Jaynes–Cummings model: Solutions without rotating-wave approximation

The Jaynes–Cummings model in the general nonresonant case without rotating-wave approximation is considered. The analysis is carried out using the resolvent formalism. It is shown that one, given the matrix of Hamiltonian resolvent, can easily find all basic physical quantities corresponding to the given model. The matrix of the resolvent of the total Hamiltonian for the given model is found. Matrix elements of the resolvent are expressed in terms of continued fractions. It is shown that these fractions uniformly converge to meromorphic functions, which corresponds to a purely point spectrum of the total Hamiltonian. The time evolution in the case of exact resonance for different coupling constants is numerically studied. It is shown that the rotating- wave approximation is not satisfactory for large coupling constants even in the case of exact resonance. In this case, probabilities of multiphoton transitions increase with increasing coupling constant.     

Gravitational Jaynes–Cummings model beyond the rotating wave approximation

In this paper, the quantum properties of a two-level atom and the cavity-field in the Jaynes?CCummings model with the gravity beyond the rotating wave approximation are investigated. For this purpose, by solving the Schr?dinger equation in the interaction picture, the evolving state of the system is found by which the influence of the counter-rotating terms on the dynamical behaviour of atomic population inversion and the probability distribution of the cavity-field as quantum properties is explored. The results in the atom?Cfield system beyond the rotating wave approximation with the gravity show that the quantum properties are not completely suppressed under certain conditions.     

Atom–field entanglement in the Jaynes Cummings model without rotating wave approximation

In this paper, we present a structure for obtaining the exact eigenfunctions and eigenvalues of the Jaynes–Cummings model(JCM) without the rotating wave approximation(RWA). We study the evolution of the system in the strong coupling region using the time evolution operator without RWA. The entanglement of the system without RWA is investigated using the Von Neumann entropy as an entanglement measure. It is interesting that in the weak coupling regime, the population of the atomic levels and Von Neumann entropy without RWA model shows a good agreement with the RWA whereas in strong coupling domain, the results of these two models are quite different.     

Grassmann phase space theory and the Jaynes–Cummings model

The Jaynes-Cummings model of a two-level atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally, involving the interaction of two simple quantum systems—one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing oscillations of the atomic population difference at the Rabi frequency when the atom is excited and the cavity is in an n$n$-photon Fock state, to collapses and revivals of these oscillations starting with the atom unexcited and the cavity mode in a coherent state. The observation of revivals for Rydberg atoms in a high-Q microwave cavity is key experimental evidence for quantisation of the EM field. Theoretical treatments of the Jaynes-Cummings model based on expanding the state vector in terms of products of atomic and n$n$-photon states and deriving coupled equations for the amplitudes are a well-known and simple method for determining the effects.     

Linear entropy dynamics of the field in the Jaynes－Cummings model with an intensity-dependent coupling in the dispersive approximation

We present the linear entropy dynamics of the field state in the dispersive cavity in the Jaynes－Cummings model with an intensity-dependent coupling in the dispersive approximation, and investigate the influence of dissipation on entanglement between the field and the atoms. We show that the coherence properties of the field are also affected by the cavity when the nonlinear process of the field interacting with the atoms with an intensity-dependent coupling is involved, and find that the dissipation constant, the intensity of the field and the atomic distribution angle have different influence on the coherence properties of the field.     

Atomic emission and cavity field spectra of the Jaynes－Cummings model

Atomic emission and cavity field spectra of the Jaynes－Cummings model are analytically compared. We show that the two spectra are in general different, except for the special case where the interaction is resonant, the cavity is initially empty and the retarded time of one-photon emission is considered in calculations of the spectra. In this case, the two spectra are the same. We also show that this result comes from the fact that the two-time autocorrelation function of the cavity field is not directly proportional to that of the atom.     

Entanglement Degree in the Time Development of the Jaynes–Cummings Model

Recently, it has been become known that a quantum entangled state plays an important role in fields of quantum information theory, such as quantum teleportation and quantum computation. Research on quantifying entangled states has been carried out using several measures. In this Letter, we will adopt this method using quantum mutual entropy to measure the degree of entanglement in the time development of the Jaynes–Cummings model.     

Geometry in the Entanglement Dynamics of the Double Jaynes–Cummings Model

We report on the geometric character of the entanglement dynamics of two pairs of qubits evolving according to the double Jaynes–Cummings model. We show that the entanglement dynamics for the initial states | ψ ₀〉 = cos α | 10〉 + sin α | 01〉 and | ? ₀〉 = cos α | 11〉 + sin α | 00〉 cover three-dimensional surfaces in the diagram C _ij × C _ik × C _il , where C _mn stands for the concurrence between qubits m and n, varying 0 ≤ α ≤ π / 2. In the first case, projections of the surfaces on a diagram C _ij × C _kl are conics. In the second case, curves can be more complex. We relate those conics with a measurable quantity, the predictability. We also derive inequalities limiting the sum of the squares of the concurrence of every bipartition and show that sudden death of entanglement is intimately connected to the size of the average radius of a hypersphere.     

Nonlinear Jaynes–Cummings Model of Atom–Field Interaction

Interaction of a two-level atom with a single mode of electromagnetic field including Kerr nonlinearity for the field and intensity-dependent atom-field coupling is discussed. The Hamiltonian for the atom-field system is written in terms of the generatorsof a closed algebra, which has SU(1,1) and Heisenberg–Weyl algebras as limitingcases. Eigenstates and eigenvalues of the Hamiltonian are constructed. With the field being in a coherent state initially, the dynamical behavior of atomic inversion, field statistics, and uncertainties in the field quadratures are studied. Appearance of nonclassical features during the evolution of the field is shown. Further, we explore the overlap of initial and time-evolved field states.     

Energy spectrum of the Hamiltonian of the Jaynes-Cummings model without rotating-wave approximation

The energy spectrum of the Hamiltonian of the Jaynes-Cummings model without a rotating-wave approximation is studied. The trajectories of eigenvalues as functions of the dimensionless coupling constant are constructed. It is shown that the spectrum approaches the equidistant spectrum, i.e., the oscillator spectrum, as the coupling constant increases. As a result, each energy level becomes doubly degenerate.     

非旋波近似下频率变化的场与原子的相互作用

研究了非旋波近似下频率随时间变化的相干态光场与二能级原子的相互作用，主要讨论了光场频率随时间作正弦和方波变化两种典型情况下，原子布居数反转随时间的演化特性. 当光场频率随时间作正弦变化时，原子布居数反转的崩塌-回复过程和由虚光子过程引起的快速振荡均会受到影响. 当光场频率随时间以方波形式变化时，脉冲调制不仅在原子布居数反转随时间演化过程中诱导出新的崩塌-回复过程，而且可以引起虚光子快速振荡的突变. 关键词： Jaynes-Cummings模型 非旋波近似 原子布居数反转     

Analytical approach to dynamics of transformed rotating-wave approximation with dephasing

We study the dynamics of the Jaynes-Cummings model within transformed rotating-wave approximation （TRWA）. We analyze this model coupled to a dephasing reservoir, through the Lindblad formalism in the master equation. Then, we examine the expectation value of the number operator. Finally, we investigate the validity of this model under dephasing using the Mandel parameter and the total number of quanta.     

Geometric phases in qubit-oscillator system beyond conventional rotating-wave approximation

In this work we investigated the geometric phases of a qubit-oscillator system beyond the conventional rotating- wave approximation. We find that in the limiting of weak coupling the results coincide with that obtained under rotating-wave approximation while there exists an increasing difference with the increase of coupling constant. It was shown that the geometric phase is symmetric with respect to the sign of the detuning of the quantized field from the one-photon resonance under the conventional rotating-wave approximation while a red-blue detuning asymmetry occurs beyond the conventional rotating-wave approximation.     

Entanglement evolution of a two-qubit system with decay beyond the rotating-wave approximation

The entanglement property of two identical atoms, initially entangled in Bell states, coupled to a single-mode cavity is considered. Based on the reduced non-perturbative quantum master equation method, the entanglement evolution of the two atoms with decay is investigated beyond the conventional rotating-wave approximation. We show that the counter-rotating wave terms, usually neglected, have a great influence on the disentanglement behaviour of the system. The phenomena of entanglement sudden death and entanglement sudden birth will occur. In addition, we show that the entanglement can be strengthened by introducing the dipole--dipole interaction of the two atoms.     

JC模型体系的几何相

利用AA相理论,给出了Jaynes-cummings模型系统在初始状态为固定光子数下的几何相.     

Dipole squeezing in the multi-photon Jaynes-Cummings model with and without the rotating-wave approximation

By virtue of the numerical method of Graham and Höhnerbach [12], we have investigated the quantum fluctuations of the atomic dipole variables in the multiphoton Jaynes-Cummings model with and without the rotating wave approximation (RWA) when it is restricted to the following initial condition: the atom in its superposition state and the field in the vacuum state. We found that even under the conditions in which the RWA is considered to be valid there are significant effects of virtual-photon field on dipole squeezing predicted in the RWA, and dipole squeezing turns to disappear for sufficiently strong coupling.     

Dipole squeezing in the multi-photon Jaynes-Cummings model with and without the rotating-wave approximation

By virtue of the numerical method of Graham and Höhnerbach [12], we have investigated the quantum fluctuations of the atomic dipole variables in the multiphoton Jaynes-Cummings model with and without the rotating wave approximation (RWA) when it is restricted to the following initial condition: the atom in its superposition state and the field in the vacuum state. We found that even under the conditions in which the RWA is considered to be valid there are significant effects of virtual-photon field on dipole squeezing predicted in the RWA, and dipole squeezing turns to disappear for sufficiently strong coupling.     

k光子Jaynes-Cummings模型光场的熵压缩

研究了k光子Jaynes-Cummings模型光场的熵压缩,讨论了光子数k和原子的初始状态对光场熵压缩的影响.结果表明,随光子数k的增大,光场的位置熵压缩愈趋明显,动量熵压缩量减小;当k≥3时,位置熵始终是被压缩的.原子的初态对光场的熵压缩也有一定的影响. 关键词： Jaynes-Cummings模型 熵压缩