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arXiv:1212.4339

Atoms and Photons - Their Interaction Dynamics

Max F. Frenzel

Published Dec 18, 2012• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.1212.4339

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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.
A two-level system driven by a classical single frequency field in rotating-wave approximation is a basic model for resonance in quantum optics. The probability of making a transition depends sinusoidally on time with a characteristic frequency called the Rabi frequency. The Jaynes-Cummings model (JCM) consists of a two-level atomic system driven by a single quantized electromagnetic field mode. The field entropy in the case of an atom interacting with an initially coherent field is expected to reflect the collapse and revival of Rabi oscillations. The photon statistics of the JCM are examined and the entropy concepts are used to describe the apparently disordered collapses. A density matrix method is used to describe the influence of photon statistics in the JCM. The quantum generalization defines entropy through where the trace is taken over a convenient basis set. The thermal field JCM shows enhanced photon variances as expected for an initially Bose-Einstein field with large fluctuations.
In this work we have studied the two photon Jaynes-Cummings model to describe the interaction of a three-level atom in the configuration with a single-mode of a cativy-field. We have used the effetive and full microscopic Jamiltonian approach to compare the results obtained in these tow descriptions. We employed the two-photon Jaynes-Cummings model int the full microscopic Hamiltonian context to implement schemes to quantuam entanglement swapping, for approximate and conditional quantuam teleportation for an unknown atomic state, for a superposition of zero- and two photon states. Both schemes were implemented using no measurement in the Bell base states.
Summary form only given. We study the behavior of classical and quantum correlations between a two level atom and a quantised electromagnetic field mode in a thermal state interacting according to the Jaynes Cummings model (JCM). This model predicts collapses and revivals of Rabi oscillations which is also seen in experiments, providing direct evidence for the quantum mechanical nature of the electromagnetic field. It also has an analytical solution for arbitrary coupling constants and can easily be extended to include a variety of initial conditions,dissipation and damping, multiple atoms, multilevel atoms, multimode fields and more elaborated interactions such as multiphoton or intensity-dependent interaction.
The Jaynes-Cummings model (JCM) of a two-level atom interacting with a quantized radiation field has been investigated theoretically. Of particular interest is the transition of a quantized electromagnetic field of the model to a classical one in the limit of very large average photon number. In this thesis, two aspects of the JCM are examined. Firstly, it is shown that, in contrast to the general case, for specic initial atom-field states, there is exact correspondence between the atomic inversion predicted by the JCM and that predicted by the semiclassical model in which the field is treated classically from the outset. Secondly, the degree of quantum entanglement of the JCM is investigated quantitatively and it is shown that, at any nite absolute temperature greater than zero, the atom and field are never separable and the degree of quantum entanglement approaches zero in the high and low temperature limits
In this paper, we study the evolution of two two-level atoms interacting with a single-mode quantized radiation field, namely, the two-atom multiphoton Jaynes–Cummings model (JCM). We assume that the field and the atoms are initially prepared in the superposition of displaced number states and excited atomic states, respectively. For this system, we investigate the atomic inversion, Wigner function, phase distribution and entanglement. We show that for symmetric (asymmetric) atoms, the system can generate asymmetric (symmetric) cat states at a quarter of the revival time. Furthermore, the degrees of entanglement for the field–atoms and the one-atom–remainder tangles depend on the rate of energy flow between the parties. The interference in phase space decreases the degree of entanglement in the bipartite.
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.