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arXiv:1003.3290 · Nanotechnology

Complex dynamics of photon entanglement in the two-mode Jaynes–Cummings model

Mikhail Erementchouk, Michael Niklaus Leuenberger

Published Jun 22, 2010• 3 citations
arXivHTMLPDF

Abstract

We study the dynamics of the N-photon entanglement, E(N)(t), for the two-mode Jaynes-Cummings model in the case of a small number N of photons coupled to a single quantum dot inside a cavity, such as a microdisk cavity or a photonic crystal cavity. The quantum dot transitions associated with the photons with different polarizations are assumed to be independent of each other and, hence, the time evolutions of the ' + '- and ' - '-polarized photons are formally separable. However, due to the indistinguishability of the photons, such an interaction still leads to the entanglement of initially disentangled photon states, owing to the nonlinear dependence of the characteristic frequencies on the photon population numbers. The time dependence of the entanglement is the result of superimposing oscillations with incommensurate frequencies. Therefore, E(N)(t) is a quasi-periodic function of time with a complex profile strongly dependent on the number of photons.

DOI
10.1088/0957-4484/21/27/274019

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A quantum dot interacting with two resonant cavity modes is described by a two-mode Jaynes-Cummings model. Depending on the quantum dot energy level scheme, the interaction of a singly doped quantum dot with a cavity photon generates entanglement of electron spin and cavity states or allows one to implement a SWAP gate for spin and photon states. An undoped quantum dot in the same structure generates pairs of polarization entangled photons from an initial photon product state. For realistic cavity loss rates, the fidelity of these operations is of order 80%.
We study the entanglement dynamics in the system of coupled quantum fields. We prove that if the coupling is linear, that is if the total Hamiltonian is a quadratic form of field operators, entanglement can only be transferred between the fields. We show that entanglement is produced in the model of the two-mode self-interacting boson field with the characteristic Gaussian decay of coherence in the limit of high number of particles. The interesting feature of this system is that the particles in different modes become entangled even if there is no direct interaction between the modes. We apply these results for analysis of the entanglement dynamics in the two-mode Jaynes-Cummings model in the limit of large number of photons. While the photon-atom interaction is assumed to conserve helicity the photons with different polarizations still get entangled due to an effective interaction mediated by the atom with the characteristic entanglement time linearly increasing with the number of photons.
The evolution of entanglement of a bipartite spin-1/2 system coupled to a micromaser cavity field in an intensity-dependent Jaynes–Cummings model is studied in this paper. The dynamical process of the entanglement is investigated for different cavity fields. We find that the interactions lead to a phenomenon of periodic entanglement and disentanglement between the qubits. Effects such as the growth of the magnitude of atomic entanglement with the increase of the cavity photon number, arising out of the intensity-dependent atom-cavity coupling lead to interesting dissimilarities from the case of entanglement generated by the standard Jaynes–Cummings interaction.
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.
In this work we investigate the thermal entanglement between two-level atoms and photons in a nonlinear cavity. We consider intensity-dependent couplings and calculate the negativity, as a measure of atom-photonentanglement. The cavity is assumed to be at a temperature T, so that all number of photons, and at the same time, both atomic states, with definite probabilities, are present. We then demonstrate a condition under which the intensity-dependent coupling leads to entanglement. It is also shown that, as in the case of linear Jaynes- Cummings model, the thermal states of atoms and photons are never separable.
In this paper a two-photon Jaynes-Cummings model interacting with a Kerr-like medium is studied. It is assumed that the electromagnetic field is in different states such as coherent, squeezed vacuum and pair coherent, and that the atom is initially in the excited state. The temporal evolution of the population of the excited level, and the second-order coherence function are studied. The results obtained show that this system has some similarities with the two-mode Stark system. Two photon entanglement are analysed at different initial conditions.