Unification of the Jaynes–Cummings model and Planck’s radiation law

Abstract

Articles you may be interested inIntegrability and superintegrability of the generalized n -level many-mode Jaynes-Cummings and Dicke models Decoherence and quantum-classical master equation dynamics A Lorentzian function based spectral filter for calculating the energy of excited bound states in quantum mechanics By combining iterative methods with Laplace transformation, we construct the solution of a dissipative Jaynes-Cummings model. The dissipative part of the model is based on the standard Markovian master equation for a harmonic oscillator that is coupled to a heat bath of nonzero temperature. Besides photon loss, we also take into account frequency detuning between atom and field. Before commencing the iteration, we subject the matrix elements of the density operator to a transformation that depends on temperature. As a result, the pole structure of all Laplace transformed matrix elements is improved. It becomes manifest which poles do not contribute to the asymptotic behavior of the density operator. In proving that our iterative process yields convergent results, we assume upper bounds on: the matrix elements of the density operator, the matrix elements of the initial density operator, the damping parameter of the heat bath, and the temperature of the heat bath. All of these bounds are physically acceptable. The photon field may start from a coherent state or a number state. For experiments in a microwave cavity, temperatures of the order of 0.1 ͓K͔ are allowed. As an application, the evolution of the atomic density matrix is studied. We propose a limit for which this matrix converges to the state of maximum von Neumann entropy. The time, the cubed initial energy density, and the inverse of the damping parameter must tend to infinity equally fast. The photon field is assumed to be in a number state at time zero, whereas the initial state of the atom can be chosen freely.

Davies theory for reservoir-induced entanglement in a bipartite system

“…Even though this seems to be somewhat counterintuitive it could be shown that the interaction of a large reservoir in an arbitrary mixed initial state with a single qubit in a pure initial state can dynamically induce a nontrivial correlation [16,17]. More than that, the time-dependent appearance of entanglement has been evident from exact solutions of simple and also more complicated versions of the Jaynes-Cummings model in quantum optics [18][19][20][21]. By coupling a bipartite system (two qubits) to a heat bath of harmonic oscillators the non-Markovian dynamics starting from a separable initial state may also induce some entanglement on shorter or, exceptionally, even longer time scales [22].…”

“…Figure 1. Degree of entanglement E W (t) according to(20), in a first interval and for different initial states according to(19). The model parameters have been set to ε = = w = 2, u = 4, α = 0.01, ω c = 30, T = 0.…”

Entanglement and Fisher Information for Atoms–Field System in the Presence of Negative Binomial States

“…The entanglement nature of the atom–photon state in the JCM was investigated in [ 5 ]. The dynamics of the atomic density operator of a dissipative JCM was examined in [ 6 ]. In that paper, the authors also provided the limit for obtaining the state with maximum value of von Neumann entropy.…”

Population inversion and entanglement in single and double glassy Jaynes-Cummings models

“…See also [10]. Evolution of the atomic density matrix of a dissipative JC model was studied in [11]. They also proposed a limit for which the matrix converges to a state of maximum von Neumann entropy.…”