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

arXiv:1903.05670

Purification Hamiltonians

Jorge Andres Anaya-Contreras, Arturo Zúñiga-Segundo, H. M. Moya-Cessa

Published Mar 13, 2019• 0 citations
arXivHTMLPDF

Abstract

We study the Jaynes-Cummings interaction when initial mixed states, for the atom or the field, are considered. The evolved mixed field density matrix is purified to a wavefunction that describes the interaction between a quantised field and an artificial four-level atom. This allows us to use the Araki-Lieb inequality to calculate the field entropy from the atomic entropy. We then generate {\it artificial} Hamiltonians that reproduce the field entropy dynamics. We finally show that more realistic Hamiltonians may be considered by using two entangled two-level atoms.

DOI
10.48550/arxiv.1903.05670

Related papers

Purification of the atom-field interaction Hamiltonian

Jorge Andres Anaya-Contreras, Arturo Zúñiga-Segundo, H. M. Moya-Cessa

We study the Jaynes-Cummings model with initial mixed states, for the atom or the field, are considered. The evolved mixed field density matrix is purified to a wavefunction that describes the interaction between a quantised field and an artificial four-level atom. This allows us to use the Araki-Lieb inequality to calculate the field entropy from the atomic entropy. We then suggest Hamiltonians that reproduce the field entropy dynamics. We finally show that more realistic Hamiltonians may be considered by using two entangled two-level atoms.

Physics Open•Nov 5, 2019•2 citations

The von Neumann Entropy for Mixed States

Jorge Andres Anaya-Contreras, Héctor M. Moya-Cessa, Arturo Zúñiga-Segundo

The Araki-Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki-Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction.

arXiv:1804.09698•Entropy•Jan 10, 2019•15 citations

Statistical Mixture of Kaleidoscope States Interacting with a Two-Level Atom: Entropy and Purification

Jorge Andres Anaya-Contreras, Arturo Zúñiga-Segundo, H. M. Moya-Cessa

We investigate some of the fundamental features of the interaction of a mixture of coherent states, namely, a Kaleidoscope states mixture, with two-level atoms in the Jaynes–Cummings model framework. We begin our analysis by calculating the von Neumann entropy of the field, which is determined with the help of the virtual atom method. The oscillations appearing in the entropy indicate a state of purity greater than the initial state, i.e., a purification of the initial state due to a transfer of coherence from the atom to the field. In this oscillatory region, we obtain a negative Wigner function that hints at a (noisy) multiple Schrödinger cat.

Photonics•Jan 31, 2023•1 citation

The Damped-vacuum-field Jaynes-Cummings Model

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

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.

Journal of Modern Optics•Feb 1, 1995•2 citations

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

Atoms and Photons - Their Interaction Dynamics

Max F. Frenzel

The Jaynes-Cummings model (JCM) describes the interaction of a two-level atom with a single quantised field mode in an optical cavity. In this BSc project we derive the basic Rabi model Hamiltonian and show how it leads to the JCM Hamiltonian. The results are then used to analyse the general time evolution of a bipartite atom-field system and its properties, such as entanglement. We extend a scheme developed by Browne and Plenio [D. Browne and M. B. Plenio, Physical Review A, vol. 67, no. 1, Jan. 2003.] to entangle two cavities that interact with an atom. Our scheme allows to produce states that are arbitrarily close to a Bell state with a success probability greater than 0.75, whereas the success rate of the original method tends to 0 for perfect fidelity. Further, we extend both schemes by allowing the atom or the cavity to be in a thermal state and find that the fidelity of the produced states is reduced with increasing temperature. Finally, we apply our scheme to quantum teleportation, where we find that the fidelity of the teleported state compared to the original state also decreases as the temperature is increased.

arXiv:1212.4339•Dec 18, 2012•0 citations
We study the Jaynes-Cummings interaction when initial mixed states, for the atom or the field, are considered. The evolved mixed field density matrix is purified to a wavefunction that describes the interaction between a quantised field and an artificial four-level atom. This allows us to use the Araki-Lieb inequality to calculate the field entropy from the atomic entropy. We then generate {\it artificial} Hamiltonians that reproduce the field entropy dynamics. We finally show that more realistic Hamiltonians may be considered by using two entangled two-level atoms.
We study the Jaynes-Cummings model with initial mixed states, for the atom or the field, are considered. The evolved mixed field density matrix is purified to a wavefunction that describes the interaction between a quantised field and an artificial four-level atom. This allows us to use the Araki-Lieb inequality to calculate the field entropy from the atomic entropy. We then suggest Hamiltonians that reproduce the field entropy dynamics. We finally show that more realistic Hamiltonians may be considered by using two entangled two-level atoms.
The Araki-Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states, as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to calculate the entropy of a large subsystem by finding the entropy of the small one. To the best of our knowledge, there does not exist a way of calculating the entropy when one of the subsystems is initially in a mixed state. For the case of a two-level atom interacting with a quantized field, we show that it is possible to use the Araki-Lieb inequality and find the von Neumann entropy for the large (infinite) system. We show this in the two-level atom-field interaction.
We investigate some of the fundamental features of the interaction of a mixture of coherent states, namely, a Kaleidoscope states mixture, with two-level atoms in the Jaynes–Cummings model framework. We begin our analysis by calculating the von Neumann entropy of the field, which is determined with the help of the virtual atom method. The oscillations appearing in the entropy indicate a state of purity greater than the initial state, i.e., a purification of the initial state due to a transfer of coherence from the atom to the field. In this oscillatory region, we obtain a negative Wigner function that hints at a (noisy) multiple Schrödinger cat.
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.
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.
The Jaynes-Cummings model (JCM) describes the interaction of a two-level atom with a single quantised field mode in an optical cavity. In this BSc project we derive the basic Rabi model Hamiltonian and show how it leads to the JCM Hamiltonian. The results are then used to analyse the general time evolution of a bipartite atom-field system and its properties, such as entanglement. We extend a scheme developed by Browne and Plenio [D. Browne and M. B. Plenio, Physical Review A, vol. 67, no. 1, Jan. 2003.] to entangle two cavities that interact with an atom. Our scheme allows to produce states that are arbitrarily close to a Bell state with a success probability greater than 0.75, whereas the success rate of the original method tends to 0 for perfect fidelity. Further, we extend both schemes by allowing the atom or the cavity to be in a thermal state and find that the fidelity of the produced states is reduced with increasing temperature. Finally, we apply our scheme to quantum teleportation, where we find that the fidelity of the teleported state compared to the original state also decreases as the temperature is increased.