Time-dependent directionality of cooperative emission after short pulse excitation

Cooperative emission from a sphere of N two-level atoms excited by a short pulse is shown to have a time-dependent angular distribution, with the possibility of reversal in the dominant direction of emission. This is a result of the different values of the frequency shifts and decay rates associated with the various collective eigenmodes of the atomic system obtained in a scalar photon model.     

Single-atom entropy squeezing for two two-level atoms interacting with a single-mode radiation field

In this paper we consider a system of two two-level atoms interacting with a single-mode quantized electromagnetic field in a lossless resonant cavity via l-photon-transition mechanism. The field and the atoms are initially prepared in the coherent state and the excited atomic states, respectively. For this system we investigate the entropy squeezing, the atomic variances, the von Neumann entropy and the atomic inversions for the single-atom case. Also we comment on the relationship between spin squeezing and linear entropy. We show that the amounts of the nonclassical effects exhibited in the entropy squeezing for the present system are less than those produced by the standard Jaynes-Cummings model. The entropy squeezing can give information on the corresponding von Neumann entropy. Also the nonclassical effects obtained from the asymmetric atoms are greater than those obtained from the symmetric ones. Finally, the entropy squeezing gives better information than the atomic variances only for the asymmetric atoms.     

Atomic squeezed states in a driven Dicke model

We consider the dissipative N two-level atom Dicke system driven by a c.w. laser field. In the steady state, the cooperativity among the atoms via the radiation field produces spin squeezing. Even in the absence of dipole-dipole interaction, the system shows spin squeezing which is attributed to strong nonlinear interaction with the driving field.     

Generation of Two-Atom Cluster State via Cavity QED

We propose a physical scheme for generating a two-atom cluster state through the simultaneous interaction of two two-level atoms with a single-mode cavity field prepared initially in an odd-coherent state under a large-detuned limit. The influence of the dissipation constant, the intensity of the field and the imperfect manipulation on the preparation scheme are investigated. It is shown that when the intensity of the cavity is large enough, the influence of the cavity decay is ettlciently suppressed. The possible error in the implementation of the cluster state is negligible when the time difference between two atoms crossing the cavity axis is small. It is suggested that the scheme can be realized by current technologies.     

The metamorphosis in the emission angular profile from an inverted two-level atoms system

A rich variety of angular distributions in the cooperative emission from a sphere of inverted N two-level atoms are shown to result from the eigenstructure of the complex kernel of scalar photon theory exp(ik₀R)/(ik₀R). This angular distribution is sensitive both to the size of the sphere and to the instant of observation of the emission.     

Quantification of Quantum Entanglement in a Multiparticle System of Two-Level Atoms Interacting with a Squeezed Vacuum State of the Radiation Field

We quantify multiparticle quantum entanglement in a system of N two-level atoms interacting with a squeezed vacuum state of the electromagnetic field. We calculate the amount of quantum entanglement present among one hundred such two-level atoms and also show the variation of that entanglement with the radiation field parameter. We show the continuous variation of the amount of quantum entanglement as we continuously increase the number of atoms from N = 2 to N = 100. We also discuss that the multiparticle correlations among the N two-level atoms are made up of all possible bipartite correlations among the N atoms.     

Squeezing in a spin chain with site-dependent periodic and long-range interactions

Numerical and analytical results for the squeezing factor, ζ², in a pseudo-spin s-1/2 chain. The open chain is composed by N two-level atoms with site-dependent interactions. The time evolution of the squeezing factor is studied, as well as its dependence on the number of atoms and on the interactions. It is found that long-range interactions may optimize the degree of spin squeezing.     

Effects of including the counterrotating term and virtual photons on the eigenfunctions and eigenvalues of a scalar photon collective emission theory

We find eigenmodes of an integral equation describing N 2-level atoms interacting with a scalar field, one atom being initially excited. Neglect of virtual field quanta would replace the correct kernel by its real part. This has serious consequences both for small and large samples.     

On the generation of a generalized superposition of displaced squeezed states

A feasible scheme is presented to generate a generalized superposition of displaced squeezed states, cosθ|α,z〉±sinθ|-α,z〉, in a single mode of the electromagnetic field inside a microwave cavity. The scheme employs a two-level (Rydberg) atom driven by an external classical field. The success probability and the interaction time of such generation are also considered.     

Quantum effect in a generalized N-atom Dicke model

We have studied the geometric phase and the sub-Poissonian photon distribution of a generalized N two-level atoms Dicke model in the thermo-dynamical limit and the off-resonant coupling case. It is found that the geometric phase in the ground state is relative to the atom number, the coupling strength between the atom and the light field, the frequency of the electromagnetic wave and the energy difference between two levels of the atom. The photons may exhibit the sub-Poissonian distribution in the ground state.     

Spin squeezing and entanglement via hole-burning in atomic coherent states

We study the generation of spin squeezing via the hole burning of selected Dicke states out of an atomic coherent state prepared for a collection of N two-level atoms or ions. The atoms or ions of the atomic coherent state are not entangled, but the removal of one or more Dicke states generates entanglement, and spin squeezing occurs for some ranges of the relevant parameters. Spin squeezing in a collection of two-level atoms or ions is of importance for precision spectroscopy.     

Controlling subluminal to superluminal behavior of group velocity in an f-deformed Bose-Einstein condensate beyond the rotating wave approximation

In this paper, we investigate tunable control of the group velocity of a weak probe field propagating through an f-deformed Bose-Einstein condensate of Λ-type three-level atoms beyond the rotating wave approximation. For this purpose, we use an f-deformed generalization of an effective two-level quantum model of the three-level Λ-configuration without the rotating wave approximation in which the Gardiner’s phonon operators for Bose-Einstein condensate are deformed by an operator-valued function, , of the particle-number operator . We consider the collisions between the atoms as a special kind of f-deformation where the collision rate κ is regarded as the deformation parameter. We demonstrate the enhanced effect of subluminal and superluminal propagation based on electromagnetically induced transparency and electromagnetically induced absorption, respectively. In particular, we find that (i) the absorptive and dispersive properties of the deformed condensate can be controlled effectively in the absence of the rotating wave approximation by changing the deformation parameter κ, the total number of atoms and the counter-rotating terms parameter λ, (ii) by increasing the values of λ, κ and η = 1/N, the group velocity of the probe pulse changes, from subluminal to superluminal and (iii) beyond the rotating wave approximation, the subluminal and superluminal behaviors of the probe field are enhanced.     

Exceptional points of a Hamiltonian and phase transitions in finite systems

For a model Hamiltonian which describesN interacting Fermions and which is typical for systems that undergo phase transitions it is shown that for finiteN the transitional point is associated with exceptional points of the Hamiltonian. In the limit of largeN these singularities move down to the real axis. The nature of the limit turns out to be quite different depending on whether it is taken for interaction strengths smaller or larger than the critical value.     

A Total Measure of Multi-Particle Quantum Correlations in Atomic Schrödinger Cat States

We propose a total measure of multi-particle quantum correlation in a system of N two-level atoms (N qubits). We construct a parameter that encompasses all possible quantum correlations among N two-level atoms in arbitrary symmetric pure states and define its numerical value to be the total measure of the net atom-atom correlations. We use that parameter to quantify the total quantum correlations in atomic Schrödinger cat states, which are generated by the dispersive interaction in a cavity. We study the variation of the net amount of quantum correlation as we vary the number of atoms from N=2 to N=100 and obtain some interesting results. We also study the variation of the net correlation, for fixed interaction time, as we increase the number of atoms in the excited state of the initial system, and notice some interesting features. We also observe the behaviour of the net quantum correlation as we continuously increase the interaction time, for the general state of N two-level atoms in a dispersive cavity.     

Entanglement and Its Dynamics with Atomic Spontaneous Decay

The atomic decay for a two-level atom interacting with a single mode of electromagnetic tield is considered. For a chosen initial state, the exact solution of the master equation is found. Therefore, effect of the atomic damping on entanglement （purity loss）, degree of entanglement by the negativity, mutual information and atomic coherence through the master equation are studied.     

The role of ergodicity and mixing in the central limit theorem for Casati-Prosen triangle map variables

In this Letter we analyse the behaviour of the probability density function of the sum of N deterministic variables generated from the triangle map of Casati-Prosen. For the case in which the map is both ergodic and mixing the resulting probability density function quickly concurs with the Normal distribution. However, when the map is weakly chaotic, and fuzzily not mixing, the resulting probability density functions are described by power-laws. Moreover, contrarily to what it would be expected, as the number of added variables N increases the distance to Gaussian distribution increases. This behaviour goes against standard central limit theorem. By extrapolation of our finite size results we preview that in the limit of N going to infinity the distribution has the same asymptotic decay as a Lorentzian (or a q=2-Gaussian).     

Electromagnetic wave scattering from two interacting small spherical particles. Influence of their optical constants, ε and μ

In this research, the influence of the optical constants ε and μ on the scattering patterns of a system consisting of two interacting Rayleigh particles is analyzed. We study specific scattering configurations in which the particles are separated by a fixed distance and where the connecting axis has fixed orientations with respect to the incident electromagnetic field. Multiple scattering effects and how they are affected by the optical properties of the particles are considered.     

Rényi entropy and quantum phase transition in the Dicke model

The Rényi entropies of the Dicke model are presented. This quantum-optical model describes a single-mode bosonic field interacting with an ensemble of N two-level atoms. There is a quantum phase transition in the N→∞ limit. It is shown that there is an abrupt change in the Rényi entropy of order β at the transition point. Around the critical value of the coupling strength λc the Rényi entropy is proportional to the logarithm of the characteristic length and diverges as ln|λc−λ| for any order β. The pseudocapacity defined here in analogy with the heat capacity exhibits the phase transition. The critical exponent for the Dicke model is found to be 1 for any value of the parameter β.     

Influence of the dipole-dipole interaction on velocity-selective coherent population trapping

We analyze the influence of the dipole-dipole interaction between ground and excited state atoms on atomic cooling by velocity-selective coherent population trapping. We consider two three-level atoms in the -configuration, interacting with two counterpropagating laser fields as well as with the electromagnetic vacuum modes. The elimination of these modes in the Born-Markov approximation results in spontaneous decay, which is essential in providing the momentum diffusion necessary for cooling, as well as a two-body dipole-dipole interaction between ground-and excited-state atoms. The corresponding two-body master equation is solved numerically by Monte-Carlo wave-function simulations. Our main result is that although a dark state survives the inclusion of dipole-dipole interactions, the presence of this interaction can significantly slow down the cooling process for sufficiently high atomic densities.Dedicated to H. Walther on the occasion of his 60th birthdayStrictly speaking, VSCPT is not a true cooling mechanism. The final atomic distribution cannot be characterized by a temperature, so that there is some ambiguity in characterizing the cooling efficiency. We return to this point in Sect. 3     

A transition in the spectral statistics of quantum optical model by different electromagnetic fields

In this paper, we have considered the effects of different quantized electromagnetic fields on the spectral statistics of two-level atoms. The Berry-Robnik distribution and the maximum likelihood estimation technique are used to analyze the effect of the mean photon numbers, the two level atoms numbers and also the quantum number of considered states on the fluctuation properties of different systems which are described by different sets of the Dicke Hamiltonian’s parameters. Our results describe the obvious effect of mean photon number on the spectral statistics and show more regular dynamics when this quantity reaches 700. Also, we observed universality in the spectral statistics of considered systems when the number of two level atoms approaches an unrealistic limit (N _A ~ 200) and there are some suggestions about the effect of the quantum number of selected levels and the atom-field coupling constant on level statistics.