We consider insulating phases of cold spin-1 bosonic particles with antiferromagnetic interactions, such as ${}^{23}\mathrm{Na},$ in optical lattices. We show that spin-exchange interactions give rise to several distinct phases, which differ in their spin correlations. In two- and three-dimensional lattices, insulating phases with an odd number of particles per site are always nematic. For insulating states with an even number of particles per site, there is always a spin-singlet phase, and there may also be a first-order transition into the nematic phase. The nematic phase breaks spin rotational symmetry but preserves time reversal symmetry, and has gapless spin-wave excitations. The spin-singlet phase does not break spin symmetry and has a gap to all excitations. In one-dimensional lattices, insulating phases with an odd number of particles per site always have a regime where translational symmetry is broken and the ground state is dimerized. We discuss signatures of various phases in Bragg scattering and time-of-flight measurements.

We study hydrodynamic behavior in expanding thermal clouds of ${}^{87}\mathrm{Rb}$ released from an elongated trap. At our highest densities the mean free path is smaller than the radial size of the cloud. After release the clouds expand anisotropically. The cloud temperature drops by as much as 30%. This is attributed to isentropic cooling during the early stages of the expansion. We present an analytical model to describe the expansion and to estimate the cooling. Important consequences for time-of-flight thermometry are discussed.

We study the quantum dynamics of optical fields in weakly confining resonators with overlapping modes. Employing a recently developed quantization scheme involving a discrete set of resonator modes and continua of external modes we derive Langevin equations and a master equation for the resonator modes. Langevin dynamics and the master equation are proved to be equivalent in the Markovian limit. Our open-resonator dynamics may be used as a starting point for a quantum theory of random lasers.

It is shown that spontaneous symmetry breaking does not modify the ground-state entanglement of two spins, as defined by the concurrence, in the XXZ chain and the transverse field Ising chain. Correlation function inequalities, valid in any dimensions for these models, are presented outlining the regimes where entanglement is unaffected by spontaneous symmetry breaking.

The Casimir-Polder force is an attractive force between a polarizable atom and a conducting or dielectric boundary. Its original computation was in terms of the Lamb shift of the atomic ground state in an electromagnetic field modified by boundary conditions along the wall and assuming a stationary atom. We calculate the corrections to this force due to a moving atom, demanding maximal preservation of entanglement generated by the moving atom-conducting wall system. We do this by using nonperturbative path integral techniques which allow for coherent backaction and thus can treat non-Markovian processes. We recompute the atom-wall force for a conducting boundary by allowing the bare atom-EMF ground state to evolve (or self-dress) into the interacting ground state. We find a clear distinction between the cases of stationary and adiabatic motions. Our result for the retardation correction for adiabatic motion is up to twice as much as that computed for stationary atoms. We give physical interpretations of both the stationary and adiabatic atom-wall forces in terms of alteration of the virtual photon cloud surrounding the atom by the wall and the Doppler effect.

The technique of quantum repeaters is a promising candidate for sending quantum states over long distances through a lossy channel. The usual discussion of this technique deals with only a finite-dimensional Hilbert space. However the qubits, with which one implements this procedure, will “ride” on continuous degrees of freedom of the carrier particles. Here we analyze the action of quantum repeaters using a model based on pulsed parametric down-conversion entanglement swapping. Our model contains the basic traits of a real experiment. We show that the state created, after the use of any number of parametric down-converters in a series of entanglement swappings, is always an entangled (actually distillable) state, although of a different form than the one that is usually assumed. Furthermore, the output state always violates a Bell inequality.

We show that it is possible to control the trade-off between information gain and disturbance in generalized measurements of qudits by utilizing a programmable quantum processor. This universal quantum machine allows us to perform a generalized measurement on the initial state of the input qudit to construct a Husimi function of this state. The trade-off between the gain and the disturbance of the qudit is controlled by the initial state of ancillary system that acts as a program for the quantum-information distributor. The trade-off fidelity does not depend on the initial state of the qudit.

The concept of a qudit (a d-level system) cluster state is proposed by generalizing the qubit cluster state [Phys. Rev. Lett. 86, 910 (2001)] to higher-dimensional Hilbert space according to the finite-dimensional representations of quantum plane algebra. We demonstrate their quantum correlations and prove a theorem which guarantees the availability of the qudit cluster states in quantum computation. We explicitly construct the network to show the universality of the one-way computer based on the defined qudit cluster states and single-qudit measurement. A protocol of implementing one-way quantum computer is suggested using the high-dimensional “Ising” model which can be found in many magnetic systems.

The formation rate of the excited hydrogen mesic molecule due to Auger process is calculated in a quasiclassic approximation. The resulted bound state may decay via predissociation with a large energy release, which leads to a considerable acceleration of the mesic atom. The calculated rates of the mesic molecule formation are compared with those obtained in a semiclassical approach.

Three-photon ionization cross sections from the ground state, and two-photon ionization from the $3{}^{1}P\left(3s3p\right)\mathrm{}$ state have been calculated for Mg in the region between the $3p$ and $4s$ ionization thresholds. These processes include an above-threshold ionization process for the last absorbed photon. We have used the Green’s-function method in the Feshbach formalism and an $L^2$ close coupling approach, with a basis of $L^2$ integrable B-spline functions. We report the positions, widths, and assignments of a number of relevant ${}^1{P}^o$ ${\mathrm{and}}^1{F}^o$ doubly excited Feshbach states. We also observe unusually high cross sections due to a bound-bound transition from the $3{}^1{S(3s}^2)$ to the $3{}^{1}P\left(3s3p\right)\mathrm{}$ state, a core excitation process, and the population of an intermediate doubly excited state. Both total cross sections and angular distributions are reported.

Starting from two identical, interacting particles in an isotropic harmonic trap, we employ first-order perturbation theory to derive the effective s-wave pseudopotential operator for a weakly anisotropic trap. It is shown that such a confinement gives rise to a correction of the s-wave scattering length which is proportional to the square of the ratio of the bare scattering length and the oscillator length. The trap pseudopotential depends on the quantum number of the trapped state, and the effect of a weak anisotropy is dominated by its nearest neighbors. Some implications for experiments with cold bosons in tightly confining potentials are discussed briefly.

The dynamics of evaporative cooling of magnetically trapped ${}^{87}\mathrm{Rb}$ atoms is studied on the basis of the quantum kinetic theory of a Bose gas. We carried out the quantitative calculations of the time evolution of conventional evaporative cooling where the frequency of the radio-frequency magnetic field is swept exponentially. This “exponential-sweep cooling” is known to become inefficient at the final stage of the cooling process due to a serious three-body recombination loss. We precisely examine how the growth of a Bose-Einstein condensate depends on the experimental parameters of evaporative cooling, such as the initial number of trapped atoms, the initial temperature, and the bias field of a magnetic trap. It is shown that three-body recombination drastically depletes the trapped ${}^{87}\mathrm{Rb}$ atoms as the system approaches the quantum degenerate region and the number of condensed atoms finally becomes insensitive to these experimental parameters. This result indicates that the final number of condensed atoms is well stabilized by a large nonlinear three-body loss against the fluctuations of experimental conditions in evaporative cooling.

Double dark resonances originate from a coherent perturbation of a system displaying electromagnetically induced transparency. We experimentally show and theoretically confirm that this leads to the possibility of extremely sharp resonances prevailing even in the presence of considerable Doppler broadening. A gas of ${}^{87}\mathrm{Rb}$ atoms is subjected to a strong drive laser and a weak probe laser and a radio frequency field, where the magnetic coupling between the Zeeman levels leads to nonlinear generation of a comb of sidebands.

Light amplification in a collective atomic recoil laser with an active medium confined in an external harmonic trap is investigated. Our study confirms the possibility of a great promotion of the lasing efficiency due to the collective atomic recoil motion being modified by the trapping potential. The physical explanation of this laser behavior is given.

We study the multiorder coherent Raman scattering of a quantum probe field in a far-off-resonance medium with a prepared coherence. Under the conditions of negligible dispersion and limited bandwidth, we derive a Bessel-function solution for the sideband field operators. We analytically and numerically calculate various quantum statistical characteristics of the sideband fields. We show that the multiorder coherent Raman process can replicate the statistical properties of a single-mode quantum probe field into a broad comb of generated Raman sidebands. We also study the mixing and modulation of photon statistical properties in the case of two-mode input. We show that the prepared Raman coherence and the medium length can be used as control parameters to switch a sideband field from one type of photon statistics to another type, or from a nonsqueezed state to a squeezed state and vice versa. We demonstrate that an even or odd coherent state of the quantum probe field can produce a multipartite entangled coherent state. We show that the concurrence reaches its maximal value at an optimal medium length that is determined by the magnitude of the Raman coherence and the orders of the Raman sidebands.

We use the quantum theory of cascaded open systems to calculate the transmitted photon flux for a weak beam of photons from a cavity QED laser strongly focused onto a single, resonant two-state atom in the narrow-bandwidth limit. We study the dependence of the transmitted flux on the quantum statistics of the incident light. Both bunched and antibunched light generated by the microlaser are considered as input. Working within and outside the semiclassical perturbative regime, we explicitly demonstrate that the normalized transmitted photon flux may coincide with the second-order correlation function of the incident bunched light, but not for incident antibunched light both of which are generated by a cavity QED laser. Interestingly, the thresholdless cavity QED laser is ideal for investigating statistical saturation effects by virtue of its small system size and the large quantum fluctuations accompanying it. It has the advantage of characterizing to a certain extent the quantum noise responsible for the statistical saturation. One can also easily vary the degree of antibunching of the incident light by manipulating the pumping rate of the laser.

We give a description of balanced homodyne detection (BHD) using a conventional laser as a local oscillator (LO), where the laser field outside the cavity is a mixed state whose phase is completely unknown. We apply our description to continuous-variable quantum teleportation (CVQT) with a laser, and show that CVQT with a laser is valid only if the unknown phase of the laser field is shared among sender’s LOs, the EPR state, and receiver’s LO. We also propose a method to generate a strongly phase-correlated quantum state necessary for CVQT without an additional optical path.

We report on high-resolution two-color photoassociation spectroscopy in the triplet system of magneto-optically trapped ${}^6\mathrm{Li}.$ Photoassociation is induced from the ground-state asymptote to the $v=59\mathrm{}$ level of the excited $1{}^3{\Sigma }_g^{+}$ state. This level is coupled to the $v=9\mathrm{}$ level of the triplet ground state $a{}^3{\Sigma }_u^{+}$ by the light field of a Raman laser. The absolute transition frequencies are measured with an iodine frequency standard and the binding energy of the ground state is determined to be $24.391\pm 0.020\mathrm{GHz}.$ Strong coupling of the bound molecular states has been observed as Autler-Townes splitting in the photoassociation signal for different detunings of the Raman laser. From the splitting we determine the spontaneous bound-bound decay rate to be $4.3\times {10}^5{\mathrm{s}}^{-1}$ and estimate the molecule formation rate. The observed line shapes are in good agreement with the theoretical model.

We present a time-dependent perturbative approach adapted to the treatment of intense pulsed interactions. We show there is a freedom in choosing secular terms and use it to optimize the accuracy of the approximation. We apply this formulation to a unitary superconvergent technique and improve the accuracy by several orders of magnitude with respect to the Magnus expansion.