We calculate the critical temperature for Bose-Einstein condensation in a gas of bosonic atoms across a Feshbach resonance and show how medium effects at negative scattering lengths give rise to pairs reminiscent of the ones responsible for fermionic superfluidity. We find that the formation of pairs leads to a large suppression of the critical temperature. Within the formalism developed by Nozières and Schmitt-Rink, the gas appears mechanically stable throughout the entire crossover region, but when interactions between pairs are taken into account we show that the gas becomes unstable close to the critical temperature. We discuss prospects of observing these effects in a gas of ultracold ${}^{133}\text{C}\text{s}$ atoms where recent measurements indicate that the gas may be sufficiently long lived to explore the many-body physics around a Feshbach resonance.

We investigate a model of a two-component Bose-Einstein condensate residing in an optical lattice. Within a Bogoliubov approach at the mean-field level, we derive exact analytical expressions for the excitation spectrum of the two-component condensate when taking into account hopping and interactions between arbitrary sites. Our results thus constitute a basis for works that seek to clarify the effects of higher-order interactions in the system. We investigate the excitation spectrum and the two branches of superfluid velocity in more detail for two limiting cases of particular relevance. Moreover, we relate the hopping and interaction parameters in the effective Bose-Hubbard model to microscopic parameters in the system, such as the laser light wavelength and atomic masses of the components in the condensate. These results are then used to calculate analytically and numerically the drag coefficient between the components of the condensate. We find that the drag is most effective close to the symmetric case of equal masses between the components, regardless of the strength of the intercomponent interaction and the lattice well depth.

We study the interaction of two optical beams of different wavelengths (colors) in a nematic liquid crystal. We consider the case for which one component carries an optical vortex and the other component describes a localized beam. It is shown that a beam in one color can stabilize a vortex in the other color, the vortex being unstable in the absence of the second beam. We also show that the bright vortex can guide the beam in a stable manner, provided that the nonlocality is large enough. In this context we find that a different type of solitary wave (nematicon) instability can arise, one for which a ring structure develops at its peak. The results of approximate modulation solutions for the interaction between the vortex and the beam are found to be in good quantitative agreement with direct numerical simulations.

Results of variational computations of the triplet $2^{3}S$ state in beryllium atom and in some berylliumlike ions (${\text{O}}^{4+}$, ${\text{Ne}}^{6+}$, and ${\text{Mg}}^{8+}$) are presented. In each of these systems we determine numerically the total energies of the $2^{3}S$ state and various bound-state properties. Analytical formulas are derived for the $Z^{-1}\left(Q^{-1}\right)$ expansion of the total energies of the triplet $2^{3}S$ states in four-electron atomic systems. The hyperfine-structure splitting in this state is evaluated for the ${}^9\text{B}\text{e}$ atom.

We study the reduced fidelity between local states of lattice systems exhibiting topological order. By exploiting mappings to spin models with classical order, we are able to analytically extract the scaling behavior of the reduced fidelity at the corresponding quantum phase transitions out of the topologically ordered phases. Our results suggest that the reduced fidelity, albeit being a local measure, generically serves as an accurate marker of a topological quantum phase transition.

We propose an experimental procedure to cool fermionic atoms loaded into an optical lattice. The central idea is to spatially divide the system into entropy-rich and -poor regions by shaping the confining potential profile. Atoms in regions of high entropy per particle are subsequently isolated from the system. We discuss how to experimentally carry out this proposal and perform a quantitative study of its efficiency. We find that the entropy per particle, $s$, can typically be reduced by a factor of 10 such that entropies lower than $s/k_B\sim 0.2$ can be reached. Cooling into highly sought-after quantum phases (such as an antiferromagnet) can thus be achieved. We show that this procedure is robust against variations of the experimental conditions.

According to Hudson’s theorem, any pure quantum state with a positive Wigner function is necessarily a Gaussian state. Here, we make a step toward the extension of this theorem to mixed quantum states by finding upper and lower bounds on the degree of non-Gaussianity of states with positive Wigner functions. The bounds are expressed in the form of parametric functions relating the degree of non-Gaussianity of a state, its purity, and the purity of the Gaussian state characterized by the same covariance matrix. Although our bounds are not tight, they permit us to visualize the set of states with positive Wigner functions.

A beam splitter is one of the most important devices in an optics laboratory because of its handiness and versatility; equivalent devices are found in various quantum systems to couple two subsystems or to interfere them. While it is normal that two independent input fields are superposed at the beam splitter to give correlated outputs, identical Gaussian states interfere there to produce totally independent output fields. We prove that the Gaussian states with same variances are the only states which bring about factorizable output fields.

We theoretically study the influence of weak interactions on the diffusive expansion of a Bose-Einstein condensate in a three-dimensional random potential. For this purpose we develop a perturbative approach and calculate analytically the first-order nonlinear correction to the ensemble-averaged atomic density as a function of position and time. We find that interactions renormalize the typical diffusion coefficient of the condensate. The magnitude of the nonlinear correction is controlled by a single dimensionless parameter that includes both interaction and disorder strengths.

We measure the temperature of ultracold ${}^{87}\text{R}\text{b}$ gases transferred into an optical lattice and compare to noninteracting thermodynamics for a combined lattice-parabolic potential. Absolute temperature is determined at low temperature by fitting quasimomentum distributions obtained using band mapping, i.e., turning off the lattice potential slowly compared with the band gap. We show that distributions obtained at high temperature employing this technique are not quasimomentum distributions through numerical simulations. To overcome this limitation, we extract temperature using the in-trap size of the gas.

We study the critical velocity of a Bose-condensed gas in a moving one-dimensional optical lattice potential at finite temperatures. Solving the Gross-Pitaevskii equation and the Bogoliubov equations, within the Popov approximation, we calculate the Bogoliubov excitations with varying lattice velocity. From the condition of the negative excitation energy, we determine the critical velocity as a function of the lattice depth and the temperature. We find that the critical velocity decreases rapidly with increasing temperature; this result is consistent with the experimental observations. Moreover, the critical velocity shows a rapid decrease with increasing lattice depth. This tendency is much more significant than in the previous works ignoring the effect of thermal excitations in the radial direction.

We explore in this paper a harmonically trapped asymmetric fermionic superfluid in a two-dimensional optical lattice with pairing interactions between the neighboring sites, by self-consistently solving Bogliubov–de Gennes equations. We find the superfluid generally phase separates into a $d$-wave pairing component and an extended $s$-wave pairing one, mixed with the unpaired normal fermions. For sufficient large number asymmetries, the ground state is found to be a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state without fourfold rotational symmetry. Both the $d$-wave and $s$-wave order parameters show spatially varying novel patterns with nodal points or nodal lines. These features are expected to be checked by the experiments on the repulsive ultracold fermionic atoms.

The problem of the transcritical flow of a Bose-Einstein condensate through a wide repulsive penetrable barrier is studied analytically using the combination of the locally steady “hydraulic” solution of the one-dimensional Gross-Pitaevskii equation and the solutions of the Whitham modulation equations describing the resolution of the upstream and downstream discontinuities through dispersive shocks. It is shown that within the physically reasonable range of parameters, the downstream dispersive shock is attached to the barrier and effectively represents the train of very slow dark solitons, which can be observed in experiments. The rate of the soliton emission, the amplitudes of the solitons in the train, and the drag force are determined in terms of the Bose-Einstein condensate oncoming flow velocity and the strength of the potential barrier. Good agreement with direct numerical solutions is demonstrated. Connection with recent experiments is discussed.

The propagation and interaction of two-color vector solitary waves in a nematic liquid crystal in the nonlocal nonlinear response regime are investigated. Approximate modulation equations governing the evolution of the beams are derived based on a variational method. These modulation equations are then extended to include the effect of the diffractive radiation shed by the beams as they evolve. Agreement between the approximate solutions and full numerical solutions of the governing equations for the momentum deviation due to diffraction is excellent. Moreover, radiative losses are shown to play a far less significant role with respect to momentum deviation in comparison with the case for the local regime.

The propagation characteristics of a single-cycle pulse, at $0.8\mu \text{m}$ wavelength, are studied numerically in one spatial dimension. It is shown that Raman term does influence the propagation characteristics by counteracting the self-steepening effect.

Very accurate variational calculations of the fundamental pure vibrational transitions of the ${}^3\text{H}\text{e}{{}^4\text{H}\text{e}}^{+}$ and ${{}^7\text{L}\text{iH}}^{+}$ ions are performed within the framework that does not assume the Born-Oppenheimer (BO) approximation. The non-BO wave functions expanded in terms of one-center explicitly correlated Gaussian functions multiplied by even powers of the internuclear distance are used to calculate the leading relativistic corrections. Up to $10000$ Gaussian functions are used for each state. It is shown that the experimental ${}^3\text{H}\text{e}{{}^4\text{H}\text{e}}^{+}$ fundamental transitions is reproduced within $0.06{\text{cm}}^{-1}$ by the calculations. A similar precision is expected for the calculated, but still unmeasured, fundamental transition of ${{}^7\text{L}\text{iH}}^{+}$. Thus, three-electron diatomic systems are calculated with a similar accuracy as two-electron systems.

Fully classical three-dimensional ensembles are examined under conditions of nonsequential double ionization and are shown to have trajectories in which both electrons apparently ionize only to have one electron bound to the nucleus after the laser pulse. These trajectories feature recollision excitation with subsequent over-the-barrier ionization at about the laser maximum. The “ionized” electron oscillates in the laser field but has small enough drift velocity to be recaptured at laser turnoff. Whether recapture can occur is shown to have extreme sensitivity to conditions at ionization.

We consider the problem of quantum multiparameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for estimating multiple unknown parameters of a quantum process and apply this method to a realistic example. The example is two electron-spin qubits coupled through the dipole and exchange interactions with unknown coupling parameters—explicitly, the position vector relating the two qubits and the magnitude of the exchange interaction are unknown. This coupling Hamiltonian generates a unitary evolution which, when combined with arbitrary single-qubit operations, produces a universal set of quantum gates. However, the unknown parameters must be known precisely to generate high-fidelity gates. We use the Cramér-Rao bound on the variance of a point estimator to construct the optimal series of experiments to estimate these free parameters and present a complete analysis of the optimal experimental configuration. Our method of transforming the constrained optimal parameter estimation problem into a convex optimization is powerful and widely applicable to other systems.

There is an increasing interest in the use of the random-phase approximation (RPA) and extensions thereof to calculate ground-state correlation energies within the Kohn-Sham formalism. However, current implementations of these RPA-based functionals resort to the use of mean-field-like approximations when obtaining Kohn-Sham eigenorbitals and eigenenergies. In this paper we exactly calculate RPA and related results for a model system in which different correlation regimes can be easily addressed. We explore the reliability of such methods in the limit of strong interactions and pay special attention to the importance of a self-consistent resolution of the corresponding Kohn-Sham equations. In particular, we show that the self-consistent implementation of these methods provides accurate correlation energies and ground-state densities even when mean-field approximations dramatically fail.

The frequency of a laser diode is stabilized onto the line centers of double-resonance optical pumping spectra, and the absolute frequencies of the hyperfine-structure components of the $5P_{3/2}\text{−}4D_{3/2}$ excited-state transition for two isotopes of ${}^{87}\text{R}\text{b}$ and ${}^{85}\text{R}\text{b}$ atoms are measured using a fiber femtosecond frequency comb system. The $4D_{3/2}$ state hyperfine-structure constants of the two Rb isotopes are determined by utilizing the measured absolute optical frequency and the ratio of the hyperfine-structure constants for the two Rb isotopes from the accurately determined values of other states of rubidium. The magnetic-dipole constants $A$ are determined to be 24.75(12) MHz for ${}^{87}\text{R}\text{b}$ and 7.329(35) MHz for ${}^{85}\text{R}\text{b}$. The uncertainties of both results are reduced by one order compared to previous results. The electric-quadrupole constants $B$ are determined to be 2.19(11) and 4.52(23) MHz for ${}^{87}\text{R}\text{b}$ and ${}^{85}\text{R}\text{b}$, respectively