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.     

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.     

Superpositions of excited–deexcited coherent states and some of their non-classical properties

Applying the operator a + a⁺ to the superposed coherent states several times, superpositions of the excited–deexcited coherent states are obtained. Compared with the original superposed coherent states, these new states can have stronger squeezing and anti-bunching effects. The operation a + a⁺ can also induce squeezing or antibunching effect if the original states do not possess these properties. Calculations about the phase properties, the Q function and the Wigner function reflect the non-classical character of the excited–deexcited states from different aspects.     

Higher-order properties of photon-added coherent states

We have studied a higher-order squeezing and a higher-order sub-Poissonian photon statistics in photon-added coherent states. We obtained analytic forms of the degree of higher-order squeezing and the degree of higher-order sub-Poissonian statistics. We show that the photon-added coherent state |α,m〉 exhibits both higher-order squeezing and higher-order sub-Poissonian character. For two different types of higher-order squeezing, the degree of squeezing becomes bigger when the added photon number is increased. In single-photon-added coherent state, the degree of squeezing depends upon the order of squeezing N. When N is increased, the degree of squeezing becomes bigger in the Hong-Mandel-type higher-order squeezing but becomes smaller in the Hillery-type higher-order squeezing. Also, the higher-order sub-Poissonian character is more pronounced than the usual sub-Poissonian character in the single-photon-added coherent state.     

Effects on squeezing and sub-poissonian of light in fourth harmonic generation up to first-order Hamiltonian interaction

The effects on squeezing and sub-poissonian of light in fourth harmonic generation (FHG) are investigated based on the fully quantum mechanically up to the first order Hamiltonian interaction in gt, where g is the coupling constant between the modes per second and t is the interaction time between the waves during the process in a nonlinear medium. FHG is a process in which an incident laser beam of the fundamental frequency ω interacts with a nonlinear medium to produce the harmonic frequency at 4ω. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The occurrence of amplitude squeezing effects in both the quadratures of the radiation field in the fundamental mode is investigated and found to be dependent on the selective phase values of the field amplitude. The photon statistics of the pump mode in this process have also been investigated and found to be sub-poissonian in nature. It is found that there is no possibility to produce squeezed light in the harmonic mode up to first-order interaction in gt. Further, we have found the case up to second-order Hamiltonian interaction in gt that the normal squeezing in the harmonic mode is directly depends upon the fourth-order squeezing of the initial pump field. This gives a method of converting higher-order (fourth-order) squeezing into normal squeezing in the harmonic mode and vice versa.     

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.     

Squeezing properties of light field in the process preparing Raman atom laser

In this paper, the squeezing properties of the probe light field in the process preparing Raman-type atom laser via stimulated Raman transition of the sodium atom Bose-Einstein condensate (BEC) interacting with two light beam of a weaker squeezed coherent probe light and a stronger classical pump light are studied. The results show that the probe light can be periodically squeezed. The squeezing period is related to the mean number of atoms in trap, the strength of interaction between squeezed light and BEC atoms, and the detuning of the light, and the squeezing depth is determined by the initial squeezing factor of the probe light.     

Superfluorescence from europium atom at 629.977 nm

Visible superfluorescence at 629.977 nm is observed in europium atom with very high optical conversion efficiency on the transition 5d6p ¹⁰F_7/2 → 5d6s ¹⁰D_7/2. The peak intensity of fluorescence varies as square of the number of atoms in the excited state (N), which shows the superfluorescence character of the transition. The ratio of average superfluorescence power to excitation laser power is observed to be ∼15% in the forward direction.     

Non-classical properties of superposition of two coherent states having phase difference ?

Recently Ahmad et al. [Optik 2009;120;68; Optics Commun. 2007;271:162; Chin. Phys. Lett. 2006;23:2438] have studied non-classical properties of superposition of two-coherent states of the form, |ψ〉=K[|α〉+eiξ|αei?〉] for the special cases with values ? = π/2,  3π/2,  and π, and for arbitrarily fixed values of ξ. We point out that some of their results are special cases of our recently published work [Physica A 319, 305 (2003); Physica A 341, 201(2004)] on the most general superposition of two arbitrary coherent states of the form ∼(Z₁|α〉+Z₂|β〉), where X_1,2, α and β are arbitrary and only restriction on these is the normalization condition for the superposed state. To make our point we first obtain results for (i) squeezing of the most general Hermitian operator X_θ = X₁ cos θ + X₂ sin θ, with X₁ + iX₂ = a, is the annihilation operator, and (ii) sub-Poissonian photon statistics, for the superposed state |ψ〉 with a general ? and, then obtain results of Ahmad et al. for ? = π/2,  3π/2,  and π and for θ = 0 and π/2. It is interesting to note that the arbitrarily fixed values ξ = |α|² and −|α|² for ? = π/2 and 3π/2, respectively by Ahmad et al. are the values at which we get maximum squeezing working in a rigorous way.     

Localization of atoms in light fields: Optical molasses,adiabatic compression and squeezing

We present a theoretical study of the localization1 of atoms with an angular momentumJ _g=3 toJ _e=4 transition (e.g., chromium atoms) in quantized optical molasses created by two counterpropagating linearly polarized laser beams. We study the localization as a function of the potential depth, the angle between the polarizations and the interaction time with the molasses in the low-intensity limit, and discuss the possibility of adiabatic compression and squeezing of the atomic distribution.Dedicated to H. Walther on the occasion of his 60th birthday     

Quantum phase properties associated to solvable quantum systems using the nonlinear coherent states approach

In this paper we study the quantum phase properties of “nonlinear coherent states” and “solvable quantum systems with discrete spectra” using the Pegg-Barnett formalism in a unified approach. The presented procedure will then be applied to few special solvable quantum systems with known discrete spectrum as well as to some new classes of nonlinear oscillators with particular nonlinearity functions. Finally the associated phase distributions and their nonclasscial properties such as the squeezing in number and phase operators have been investigated, numerically.     

Entanglement dynamics and quasiprobability distribution for the degenerate Raman process

In this paper, we consider the model which consists of a degenerate Raman process involving two degenerate Rydberg energy levels of an atom interacting with a single-mode cavity field. The influence of the atomic coherence on the von Neumann entropy of the atom and the atomic inversion is investigated. It is shown that the atomic coherence decreases the amount of atom-field entanglement. It is also found that the collapse and revival times are independent of the atomic coherence, while the amplitude of the revivals is sensitive to this coherence. Moreover, the Q function and the entropy squeezing of the field are examined. Some new conclusions can be obtained.     

A degenerate three-level laser with a parametric amplifier

The aim of this paper is to study the squeezing and statistical properties of the light produced by a degenerate three-level laser whose cavity contains a degenerate parametric amplifier. In this quantum optical system the top and bottom levels of the three-level atoms injected into the laser cavity are coupled by the pump mode emerging from the parametric amplifier. For a linear gain coefficient of 100 and for a cavity damping constant of 0.8, the maximum intracavity squeezing is found at steady state and at threshold to be 93%.     

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.     

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.     

Coherent excitation of Rydberg atoms in an ultracold gas

We demonstrate two schemes for the coherent excitation of Rydberg atoms in an ultracold gas of rubidium atoms employing the three-level ladder system 5S_1/2-5P_3/2-n?_j. In the first approach rapid adiabatic passage with pulsed laser fields yields Rydberg excitation probabilities of 90% in the center of the laser focus. In a second experiment two-photon Rydberg excitation with continuous-wave fields is applied which results in Rabi oscillations between the ground and Rydberg state. The experiments represent a prerequisite for the control of interactions in ultracold Rydberg gases and the application of ultracold Rydberg gases for quantum information processing.     

1/N-Expansion for the Dicke model and the decoherence program

An analysis of the Dicke model, N two-level atoms interacting with a single radiation mode, is done using the Holstein-Primakoff transformation. The main aim of the paper is to show that, changing the quantization axis with respect to the common usage, it is possible to prove a general result either for N or the coupling constant going to infinity for the exact solution of the model. This completes the analysis, known in the current literature, with respect to the same model in the limit of N and volume going to infinity, keeping the density constant. For the latter the proper axis of quantization is given by the Hamiltonian of the two-level atoms and for the former the proper axis of quantization is defined by the interaction. The relevance of this result relies on the observation that a general measurement apparatus acts using electromagnetic interaction and so, one can state that the thermodynamic limit is enough to grant the appearance of classical effects. Indeed, recent experimental results give first evidence that superposition states disappear interacting with an electromagnetic field having a large number of photons.     

Optical Ramsey spectroscopy on laser-trapped and thermal Mg atoms

High-resolution spectroscopic measurements on the 457 nm Mg intercombination line are reported. Studies have been performed both on atoms contained in a magneto-optical trap and on atoms in a thermal beam. We present a detailed analysis of various factors influencing resolution and accuracy for both setups, including direct comparisons. With the trapped cold atoms, a stability of 8.7 × 10^–13 within 20 s has been achieved together with an accuracy of 2 × 10^–15. The direct comparison shows the limited stability of the thermal beam apparatus for integration times larger than 300 s. For shorter times, the thermal beam setup is at present more stable by a factor of three, mainly because of a better signal-to-noise ratio.     

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.     

Single atom entropy squeezing for two two-level atoms interacting with a binomial field

In this paper we consider a system of two two-level atoms interacting with a binomial field in an ideal cavity. We investigate the time evolution of the single atom entropy squeezing, atomic inversion and the linear entropy for the present system. Furthermore, the relationship between the entropy squeezing and the entanglement is investigated. It is shown that the amounts of the nonclassical effects exhibited in the entropy squeezing are dependent on the different initial conditions. The entropy squeezing can give information on the corresponding linear entropy.