\sqrt {n + 1} $$ , where k is the constant of the atom-field oscillator interaction and n is the number of photons. The constructed squeezed vacuum states are not two-photon states, because the probability of finding an odd number of photons is not equal to zero and varies with time.

DOI
10.1134/1.1517082

Related papers

Anti-Jaynes-Cummings interaction of a two-level atom with squeezed light: A comparison with the Jaynes-Cummings interaction

Christopher Mayero, Joseph Akeyo Omolo

We considered the anti-Jaynes-Cummings (AJC) interaction of a two-level atom in an initial ground state interacting with a field mode in an initial squeezed coherent state at arbitrary values of squeeze parameter r and provided the Jaynes-Cummings (JC) interaction as a comparison. We analysed the degree of entanglement (DEM) measured by the von Neumann entropy and the nature of the field quantified by the Mandel Q parameter in relation to the atomic population inversion during the AJC interaction and separately the corresponding JC interaction. We noted in our examples that at r>1.4, photon statistics evolved to super-Poissonian from sub-Poissonian during the respective AJC, JC interactions. Further, for high values of r, the form of the time evolution of atomic population inversion depicted enhanced ringing revivals at the collapse region in comparison to the case of an initial coherent state. What is more, at higher values of r the time evolution of DEM showed more rapid oscillations and recorded higher values, concurrently, an increase in the degree of mixedness.

arXiv:2211.13149•Nov 23, 2022•0 citations

Features of collapses and revivals in a two-photon Jaynes–Cummings model with a squeezed field

Lin-sheng He

With the help of a two-photon Jaynes-Cummings model, which is an exactly solvable model, we have dealt analytically with the dynamical behavior of the atom and the field for a two-photon process in squeezed and coherent fields under the appropriate approximation. The features of collapses and revivals of Rabi oscillations for the atom and the field in a two-photon process represent strict periodicity. The phase jump and the large and negative frequency for the combination Rabi oscillation are exhibited in the case of a squeezed field. The results show that squeezing in a field strikingly affects the evolution behavior of the atom and the field.

Journal of the Optical Society of America B•Oct 1, 1989•18 citations

Effect of Squeezing on the Atomic and the Entanglement Dynamics in the Jaynes-Cummings Model

T. Subeesh, Vivishek Sudhir, A.B.M.a d Ahmed +1 more

The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of the radiation field is investigated, as the state of the field is gradually changed from a coherent state to a squeezed coherent state. The effect of mild squeezing on the coherent light is shown to be striking: the photon number distribution gets localized and it peaks maximally for a particular value of squeezing. The atomic inversion retains its structure for a longer time. The mean linear entropy shows that the atom has a tendency to get disentangled from field within the collapse region and also in the revival region, for mild squeezing. These properties are absent for the case of a coherent state or for an excessively squeezed coherent state. We also elucidate a connection between these properties and the photon statistics of the mildly squeezed coherent state; these states have the minimum variance and are also maximally sub-Poissonian.

arXiv:1203.4792•Mar 21, 2012•1 citation

Generalized Jaynes-Cummings models with a time-dependent atom-field coupling

Amitabh Joshi, S. V. Lawande

An extension of the standard one-photon as well as the two-photon Jaynes-Cummings (JC) model has been done to include transient effects due to a modulation of the atom-field coupling coefficient. An explicit time dependence is given for the case of a linear sweep of the coupling parameter. We have shown the effects of such a sweep on the dynamical evolution of a two-level atom undergoing a one- or two-photon process in a single nondecaying mode of the field in a coherent state. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated and are found to be both qualitatively as well as quantitatively different from the standard JC models.

Physical Review A•Sep 1, 1993•73 citations

Correlated coherent states in the Jaynes-Cummings model: I

É. M. Verlan, Margarita A. Razumova

In the representation of dressed states, which diagonalizes the Hamiltonian in the Jaynes-Cummings model, the Bose operator for excitation annihilation Â, the spin operator $$\hat \Sigma \_$$ , and the corresponding Hermitian-conjugate operators are found. Using these operators, correlated coherent states were constructed and statistical properties of a field mode and an atom in these states are studied. Nonclassical field properties, such as the deviation of the probability distribution for the number of photons from the Poissonian distribution, its time dependence, and the squeezing of quadrature field components are found. For small interaction coefficients k, all these characteristics of the model vary weakly in time in the resonance case.

Optics and Spectroscopy•Jun 1, 2001•1 citation

Analysis of a multiphoton Jaynes-Cummings model with squeezed inputs

Tariq Maqbool, M. S. K. Razmi

An m-photon Jaynes-Cummings model is analyzed assuming the field to be initially in the squeezed vacuum state or in a more general squeezed state. Collapses and revivals of the Rabi oscillations in the atomic population inversion appear for a general squeezed input, but not for a squeezed vacuum input. The second-order coherence function is found to exhibit collapses and revivals for large initial average photon numbers. With a low-intensity input field and large m, one can achieve nearly steady-state squeezing.

Physical Review A•Nov 1, 1991•14 citations
Squeezed states of the Jaynes-Cummings (JC) model are constructed and the statistical properties of the field oscillator in these states are studied. The presence of interaction between the field oscillator and the atom results in the appearance of slow temporal variations in the average values of the dynamic quantities. Two cases essentially differ: When only one of two modes of the JC model is excited, the variations in time, in particular, of the average value of the coordinate are governed by the mode anharmonicity. In the case when both modes of the JC model with close frequencies are excited, the temporal variations represent collapse and revival of oscillations with the frequency 2kn+12k\sqrt {n + 1} 2kn+1​ , where k is the constant of the atom-field oscillator interaction and n is the number of photons. The constructed squeezed vacuum states are not two-photon states, because the probability of finding an odd number of photons is not equal to zero and varies with time.
We considered the anti-Jaynes-Cummings (AJC) interaction of a two-level atom in an initial ground state interacting with a field mode in an initial squeezed coherent state at arbitrary values of squeeze parameter r and provided the Jaynes-Cummings (JC) interaction as a comparison. We analysed the degree of entanglement (DEM) measured by the von Neumann entropy and the nature of the field quantified by the Mandel Q parameter in relation to the atomic population inversion during the AJC interaction and separately the corresponding JC interaction. We noted in our examples that at r>1.4, photon statistics evolved to super-Poissonian from sub-Poissonian during the respective AJC, JC interactions. Further, for high values of r, the form of the time evolution of atomic population inversion depicted enhanced ringing revivals at the collapse region in comparison to the case of an initial coherent state. What is more, at higher values of r the time evolution of DEM showed more rapid oscillations and recorded higher values, concurrently, an increase in the degree of mixedness.
With the help of a two-photon Jaynes-Cummings model, which is an exactly solvable model, we have dealt analytically with the dynamical behavior of the atom and the field for a two-photon process in squeezed and coherent fields under the appropriate approximation. The features of collapses and revivals of Rabi oscillations for the atom and the field in a two-photon process represent strict periodicity. The phase jump and the large and negative frequency for the combination Rabi oscillation are exhibited in the case of a squeezed field. The results show that squeezing in a field strikingly affects the evolution behavior of the atom and the field.
The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of the radiation field is investigated, as the state of the field is gradually changed from a coherent state to a squeezed coherent state. The effect of mild squeezing on the coherent light is shown to be striking: the photon number distribution gets localized and it peaks maximally for a particular value of squeezing. The atomic inversion retains its structure for a longer time. The mean linear entropy shows that the atom has a tendency to get disentangled from field within the collapse region and also in the revival region, for mild squeezing. These properties are absent for the case of a coherent state or for an excessively squeezed coherent state. We also elucidate a connection between these properties and the photon statistics of the mildly squeezed coherent state; these states have the minimum variance and are also maximally sub-Poissonian.
An extension of the standard one-photon as well as the two-photon Jaynes-Cummings (JC) model has been done to include transient effects due to a modulation of the atom-field coupling coefficient. An explicit time dependence is given for the case of a linear sweep of the coupling parameter. We have shown the effects of such a sweep on the dynamical evolution of a two-level atom undergoing a one- or two-photon process in a single nondecaying mode of the field in a coherent state. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated and are found to be both qualitatively as well as quantitatively different from the standard JC models.
In the representation of dressed states, which diagonalizes the Hamiltonian in the Jaynes-Cummings model, the Bose operator for excitation annihilation Â, the spin operator Σ^_\hat \Sigma \_Σ^_ , and the corresponding Hermitian-conjugate operators are found. Using these operators, correlated coherent states were constructed and statistical properties of a field mode and an atom in these states are studied. Nonclassical field properties, such as the deviation of the probability distribution for the number of photons from the Poissonian distribution, its time dependence, and the squeezing of quadrature field components are found. For small interaction coefficients k, all these characteristics of the model vary weakly in time in the resonance case.
An m-photon Jaynes-Cummings model is analyzed assuming the field to be initially in the squeezed vacuum state or in a more general squeezed state. Collapses and revivals of the Rabi oscillations in the atomic population inversion appear for a general squeezed input, but not for a squeezed vacuum input. The second-order coherence function is found to exhibit collapses and revivals for large initial average photon numbers. With a low-intensity input field and large m, one can achieve nearly steady-state squeezing.