We investigate the cooling of trapped atoms by electromagnetically induced transparency under conditions of weak confinement and beyond the Lamb-Dicke limit, i.e., the spontaneous decay width is large compared to the trap oscillation frequency and the recoil energy is a substantial fraction of the vibrational energy spacing of the trap. Numerical solutions of the Liouville equation for a density matrix describing states of vibrational and electronic degrees of freedom show that vibrational cooling is feasible at even substantial values of the Lamb-Dicke parameter and under conditions of weak confinement, a situation where sideband pumping is inefficient. Our approach permits us to predict cooling efficiency and cooling rates under realistic experimental conditions for neutral atoms in optical dipole traps.

We investigate two-species Bose gases in traps with various interactions using variational quantum Monte Carlo (VMC) techniques at zero temperature. The bosons are represented by hard spheres whose diameter is equivalent to the $s$-wave scattering length in the low-energy and long-wavelength approximation. We explore the role of repulsive and attractive interspecies or intraspecies interactions on the condensate properties of the mixtures, particularly the condensate fraction of each species as compared to the case when each species is in a separate trap of its own. We model the repulsive interactions by a hard-core (HC) potential and the attractive interactions by a shallow model potential. The VMC density profiles and energies are evaluated at various interactions and two mass ratios of the species.

We present an approach of the kicked-rotor quantum resonances in position space, based on its analogy with the optical Talbot effect. This leads to a very simple picture of the physical mechanism underlying the dynamics and to analytical expressions for relevant physical quantities. The ballistic behavior, which is closely associated with quantum resonances, is analyzed and shown to emerge from a coherent adding of successive kicks thanks to a periodic reconstruction of the spatial wave packet.

We consider a system of repulsively interacting Bose-Fermi mixtures of spin-polarized uniform atomic gases at zero temperature. We examine possible realization of $p$-wave superfluidity of fermions due to an effective attractive interaction via density fluctuations of Bose-Einstein condensate within mean-field approximation. We find the ground state of the system by direct energy comparison of the $p$-wave superfluid state in a single uniform mixed phase and normal Fermi gas state in a phase-separated phase, and suggest an occurrence of the $p$-wave superfluidity for a strong boson-fermion interaction regime. We study some signatures of the $p$-wave superfluid, such as anisotropic energy gap and quasiparticle energy in the axial state, that have not been observed in spin-unpolarized superfluid of atomic fermions. We also show that a Cooper pair is a tightly bound state, such as a diatomic molecule in the strong boson-fermion coupling regime, and suggest an observable indication of the $p$-wave superfluid in the real experiment.

A method is described which elucidates propagation of an electromagnetic field generated by a stochastic, electromagnetic source within the short wavelength limit. The results can be used to determine statistical properties of fields using ray tracing methods.

The validity of the work by Lamata et al. [Phys. Rev. Lett. 98, 253005 (2007)] can be further shown by quantum field-theory considerations.

We show that a laser pulse designed as an adiabatic ramp followed by a kick allows one to reach a perfect postpulse molecular alignment, free of saturation. The mechanism is based on an optimized distribution of the energy between a weakly efficient but nonsaturating adiabatic ramp and an efficient but saturating impulsive field. Unprecedented degrees of alignment are predicted using state-of-the-art pulse shaping techniques and nondestructive field intensities. The scheme can be extended to reach high degrees of orientation of polar molecules using designed half-cycle pulses.

The study of ultracold optically trapped atoms has opened new vistas in the physics of correlated quantum systems. Much attention has now turned to mixtures of bosonic and fermionic atoms. A central puzzle is the disagreement between the experimental observation of a reduced bosonic visibility ${\mathcal{V}}_b$, and quantum Monte Carlo (QMC) calculations which show ${\mathcal{V}}_b$ increasing. In this paper, we present QMC simulations which evaluate the density profiles and ${\mathcal{V}}_b$ of mixtures of bosons and fermions in one-dimensional optical lattices. We resolve the discrepancy between theory and experiment by identifying parameter regimes where ${\mathcal{V}}_b$ is reduced, and where it is increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott-insulating domains before and after the fermions are included. Finally, we show that ${\mathcal{V}}_b$ exhibits kinks which are tied to the domain evolution present in the pure case, and also additional structure arising from the formation of boson-fermion molecules, a prediction for future experiments.

We introduce several possible generalizations of tomography to curved surfaces. We analyze different types of elliptic, hyperbolic, and hybrid tomograms. In all cases it is possible to consistently define the inverse tomographic map. We find two different ways of introducing tomographic sections. The first method operates by deformations of the standard Radon transform. The second method proceeds by shifting a given quadric pattern. The most general tomographic transformation can be defined in terms of marginals over surfaces generated by deformations of complete families of hyperplanes or quadrics. We discuss practical and conceptual perspectives and possible applications.

An iterative algorithm for state determination, that uses as physical input the probability distributions for the eigenvalues of two or more observables in an unknown state $\Phi$ is presented. Starting from an arbitrary state ${\Psi }_0$, a succession of states ${\Psi }_n$ is obtained that converges to $\Phi$ or to a Pauli partner. This algorithm for state reconstruction is efficient and robust as is seen in the numerical tests presented and is a useful tool not only for state determination but also for the study of Pauli partners. Its main ingredient is the physical imposition operator that changes any state to have the same physical properties, with respect to an observable, of another state.

We address the problem of unambiguous discrimination and identification among quantum observables. We set a general framework and investigate in detail the case of qubit observables. In particular, we show that perfect discrimination with two shots is possible only for sharp qubit observables (e.g., Stern-Gerlach apparatuses) associated with mutually orthogonal directions. We also show that for sharp qubit observables associated to nonorthogonal directions unambiguous discrimination with an inconclusive result is always possible.

The focusing of coherent light, modified by a spatial light modulator (SLM) based 4-$f$ pulse shaper, is discussed in the context of scalar diffraction theory. Diffractive effects (including space-time coupling) in SLMs may alter the size and shape of a subsequent laser focus. A numerical approach is used to investigate the effects of some common phase masks on the properties of the laser focus. The extreme case of an alternating phase mask is considered in some detail, as it clearly illustrates the effects of space-time coupling. The results are compared to a simple analytic model. The potential influence of SLM diffractive effects on multiphoton quantum control studies is discussed and some approaches to minimizing undesirable diffractive effects are suggested.

We theoretically study the influence of Coulomb potential for photoionization of hydrogen atoms in an intense laser field with elliptical polarization. The total ionization rates, photoelectron energy spectra, and photoelectron angular distributions are calculated with the Coulomb-Volkov wave functions in the velocity gauge and compared with those calculated in the length gauge as well as those calculated with the Volkov wave functions. By comparing the results obtained by the Coulomb-Volkov and Volkov wave functions, we find that for linear polarization the influence of Coulomb potential is obvious for low-energy photoelectrons, and as the photoelectron energy and/or the laser intensity increase, its influence becomes smaller. This trend, however, is not so clear for the case of elliptical polarization. We also find that the twofold symmetry in the photoelectron angular distributions for elliptical polarization is caused by the cooperation of Coulomb potential and interference of multiple transition channels. About the gauge issue, we show that the difference in the photoelectron angular distributions obtained by the velocity and length gauges becomes rather obvious for elliptical polarization, while the difference is generally smaller for linear polarization.

With full consideration given to symmetry, we derive an exact analytical formula governing the evolution of the average populations of the spin components for spin-1 condensates. Based on the formula, a number of peculiarities of the evolution can be better understood. Our numerical results are consistent with existing experimental data. A special initial state is found; starting from this state, the average populations remain constant during a very long time, much longer than the duration observed during experiments.

We discuss several possible experimental signatures of the Bose-Einstein condensation (BEC) transition for an ultracold Bose gas in an inhomogeneous optical lattice. Based on the commonly used time-of-flight imaging technique, we show that the momentum-space density profile in the first Brillouin zone, supplemented by the visibility of interference patterns, provides valuable information about the system. In particular, by crossing the BEC transition temperature, the appearance of a clear bimodal structure sets a qualitative and universal signature of this phase transition. Furthermore, the momentum distribution can also be applied to extract the condensate fraction, which may serve as a promising thermometer in such a system.

We present a theoretical model for electromagnetically induced transparency (EIT) in vapor that incorporates atomic motion and velocity-changing collisions into the dynamics of the density-matrix distribution. Within a unified formalism, we demonstrate various motional effects, known for EIT in vapor: Doppler broadening of the absorption spectrum; Dicke narrowing and time-of-flight broadening of the transmission window for a finite-sized probe; diffusion of atomic coherence during storage of light and diffusion of the light-matter excitation during slow-light propagation; and Ramsey narrowing of the spectrum for a probe and pump beams of finite size.

A scheme is presented for the teleportation of an unknown atomic state between two separated cavities. The scheme involves two interaction-detection cycles and uses resonantly coupled atoms with an additional ground state not coupled to the cavity field. Remarkably, the damping of one basis state is balanced by that of the other basis state and the state with photon loss in the first interaction-detection cycle is eliminated by the second cycle. Therefore, the fidelity of teleportation is independent of the teleported state and insensitive to the atomic spontaneous emission, cavity decay, and detection inefficiency, which is obviously in contrast to the original scheme by Bose et al. [Phys. Rev. Lett. 83, 5158 (1999)].

An experimental scheme is proposed that allows direct measurement of the concurrence of a two-qubit cavity system. It is based on the cavity-QED technology using atoms as flying qubits and relies on the identity of the two-particle visibility of the atomic probability with the concurrence of the cavity system. The scheme works for any arbitrary pure initial state of the two-qubit cavity system.

We propose a scheme to generate four-photon polarization-entangled states, which enables the encoding of an arbitrary qubit into a four-qubit decoherence-free subspace robust against collective decoherence. The scheme is based on linear optical elements and postselection strategy, which is feasible with existing experimental technology.

We generalize in higher dimensions the so-called “flying-qubit scheme” that was described in the paper by Lim, Beige, and Kwek [Phys. Rev. Lett. 95, 030505 (2005)]. In that paper, the authors proposed a scheme according to which distant atoms get entangled during a measurement, in the Bell basis, of photons (flying qubits) emitted by them. We show that although in principle a generalization of this scheme to arbitrary dimensions is possible, this theoretical proposal is not presently feasible in all dimensions because only qubit Bell states have been successively measured until now. Nevertheless we show that a many-qubits generalization of the flying-qubit scheme factorizes and reduces to the realization, in parallel, of many individual single-qubit schemes, for which it is known that they are realizable experimentally with the techniques that are available today. In other words, our approach shows that when $d$ is an even prime power $\left(d=2^m\right)$, the flying-qudit scheme reduces to $m$ flying-qubit schemes. For $d=2^m$ and arbitrary $m$ the implementation of a generalized, maximally entangling, conditional qudit phase gate “with insurance” or “repeat-until-success” is thus shown to be feasible in practice by coupling $m$ (pairs of) two-level atoms to $m$ (pairs of) two-level (polarized) photons. Moreover, due to the parallelism of the task, the time necessary for completing successfully the task scales logarithmically in a function of $m$ while at the same time the dimension of the Hilbert space scales exponentially which presents promising perspectives regarding quantum informational realizations such as the quantum computer.