We present a theoretical treatment of the surprisingly large damping observed recently in one-dimensional Bose-Einstein atomic condensates in optical lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB) calculations can describe qualitatively the main features of the damping observed over a range of lattice depths. We also derive a formula of the fluctuation-dissipation type for the damping, based on a picture in which the coherent motion of the condensate atoms is disrupted as they try to flow through the random local potential created by the irregular motion of noncondensate atoms. When parameters for the characteristic strength and correlation times of the fluctuations, obtained from the HFB calculations, are substituted in the damping formula, we find very good agreement with the experimentally observed damping, as long as the lattice is shallow enough for the fraction of atoms in the Mott insulator phase to be negligible. We also include, for completeness, the results of other calculations based on the Gutzwiller ansatz, which appear to work better for the deeper lattices.

We analyze electromagnetically induced transparency and light storage in an ensemble of atoms with multiple excited levels (multi-$\Lambda$ configuration) which are coupled to one of the ground states by quantized signal fields and to the other one via classical control fields. We present a basis transformation of atomic and optical states which reduces the analysis of the system to that of electromagnetically induced transparency in a regular three-level configuration. We demonstrate the existence of dark state polaritons and propose a protocol to transfer quantum information from one optical mode to another by an adiabatic control of the control fields.

A quantum-field-theory approach is put forward to generalize the concept of classical spatial light beams carrying orbital angular momentum to the single-photon level. This quantization framework is carried out both in the paraxial and nonparaxial regimes. Upon extension to the optical phase space, closed-form expressions are found for a photon Wigner representation describing transformations on the orbital Poincaré sphere of unitarily related families of paraxial spatial modes.

The two-mode relative phase associated with Gaussian states plays an important role in quantum information processes in optical, atomic, and electronic systems. In this work, the origin and structure of the two-mode relative phase in pure Gaussian states is studied in terms of its dependences on the quadratures of the modes. This is done by constructing local canonical transformations to an associated two-mode squeezed state. The results are illustrated by studying the time dependence of the phase under a nonlocal unitary model evolution containing correlations between the modes. In a more general context, this approach may allow the two-mode phase to be studied in situations sensitive to different physical parameters within experimental configurations relevant to quantum information processing tasks.

We claim that the concept of electromagnetically induced transparency is only valid for low atomic densities, and for high densities stimulated Raman scattering is totally dominant, where the incident probe wave is not transmitted but is converted to the Stokes wave. This behavior can be explained by the large difference in linear absorption coefficients between the probe and the Stokes waves. We have verified this claim by the experiments using sodium atomic vapor samples with and without a buffer gas. Theoretical analyses using the Liouville-Maxwell equations and numerical simulations also supported our observations.

We present a scheme for the realization of a stationary source of nonclassical light, which approximates very well a continuous single-photon source. It consists of a single four-level atom trapped inside a high-finesse optical cavity and Raman coupled to a cavity mode. A selectivity mechanism, based on a field-dependent Stark shift of electronic levels, prevents the occupation of two or more photon states of the quantized mode being excited. The output light of such a source exhibits sub-Poissonian photon-number statistics and antibunching behavior.

Recently, Ye and Guo [Phys. Rev. A 70, 054303 (2004)] have presented a scheme for implementing quantum teleportation of atomic states in cavity QED. In this Comment, we show that contrary to the authors' claim, the scheme is based on Bell-state measurement.

We agree with the criticism in the Comment by Chhajlany et al. that the parlance “without the Bell-state measurement” in our early scheme [Phys. Rev. A 70, 054303 (2004)] is improper. But the inaccurate statement does not influence the correctness of our whole scheme. Furthermore we do not think that for enhancing the successful probability the unitary transformation of their Comment can be implemented experimentally in cavity QED system.

Recently, Yan and Gao [Phys. Rev. A 72, 012304 (2005)] presented a quantum secret sharing protocol which allows a secret message to be shared between two groups of parties ($m$ parties in group 1 and $n$ parties in group 2). Their protocol is claimed to be secure that, except with the cooperation of the entire group 1 or group 2, no subgroup of either group 1 or group 2 can extract the secret message. However, this study points out that the $m\text{th}$ party (the last party to process the quantum state) of group 1 can maliciously replace the secret message with an arbitrary message without the detection of the other parties.

We study the differences between the processes of decoherence induced by chaotic and regular environments. For this we analyze a family of simple models that contain both regular and chaotic environments. In all cases the system of interest is a “quantum walker,” i.e., a quantum particle that can move on a lattice with a finite number of sites. The walker interacts with an environment which has a $D$-dimensional Hilbert space. The results we obtain suggest that regular and chaotic environments are not distinguishable from each other in a (short) time scale $t^{*}$, which scales with the dimensionality of the environment as $t^{*}\propto {\log }_2\left(D\right)$. However, chaotic environments continue to be effective over exponentially longer time scales while regular environments tend to reach saturation much sooner. We present both numerical and analytical results supporting this conclusion. The family of chaotic evolutions we consider includes the so-called quantum multibaker map as a particular case.

In this work, our primary goal has been to explore the range of validity of two-mode models for Bose-Einstein condensates in double-well potentials. Our derivation, like others, uses symmetric and antisymmetric condensate basis functions for the Gross-Pitaevskii equation. In what we call an “improved two-mode model” (I2M), the tunneling coupling energy explicitly includes a nonlinear interaction term, which has been given previously in the literature but not widely appreciated. We show that when the atom number (and hence the extent of the wave function) in each well vary appreciably with time, the nonlinear interaction term produces a temporal change in the tunneling energy or rate, which has not previously been considered to our knowledge. In addition, we obtain a parameter, labeled “interaction tunneling,” that produces a decrease of the tunneling energy when the wave functions in the two wells overlap to some extent. Especially for larger values of the nonlinear interaction term, results from this model produce better agreement with numerical solutions of the time-dependent Gross-Pitaevskii equation in one and three dimensions, as compared with models that have no interaction term in the tunneling energy. The usefulness of this model is demonstrated by good agreement with recent experimental results for the tunneling oscillation frequency [Albiez et al., Phys. Rev. Lett. 95, 010402 (2005)]. We also present equations and results for a multimode approach, and use the I2M model to obtain modified equations for the second-quantized version of the Bose-Einstein double-well problem.

We consider an analog of entanglement-swapping for a set of black boxes with the most general nonlocal correlations consistent with relativity (including correlations which are stronger than any attainable in quantum theory). In an attempt to incorporate this phenomenon, we consider expanding the space of objects to include not only correlated boxes, but “couplers,” which are an analog for boxes of measurements with entangled eigenstates in quantum theory. Surprisingly, we find that no couplers exist for two binary-input–binary-output boxes, and hence that there is no analog of entanglement swapping for such boxes.

The Zeeman effect in the ground and low-lying excited electronic states of calcium monohydride $\mathrm{CaH}$ has been experimentally investigated using optical Zeeman spectroscopy of the (0,0) band of the $B{}^2\Sigma ^{+}\text{−}X{}^2\Sigma ^{+}$ and the (0,0) band of the $A{}^2\Pi \text{−}X{}^2\Sigma ^{+}$ systems. The observed Zeeman-induced shifts and splittings of numerous branch features recorded near the natural linewidth limit were successfully modeled using a traditional effective Hamiltonian approach to account for the interaction between the $(v=0)$ $A{}^2\Pi$ and $(v=0)$ $B{}^2\Sigma ^{+}$ states and explicit inclusion of the interaction matrix elements for the heterogeneous perturbations between the $(v=1)$ $A{}^2\Pi$ and $(v=0)$ $B{}^2\Sigma ^{+}$ states. The determined magnetic $g$ factors for the $X{}^2\Sigma ^{+}$, $B{}^2\Sigma ^{+}$, and $A{}^2\Pi$ states are compared with previously assumed values and those predicted by perturbation theory.

We study coherent backscattering of a monochromatic laser by a dilute gas of cold two-level atoms in the weakly nonlinear regime. The nonlinear response of the atoms results in a modification of both the average field propagation (nonlinear refractive index) and the scattering events. Using a perturbative approach, the nonlinear effects arise from inelastic two-photon scattering processes. We present a detailed diagrammatic derivation of the elastic and inelastic components of the backscattering signal for both scalar and vectorial photons. In particular, we show that the coherent backscattering phenomenon originates in some cases from the interference between three different scattering amplitudes. This is in marked contrast with the linear regime where it is due to the interference between two different scattering amplitudes. In particular we show that, if elastically scattered photons are filtered out from the photodetection signal, the nonlinear backscattering enhancement factor exceeds the linear barrier of 2, consistently with a three-amplitude interference effect.

We consider the problem of decoherence and relaxation of open bosonic quantum systems from a perspective alternative to the standard master equation or quantum trajectories approaches. Our method is based on the dynamics of expectation values of observables evaluated in a coherent state representation. We examine a model of a quantum nonlinear oscillator with a density-density interaction with a collection of environmental oscillators at finite temperature. We derive the exact solution for dynamics of observables and demonstrate a consistent perturbation approach.

We point out some logical inconsistencies in the model proposed in [Phys. Rev. A 71, 043604 (2005)] as well as in the calculations performed on it. The proposed model is not able to describe Feshbach resonances in optical lattices.

We show that the Comment by Diener and Ho [Phys. Rev. A 73, 017601 (2006)] is based on the misunderstanding that the Hamiltonian used by Dickerscheid et al. to describe Feshbach resonances in an optical lattice is a microscopic Hamiltonian as opposed to an effective Hamiltonian.

We present a full quantum treatment of a five-level atomic system coupled to two quantum and two classical light fields. The two quantum fields undergo a cross-phase-modulation induced by electromagnetically induced transparency. The performance of this configuration as a two-qubit quantum phase gate for traveling single photons is examined. A trade-off between the size of the conditional phase shift and the fidelity of the gate is found. Nonetheless, a satisfactory gate performance is still found to be possible in the transient regime, corresponding to a fast gate operation.

We study the vortex distribution of the wave functions minimizing the Gross-Pitaevskii energy for a fast rotating condensate in the lowest Landau level (LLL): we prove that the minimizer cannot have a finite number of zeroes, thus the lattice is infinite, but not uniform. This uses the explicit expression of the projector onto the LLL. We also show that any slow varying envelope function can be approximated in the LLL by distorting the lattice. This is used in particular to approximate the inverted parabola and understand the role of “invisible” vortices: the distortion of the lattice is very small in the Thomas-Fermi region but quite large outside, where the “invisible” vortices lie.