Bimodal Cavity Field Research Articles

Mutual cooperative effects between the mode components of two-photon and Raman induced cavity lasing processes

The paper proposes to unify the two-photon laser and induced cooperative scattering Raman lasing in which the flying ensemble of two-level excited radiators are coupled with the bimodal cavity field in nonlinear two-photon and scattering interactions. It discusses the situation in which the induced two-quantum lasing takes place together with the cooperative scattering conversion of photons between the pump, Stokes, and anti-Stokes cavity modes. The proposed master equation describes cooperative energy exchanges between Raman and two-photon lasing processes by portions of energies multiple to the energy of the entangled photon pair.The generators of such emission and absorption processes belonging to the symmetries of Raman conversion and two-photon cooperative generation are unified. The first symmetry belongs to su(2) algebra connected to the scattering conversion in the Stokes, pump, and anti-Stokes modes of cavity (Opt. Commun.,285(5) (2012) 686–692). The second one belongs to multi-mode su(1,1) symmetry which quantifies the cooperative process belonging to two-photon emission in cavity/fiber mode components of field (see Opt. Commun. 247(4–6) (2005) 381–392). The bimodal collective photon operators are introduced describing the emission or absorption acts of the fixed portion of energy from the cavity equal to the transition energy between the states of each excited atom. A key impact of the study focuses on the statistical properties of the bimodal field and their detection possibilities are proposed for the description of the time evolution of quantum correlations between the field components of Raman conversion and two-photon emission.

Quantum reversibility in cooperative interaction of the atom system with bi-modal cavity field in Raman conversion

The restoration of the initial state in the Raman interaction of the two atoms with the quantified pump and Stokes (anti-Stokes) cavity modes is analytically obtained. For this the su (2) symmetry representation of the bimodal field and a system of two atoms in scattering interaction is proposed for the simplification of the problem. Using the proprieties of the generators su (2) algebra the exact non-stationary solution of the system of two atoms in interaction with the bimodal field is found, taking into consideration the initial disentangled state between the atomic and field superposition. It is demonstrated that after this collapse and revivals of the inversion of flying atoms in the processes of absorption and emission of the photons from Stokes and pump modes the system atoms and field becomes entangled. The conditions of the restoration of the initial state of the atom-field system were established as a function of the flying time through the resonator possible. A set of discrete flying time intervals for the restoration of the initial disentangled state was found.

Variance squeezing and information entropy squeezing via Bloch coherent states in two-level nonlinear spin models

The nonclassical squeezing effect emerging from a nonlinear coupling model (generalized Jaynes–Cummings model) of a two-level atom interacting resonantly with a bimodal cavity field via two-photon transitions is investigated in the rotating wave approximation. Various Bloch coherent initial states (rotated states) for the atomic system are assumed, i.e., (i) ground state, (ii) excited state, and (iii) linear superposition of both states. Initially, the atomic system and the field are in a disentangled state, where the field modes are in Glauber coherent states via Poisson distribution. The model is numerically tested against simulations of time evolution of the based Heisenberg uncertainty relation variance and Shannon information entropy squeezing factors. The quantum state purity is computed for the three possible initial states and used as a criterion to get information about the entanglement of the components of the system. Analytical expression of the total density operator matrix elements at t>0 shows, in fact, the present nonlinear model to be strongly entangled, where each of the definite initial Bloch coherent states is reduced to statistical mixtures. Thus, the present model does not preserve the modulus of the Bloch vector.

Tripartite entanglement dynamics and entropic squeezing of a three-level atom interacting with a bimodal cavity field

In this paper, we study the interaction between a Λ-type three-level atom and two quantized electromagnetic fields which are simultaneously injected in a bichromatic cavity surrounded by a Kerr medium in the presence of field–field interaction (parametric down conversion) and detuning parameters. By applying a canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes–Cummings model. Under particular initial conditions which may be prepared for the atom and the field, the time evolution of the state vector of the entire system is analytically evaluated. Then, the dynamics of the atom is studied through the evolution of the atomic population inversion. In addition, two different measures of entanglement between the tripartite system (three entities make the system: two field modes and one atom), i.e., von Neumann and linear entropy are investigated. Also, two kinds of entropic uncertainty relations, from which entropy squeezing can be obtained, are discussed. In each case, the influences of the detuning parameters and Kerr medium on the above nonclassicality features are analyzed in detail via numerical results. It is illustrated that the amount of the above-mentioned physical phenomena can be tuned by choosing the evolved parameters, appropriately.

Some statistical properties for a moving three-level atom in interaction with a bimodal cavity field

In this paper we consider the problem of the interaction between a three-level atom and a quantized bimodal cavity field. The coupling parameter between the atom and the field is taken to be time-dependent by taking the atomic motion into consideration. In the absence of the detuning parameter Δ as well as the Kerr-like medium χ the analytic solution of the wave function is obtained. In our examination of the atomic population the phenomenon of collapses and revivals is observed, however, after a considerable period of time. It is also shown that under the effect of the acceleration parameter δ0 the state of the system loses purity and becomes partially mixed. In the examination of the geometric phase we have observed the regularity behavior when the velocity parameter δ1 takes place, while, in the presence of the Kerr-like medium δ1, the system shows irregular behavior.

Unitary decoupling treatment of a quadratic bimodal cavity quantum electrodynamics model

We consider a two-photon quantum model of radiation–matter interaction between a single two-level atom and a degenerate bimodal high-Q cavity field. Within this tripartite system, the explicit construction of two collective radiation modes, one of which is freely evolving and the other one quadratically coupled to the matter subsystem, is reported. The meaning and advantages of such a decoupling treatment are carefully discussed.

三纠缠原子与双模腔场相互作用系统的纠缠演化特性

三纠缠原子与双模腔场相互作用系统的纠缠演化特性

Nonclassical effects in a highly nonlinear generalized homogeneous Dicke model

An intensity dependent nonlinear coupling model of N two-level atoms (generalized Dicke model) interacting dispersively with a bimodal cavity field via two-photon transitions is investigated in a scenario where the rotating wave approximation is assumed. The model becomes homogeneous in the sense that the spin transition frequency is the same for all atoms and the coupling constants emerging from the collective interactions of the atomic system with the cavity field depend only on the particular radiation field mode. This allows us to represent the Dicke Hamiltonian entirely in terms of the total angular momentum J . It is assumed that, initially, the atomic system and the field are in a disentangled state where the field modes are in Glauber coherent states and the atomic system is a superposition of states | J M 〉 (Dicke states). The model is numerically tested against simulations of normal squeezing variance of the field, squeezing factors based on the Heisenberg uncertainty principle, along with the statistical properties of the light leading to the possible production of nonclassical effects, such as degree of second-order coherence in the modes, degree of intermode correlation, as well as violation of the Cauchy–Schwartz inequality. Analytical expression of the total density operator matrix elements at t > 0 shows the present nonlinear model to be strongly entangled, which is reflected in the time evolution of the linear entropy, where the superposition states are reduced to statistical mixtures. Thus, the present generalized Dicke model does not preserve the modulus of the Bloch vector. The computations, performed in the weak coupling and strong field limits, were conducted via second-order Dyson perturbative expansion of the time evolution operator matrix elements for the totality of the angular momentum states of the atomic system.

QUADRATURE SQUEEZING AND INFORMATION ENTROPY SQUEEZING IN NONLINEAR TWO-LEVEL SPIN MODELS

Normal squeezing, variance and entropy squeezing factors based on the Heisenberg uncertainty principle and Shannon information entropy theory, respectively, derived from the entangled states of two-mode coherent states in two-photon processes are numerically investigated through a previously developed generalized nonlinear Jaynes–Cummings two-level spin model. Numerical simulations are performed and discussed for two two-photon model Hamiltonians in both resonant and off-resonant states of the spin system with the bimodal cavity field.

Entanglement sudden death and sudden birth of an atom coupled to a bimodal lossy cavity

We propose another method for realizing entanglement sudden death and sudden birth using a single atom interacting with a bimodal cavity field in a dissipative environment. By suitably choosing the system's parameters and precisely controlling the dynamics, we find a novel connection between maximum entanglement and mixed state parameters. We discuss the intricate relationship between the entanglement dynamics and the dissipative environment.

Beyond the rotating wave approximation. An intensity dependent nonlinear coupling model in two-level systems

An intensity dependent nonlinear coupling model of a two-level system interacting with a bimodal cavity field via two-photon transitions is investigated in a scenario where the rotating wave approximation is lifted. The model is numerically tested against simulations of normal squeezing variance and entropy squeezing factors based on the Heisenberg uncertainty principle and Shannon information theory derived from entangled states.

Influence of Kerr Medium on Entanglement of Cascade-Type Three-Level Atoms and a Bimodal Cavity Field

We investigate the influence of Kerr medium on atomic population probability and residual entanglement of the system which consists of cascade-type three-level atoms and a bimodal cavity field filled with Kerr medium. The results show that the period of residual entanglement is shortened and the value of residual entanglement is enhanced by appropriately adjusting the nonlinear Kerr constant. Furthermore, we also study the influence of Kerr medium on entanglement evolution of the two atoms, and find that it decreases the value of entanglement between two atoms.

Entanglement for a Bimodal Cavity Field Interacting with a Two-Level Atom

Negativity has been adopted to investigate the entanglement in a system composed of a two-level atom and a two-mode cavity field. Effects of Kerr-like medium and the number of photon inside the cavity on the entanglement are studied. Our results show that atomic initial state must be superposed, so that the two cavity field modes can be entangled. Moreover, we also conclude that the number of photon in the two cavity mode should be equal. The interaction between modes, namely, the Kerr effect, has a significant negative contribution. Note that the atom frequency and the cavity frequency have an indistinguishable effect, so a corresponding approximation has been made in this article. These results may be useful for quantum information in optics systems.

Effect of Cavity Decay on Entanglement of Ladder-Type Three-Level Atoms and a Two-Mode Cavity Field

Considering the adiabatical approximation and the large detuning condition, we give the effective Hamiltonian of a ladder-type three levels atom interacting with a bimodal cavity field. If two identical three-level atoms are sent through the cavity one by one, a two-atom entangled state can be generated. With the choice of the appropriate interaction time, a maximally entangled state of two atoms can be obtained if decoherence effect is ignored. Moreover, we discuss the effect of cavity decay on four physical quantities including atomic population probability, residual entanglement of the first atom and the cavity field, concurrence between the two atoms, and fidelity for generating atomic EPR state, all of which decrease with the increase of cavity decay when the other parameters are fixed.

Quantum trapping conditions for three-level atom flying through bimodal cavity field

A new trapping effect of a three-level atom in interaction with a bimodal cavity field is proposed. This problem consists of the possibility for realization of initially separated states of an atom and an electromagnetic field after interaction. The quantum properties of a bimodal field, which satisfy the reversible conditions for the atom flying through the cavity, were studied.

Entanglement in the Bimodal Jaynes–Cummings Model with the Two-Mode Squeezed Vacuum State

In this paper, we study the interaction between the two-level atom and a bimodal cavity field, namely, two-mode Jaynes–Cummings model when the atom and the modes are initially in the atomic superposition state and two-mode squeezed vacuum state, respectively. For this system we investigate the atomic inversion, linear entropy and atomic Wehrl entropy. We show that there is a connection between all these quantities. Also we prove that the atomic Wehrl entropy exhibits behaviors similar to those of the linear entropy and the von Neumann entropy. Moreover, we show that the bipartite exhibits periodical disentanglement and derive the explicit forms of the states of the atom and the modes at these values of the interaction times.

Entanglement swapping without joint measurement via a Λ-type atom interacting with bimodal cavity field

This paper proposes a scheme for realizing entanglement swapping in cavity QED. The scheme is based on the resonant interaction of a two-mode cavity field with a Λ-type three-level atom. In contrast with the previously proposed schemes, the present scheme is ascendant, since the fidelity is 1.0 and the joint measurement isn't needed. And the scheme is experimentally feasible based on the current cavity QED technique.

Quantum phase entropy and entanglement of a multiphoton three-level atom near the edge of a photonic band gap

Motivated by recent developments in quantum entanglement, we study the relations among concurrence and phase entropy of a three-level atom interacting with a bimodal cavity field. Analytical results are presented when the photonic band gap is exhibited by the presence of photonic crystals. The evolution of the atomic inversion with the field initially in a coherent state is examined, and different nonclassical effects in its dynamics are discussed. An extension of the notion of concurrence introduced by Wooters is used to quantify the entanglement. We conclusively calculate the phase entropy and entanglement using the Pegg-Barnett phase formalism. Evidence has been found to support the idea that phase entropy and concurrence are correlated in this particular model. One feature of the regime considered here is that closed-form evaluation of the time evolution may be carried out in the presence of the detuning and the photonic band gap, which provides insight into the difference in the nature of the concurrence function for atom-field coupling, mode frequency, and different cavity parameters. We demonstrate how fluctuations in the concurrence and phase entropy are affected by the presence of the photonic band gap. Explicit results with numerical simulations applied to GaAs are obtained.

Scheme for quantum information processing via Λ-type atoms interacting with bimodal cavity field

Some schemes for the entanglement generation of two and three distant cavity-fields and the distant transfer of a qubit atomic state and atomic entangled state are presented. The realization of entanglement swapping without measurement on Bell basis vectors and the operation of swap gate are proposed. These schemes are all based on Λ-type atoms interacting with bimodal under one-photon detuning and two-photon resonance. Finally, a discussion of experimental feasibility is given.

Quantum theory of the micromaser with ultracold three-level atoms interactingwith a bimodal cavity field: spatial variation along the cavity axis

The analytical form of the emission probability produced by the interaction of anultracold three-level atom with an electromagnetic bimodal cavity field withmulti-photon transitions of the atoms (multi-photon mazer) is analysed inthe framework of the dressed-state formalism, but is distinguished fromother treatments by the inclusion of the spatial variation along the cavityaxis. In particular, the cavity field mode profile is considered by usingthe mesa-mode function and differences in the collapse–revival patternsare reported. We demonstrate that, when propagation effects are takeninto consideration, the emission probability is influenced significantly. Weprovide the necessary arguments to justify the validity of our conclusions foremission probability and the micromaser, whose dynamics are governed bythe wavefunction. Our main conclusion is that, in the present system,the inclusion of the spatial dependence is necessary and important. Thenumerical illustrations provide evidence that, in cases of physical interest, theemission probability can be significant and can be reliably estimated fora broad range of field parameters using the present formalism.