We propose an experimental scheme to realize the quantum anomalous Hall effect in an anisotropic square optical lattice which can be generated from available experimental setups of double-well lattices with minor modifications. A periodic gauge potential induced by atom-light interaction is introduced to give a Peierls phase for the nearest-neighbor site hopping. The quantized anomalous Hall conductivity is investigated by calculating the Chern number as well as the chiral gapless edge states of our system. Furthermore, we show in detail the feasability for its experimental detection through light Bragg scattering of the edge and bulk states with which one can determine the topological phase transition from usual insulating phase to quantum anomalous Hall phase.

We numerically investigate the damping of Bloch oscillations in a one-dimensional lattice potential whose translational symmetry is broken in a systematic manner, either by making the potential bichromatic or by introducing scatterers at distinct lattice sites. We find that the damping strongly depends on the ratio of lattice constants in the bichromatic potential and that even a small concentration of scatterers can lead to strong damping. Moreover, collisional interparticle interactions are able to counteract aperiodicity-induced damping of Bloch oscillations. The discussed effects should readily be observable for ultracold atoms in optical lattices.

This article develops a model that shows the effects of decoherence originating from both dephasing and population relaxation on rubidium vapor in the electromagnetically induced transparency regime. This article quantifies the effect of decoherence on the large Faraday rotation, susceptibility, transmission, population, and coherence relationships of the system. The model derived in this article is in excellent agreement with experimental results [H. Gao, M. Rosenberry, J. Wang, and H. Batelaan, J. Phys. B 38, 1857 (2005)]. The total decoherence rate for the experiment has been found by fitting the experimental data to the model. This article also includes a discussion of other types of experiments that this model could be adapted to, such as dipole-induced transmission and the detection of single atoms.

Millimeter-wave transitions between high-$n$ Rydberg states of several isotopes of xenon have been recorded at sub-megahertz resolution. The fine and, for ${}^{129}\mathrm{Xe}$ and ${}^{131}\mathrm{Xe}$, hyperfine structures of $s$, $p$, $d$, and $f$ Rydberg states with principal quantum number in the range $52⩽n⩽64$ have been determined from combination differences and analyzed using multichannel quantum defect theory. Improved eigenquantum defects and channel interaction parameters for the odd- and even-parity Rydberg states of xenon and the hyperfine structure of the ${}^2{P}_{3/2}$ ground state of ${}^{129}\mathrm{Xe}{}^{+}$ and ${}^{131}\mathrm{Xe}{}^{+}$ have been obtained. Nearly degenerate $p$ and $d$ fine or hyperfine levels are very easily mixed by even weak stray electric fields.

Results of calculations of the integrated cross section and the energy distribution for ionization of ground-state hydrogen by ${}^1\mathit{S}$-wave electron impact are presented. The breakup amplitude is expressed as a volume integral that contains an approximate final-state wave function which accounts for postcollision dynamic screening. The error in this wave function is accounted for by the response function, which is represented on a real discrete (Sturmian) basis, with its physical branch specified by the arrow of time. It is found that the energy distribution is primarily convex for impact energies from about $2$ to $10$ eV above threshold, and primarily flat from about $10$ to $20$ eV above threshold. The shape of the energy distribution appears to reflect both the competition between escape and recapture, and the substantial postcollision exchange of energy between the electrons. A rough, nonclassical criterion for predicting the curvature of the energy distribution is derived.

We analyze the dipole spectrum of a two-level atom excited by a nonresonant intense monochromatic field under the electric dipole approximation and beyond the rotating wave approximation. We show that the apparently complex spectral structure can be completely described by two families: harmonic frequencies of the driving field and field-induced nonlinear fluorescence. Our formulation of the problem provides quantitative laws for the most relevant spectral features: harmonic ratios and phases, nonperturbative Stark shift, and frequency limits of the harmonic plateau. In particular, we demonstrate the locking of the harmonic phases at the wings of the plateau opening the possibility of ultrashort pulse generation through harmonic filtering.

We theoretically investigate the scattering of bright solitons in a Bose-Einstein condensate on narrow attractive potential wells. Reflection, transmission, and trapping of an incident soliton are predicted to occur with remarkably abrupt transitions upon varying the potential depth. Numerical simulations of the nonlinear Schrödinger equation are complemented by a variational collective coordinate approach. The mechanism for nonlinear trapping is found to rely both on resonant interaction between the soliton and bound states in the potential well and on the radiation of small-amplitude waves. These results suggest that solitons can be used to probe bound states that are not accessible through scattering with single atoms.

We find the universal structure and scaling of the Bose-Einstein condensation (BEC) statistics and thermodynamics (Gibbs free energy, average energy, heat capacity) for a mesoscopic canonical-ensemble ideal gas in a trap with an arbitrary number of atoms, any volume, and any temperature, including the whole critical region. We identify a universal constraint-cutoff mechanism that makes BEC fluctuations strongly non-Gaussian and is responsible for all unusual critical phenomena of the BEC phase transition in the ideal gas. The main result is an analytical solution to the problem of critical phenomena. It is derived by, first, calculating analytically the universal probability distribution of the noncondensate occupation, or a Landau function, and then using it for the analytical calculation of the universal functions for the particular physical quantities via the exact formulas which express the constraint-cutoff mechanism. We find asymptotics of that analytical solution as well as its simple analytical approximations which describe the universal structure of the critical region in terms of the parabolic cylinder or confluent hypergeometric functions. The obtained results for the order parameter, all higher-order moments of BEC fluctuations, and thermodynamic quantities perfectly match the known asymptotics outside the critical region for both low and high temperature limits. We suggest two- and three-level trap models of BEC and find their exact solutions in terms of the cutoff negative binomial distribution (which tends to the cutoff gamma distribution in the continuous limit) and the confluent hypergeometric distribution, respectively. Also, we present an exactly solvable cutoff Gaussian model of BEC in a degenerate interacting gas. All these exact solutions confirm the universality and constraint-cutoff origin of the strongly non-Gaussian BEC statistics. We introduce a regular refinement scheme for the condensate statistics approximations on the basis of the infrared universality of higher-order cumulants and the method of superposition and show how to model BEC statistics in the actual traps. In particular, we find that the three-level trap model with matching the first four or five cumulants is enough to yield remarkably accurate results for all interesting quantities in the whole critical region. We derive an exact multinomial expansion for the noncondensate occupation probability distribution and find its high-temperature asymptotics (Poisson distribution) and corrections to it. Finally, we demonstrate that the critical exponents and a few known terms of the Taylor expansion of the universal functions, which were calculated previously from fitting the finite-size simulations within the phenomenological renormalization-group theory, can be easily obtained from the presented full analytical solutions for the mesoscopic BEC as certain approximations in the close vicinity of the critical point.

Recently, the Berezinskii-Kosterlitz-Thouless transition was found to be mediated by half-quantum vortices (HQVs) in two-dimensional (2D) antiferromagnetic Bose gases [S. Mukerjee, C. Xu, and J. E. Moore, Phys. Rev. Lett. 97, 120406 (2006)]. We study the thermal activation of HQVs in the experimentally relevant trapped quasi-2D system and find a crossover temperature at which free HQVs proliferate at the center of the trap. Above the crossover temperature, we observe transitions corresponding to the onset of a coherent condensate and a quasicondensate and discuss the absence of a fragmented condensate.

Based on the semiclassical theory, we investigate the thermodynamic properties of a dipolar Fermi gas. Through a self-consistent procedure, we numerically obtain the phase-space distribution function at finite temperature. We show that the deformations in both momentum and real space become smaller and smaller as the temperature is increased. For the homogeneous case, we also calculate pressure, entropy, and heat capacity. In particular, at the low-temperature limit and in the weak interaction regime, we obtain an analytic expression for the entropy which agrees qualitatively with our numerical result. The stability of a trapped gas at finite temperature is also explored.

By numerical simulations of the Gross-Pitaevskii mean-field equations, we show that the dynamical creation of stable complex vector solitons in a homogeneous spin-1 Bose-Einstein condensate can be achieved by applying a localized magnetic field for a certain duration, with the initial uniform density prepared differently for the formation of different vector solitons. In particular, it is shown that stable dark-bright-dark vector solitons, dark-bright-bright vector solitons, and other analogous solutions can be dynamically created. It is also found that the peak intensity and the group velocity of the vector solitons thus generated can be tuned by adjusting the applied magnetic field. Extensions of our approach also allow for the creation of vector-soliton chains or the pumping of many vector solitons. The results can be useful for possible vector-soliton-based applications of dilute Bose-Einstein condensates.

Variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the properties of the zero-temperature fermionic gas at unitarity are reported. Our study differs from earlier ones mainly in that we have constructed more accurate trial wave functions and used a larger system size, we have studied the dependence of the energy on the particle density and well width, and we have achieved much smaller statistical error bars. The correct value of the universal ratio of the energy of the interacting to that of the noninteracting gas, $\xi$, is still a matter of debate. We find DMC values of $\xi$ of $0.4244(1)$ with 66 particles and $0.4339(1)$ with 128 particles. The spherically averaged pair-correlation functions, momentum densities, and one-body density matrices are very similar in VMC and DMC, which suggests that our results for these quantities are very accurate. We find, however, some differences between the VMC and DMC results for the two-body density matrices and condensate fractions, which indicates that these quantities are more sensitive to the quality of the trial wave function. Our best estimate of the condensate fraction of 0.51 is smaller than the values from earlier quantum Monte Carlo calculations.

A rapidly rotating Bose-Einstein condensate in a symmetric two-dimensional harmonic trap can be described with the lowest Landau-level set of single-particle states. The condensate wave function $\psi (x,y)$ is a Gaussian $\propto \exp (-r^2/2)$, multiplied by an analytic function $f(z)$ of the complex variable $z=x+iy$. The criterion for a quantum phase transition to a non-superfluid correlated many-body state is usually expressed in terms of the ratio of the number of particles to the number of vortices. Here a similar description applies to a rapidly rotating nonsymmetric two-dimensional trap with arbitrary quadratic anisotropy (${\omega }_x^2<{\omega }_y^2$). The corresponding condensate wave function $\psi (x,y)$ is a complex anisotropic Gaussian with a phase proportional to $\mathit{xy}$, multiplied by an analytic function $f(z)$, where $z=x+i{\beta }_{-}y$ is a stretched complex variable and $0⩽{\beta }_{-}⩽1$ is a real parameter that depends on the trap anisotropy and the rotation frequency. Both in the mean-field Thomas-Fermi approximation and in the mean-field lowest Landau level approximation with many visible vortices, an anisotropic parabolic density profile minimizes the energy. An elongated condensate grows along the soft trap direction yet ultimately shrinks along the tight trap direction. The criterion for the quantum phase transition to a correlated state is generalized ($1$) in terms of $N/L_z$, which suggests that a nonsymmetric trap should make it easier to observe this transition, or ($2$) in terms of a “fragmented” correlated state, which suggests that a nonsymmetric trap should make it harder to observe this transition. An alternative scenario involves a crossover to a quasi one-dimensional condensate without visible vortices, as suggested by Aftalion et al., Phys. Rev. A 79, 011603(R) (2009).

We consider the absorption spectrum of a Fermi gas mixed with a minority species when majority fermions are transferred to another internal state by an external probe. In the limit when the minority species is much more massive than the majority one, we show that the minority species may be treated as static impurities and the problem can be solved in closed form. The analytical results bring out the importance of vertex corrections, which change qualitatively the nature of the absorption spectrum. It is demonstrated that large line shifts are not associated with resonant interactions in general. We also show that the commonly used ladder approximation fails when the majority component is degenerate for large mass ratios between the minority and majority species and that bubble diagrams, which correspond to the creation of many particle-hole pairs, must be taken into account. We carry out detailed numerical calculations, which confirm the analytical insights, and we point out the connection to shadowing phenomena in nuclear physics.

The generation of nonclassical states of light via photon blockade with time-modulated input is analyzed. We show that improved single-photon statistics can be obtained by adequately choosing the parameters of the driving laser pulses. An alternative method, where the system is driven via a continuous-wave laser and the frequency of the dipole is controlled (e.g., electrically) at very fast time scales is presented.

We propose a large low-loss cross-phase modulation between two coupled surface polaritons propagating through a double electromagnetically induced transparency medium situated close to a negative-index metamaterial. In particular, a mutual $\pi$ phase shift is attainable between the two pulses at the single-photon level.

We analyze optical soliton propagation in the presence of weak absorption lines with much narrower linewidths as compared to the soliton spectrum width by using a perturbation analysis technique based on an integral representation in the spectral domain. The stable soliton acquires a spectral modulation that follows the associated index of refraction of the absorber. The model can be applied to ordinary soliton propagation and to an absorber inside a passively mode-locked laser. In the latter case, a comparison with water vapor absorption in a femtosecond Cr:ZnSe laser yields a very good agreement with experiment. Compared to the conventional absorption measurements in a cell of the same length, the signal is increased by an order of magnitude. The obtained analytical expressions allow further improvement in the sensitivity and spectroscopic accuracy, which makes soliton absorption spectroscopy a promising measurement technique.

We report an experimental realization of ultracold atoms confined in a time-averaged, adiabatic potential (TAAP). This trapping technique involves using a slowly oscillating ($~$kHz) bias field to time-average the instantaneous potential given by dressing a bare magnetic potential with a high-frequency ($~$MHz) magnetic field. The resultant potentials provide a convenient route to a variety of trapping geometries with tunable parameters. We demonstrate the TAAP trap in a standard time-averaged orbiting potential trap with additional Helmholtz coils for the introduction of the radio frequency dressing field. We have evaporatively cooled $5\times {10}^4$ atoms of ${}^{87}\mathrm{Rb}$ to quantum degeneracy and observed condensate lifetimes of longer than $3$ s.

We propose to realize a $p$-wave superfluid using bosons mixed with a single species of fermions in a deep optical lattice. We analyze with a self-consistent method its excitation spectrum in presence of a vortex, and we point out the range of interaction strengths in which the zero-energy mode with topological character exists on a finite optical lattice. Lattice effects are strongest close to fermionic half filling: here the linearity of the low-lying spectrum is lost, and a new class of extended zero-energy modes with checkerboard structure and $d$-wave symmetry appears.

We perform numerical analysis of the first 20 and 14 coefficients for $1\hspace{0.5em}{}^{1}S$ and $2\hspace{0.5em}{}^{3}S$ states of the $1/Z$ expansion of the energy of two-electron atoms, respectively. The radius of convergence and large-order behavior of the coefficients are determined. The results obtained are in disagreement with those given so far in the literature. We sum the terms of the series with known coefficients and the remainder of the series where we replace the actual coefficients by their large-order values. We show that inclusion of the remainder improves agreement with variational results by more than three orders of magnitude. We argue that the energy is at least three times and most likely infinitely degenerate at the singularity. Numerical result for the effective characteristic polynomial supports this conclusion.