We present measurements of the rate of hyperfine-state-changing collisions of unpolarized cesium $\left({}^{133}\mathrm{Cs}\right)$ and lithium $\left({}^7\mathrm{Li}\right)$ atoms confined in an optical dipole trap in the temperature range between 30 and $130\mu \mathrm{K}$. To infer rate coefficients from trap-loss data, we derive a simple thermodynamic model describing relaxation heating as a consequence of atom loss in a conservative potential. For hyperfine-changing $\mathrm{Cs}\text{−}\mathrm{Cs}$ collisions, the experimental results are compared with theoretical predictions and excellent agreement is found. Hyperfine-state-changing collisions in a mixture of lithium and cesium atoms are observed and rate coefficients are inferred for all combinations of hyperfine ground-state asymptotes.

In this work, we propose a modified continuum distorted wave (CDW) theory for ion-atom ionization that incorporates an electron effective-mass model for the bound electron-projectile distortion in the entrance channel. Distorted wave theories have been shown to be adequate when the projectile impact energy is high enough but, as the projectile velocity decreases, both CDW and continuum distorted wave–eikonal initial state (CDW-EIS) approximations exhibit remarkable discrepancies when compared with the available experimental data, in particular for highly charged ion impact. Our modified CDW approximation incorporates the active electron binding energy in the distorted wave description of the initial state. We found very good agreement with experimental data in a single ionization doubly differential cross section for multiply charged projectiles and impact energies as low as 50 keV∕amu.

The interaction of a two-level dipolar molecule with two laser pulses, where one laser’s frequency is tuned to the energy level separation (pump laser) while the second laser’s frequency is extremely small (probe laser), is investigated. A dipolar molecule is one with a nonzero difference between the permanent dipole moments of the molecular states. As shown previously [A. Brown, Phys. Rev. A 66, 053404 (2002)], the final population transfer between the two levels exhibits a dependence on the carrier-envelope phase of the probe laser. Based on the rotating-wave approximation (RWA), an effective Hamiltonian is derived to account for the basic characteristics of the carrier-envelope phase dependence effect. By analysis of the effective Hamiltonian, scaling properties of the system are found with regard to field strengths, pulse durations, and frequencies. According to these scaling properties, the final-state population transfer can be controlled by varying the carrier-envelope phase of the probe laser field using lasers with weak field strengths (low intensities) and relatively long pulse durations. In order to examine the possible roles of background states, the investigation is extended to a three-level model. It is demonstrated that the carrier-envelope phase effect still persists in a well-defined manner even when neighboring energy levels are present. These results illustrate the potential of utilizing excitation in dipolar molecules as a means of measuring the carrier-envelope phase of a laser pulse or if one can manipulate the carrier envelope phase, as a method of controlling population transfer in dipolar molecules. The results also suggest that the carrier-envelope phases must be taken into account properly when performing calculations involving pump-probe excitation schemes with laser frequencies which differ widely in magnitude.

The collective excitations in the Bose-Hubbard model in a trap are studied by means of numerical diagonalization in one dimension. The strength function is calculated for monopole and dipole perturbations, and moments of the strength function are utilized in order to obtain information about the collective behavior under external forces. In the superfluid regime, the spectrum is found to be exhausted by one single frequency, while in systems that contain a Mott insulating plateau, several frequencies are excited. An explanation of recent experimental findings in terms of a Mott plateau is suggested.

We study quantum chaos for systems with more than one degree of freedom, for which we present an analysis of the dynamics of entanglement. Our analysis explains the main features of entanglement dynamics and identifies entanglement-based signatures of quantum chaos. We discuss entanglement dynamics for a feasible experiment involving an atom in a magneto-optical trap and compare the results with entanglement dynamics for the well-studied quantum kicked top.

Generalizing the one-component case, we demonstrate that the propagation of sound waves in two-component Bose-Einstein condensates can also be described in terms of effective sonic geometries under appropriate conditions. In comparison with the one-component case, the two-component setup offers more flexibility and several advantages. In view of these advantages, we propose an experiment in which the evolution of the inflaton field, and thereby the generation of density fluctuations in the very early stages of our universe during inflation, can be simulated, realizing a quantum simulation via analogue gravity models.

The dynamics of stimulated emission in random lasers is studied using the system of rate equations for population inversion and density of emitted photons. In order to model the behavior of random lasers with nonresonant feedback, no coherence effects are intentionally taken into account. It has been shown that the feedback in the system is necessary for the realization of the regime of relaxation oscillations and spatial confinement of the stimulated emission to the interior regions of the pumped volume. The model also predicts the possibility of localization of stimulated emission in several spatially separated subvolumes of the random laser medium. Finally, it has been demonstrated that two adjacent random laser volumes can strongly enhance the stimulated emission in each other (the “critical mass” effect in random lasers).

Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. It has recently been shown that this problem is NP-hard, suggesting that an efficient, general solution does not exist. There is a highly inefficient “basic algorithm” for solving the quantum separability problem which follows from the definition of a separable state. By exploiting specific properties of the set of separable states, we introduce a classical algorithm that solves the problem significantly faster than the “basic algorithm,” allowing a feasible separability test where none previously existed, e.g., in $3\times 3$-dimensional systems. Our algorithm also provides a unique tool in the experimental detection of entanglement.

We study the effect of external trapping potentials on the phase diagram of bosonic atoms in optical lattices. We introduce a generalized Bose-Hubbard Hamiltonian that includes the structure of the energy levels of the trapping potential, and show that these levels are in general populated both at finite and zero temperature. We characterize the properties of the superfluid transition for this situation and compare them with those of the standard Bose-Hubbard description. We briefly discuss similar behaviors for fermionic systems.

Electromagnetically induced transparency in a four-level atomic system suppresses the linear susceptibility and enhances the nonlinear susceptibilities, which leads to the resonantly enhanced slow-light four-wave mixing at low light intensities. We report an experimental observation of such resonant four-wave mixing in cold Rb atoms.

The existence of image states in small clusters is shown, using a quantum-mechanical many-body approach. We present image state energies and wave functions for spherical jellium clusters up to 186 atoms, calculated in the $GW$ approximation, where $G$ is the Green’s function and $W$ is the dynamically screened Coulomb interaction, which by construction contains the dynamic long-range correlation effects that give rise to image effects. In addition, we find that image states are also subject to quantum confinement. To extrapolate our investigations to clusters in the mesoscopic size range, we propose a semiclassical model potential, which we test against our full $GW$ results.

This work explores the effect of phase relaxation on the population transfer efficiency in stimulated Raman adiabatic passage (STIRAP). The study is based on the Liouville equation, which is solved analytically in the adiabatic limit. The transfer efficiency of STIRAP is found to decrease exponentially with the dephasing rate; this effect is stronger for shorter pulse delays and weaker for larger delays, since the transition time is found to be inversely proportional to the pulse delay. Moreover, it is found that the transfer efficiency of STIRAP in the presence of dephasing does not depend on the peak Rabi frequencies at all, as long as they are sufficiently large to enforce adiabatic evolution; hence increasing the field intensity cannot reduce the dephasing losses. It is shown also that for any dephasing rate, the final populations of the initial state and the intermediate state are equal. For strong dephasing all three populations tend to $\frac{1}{3}$.

Nonadiabatic alignment of an asymmetric top molecule induced by a short, moderately intense laser pulse is studied theoretically and experimentally. Numerically, we solve nonperturbatively the time-dependent Schrödinger equation for a general asymmetric top molecule subject to a moderately intense laser field, and analyze the dependence of the alignment dynamics on the field strength and on the rotational temperature. Experimentally, we use time-resolved photofragment imaging to measure the time-dependent angular distributions of the spatial orientation of the molecules. Our studies, using iodobenzene as a test molecule, focus on the short-time alignment dynamics, during and after the pulse.

We investigate the dipole mode in a superfluid gas of Fermi atoms trapped in a harmonic potential. According to Kohn’s theorem, the frequency of this collective mode is not affected by an interaction between the atoms and is always equal to the trap frequency. This remarkable property, however, does not necessarily hold in an approximate theory. We explicitly prove that the Hartree-Fock-Bogoliubov generalized random phase approximation (HFB-GRPA), including a coupling between fluctuations in the density and Cooper channels, is consistent with both Kohn’s theorem as well as Goldstone’s theorem. This proof can be immediately extended to the strong-coupling superfluid theory developed by Noziéres and Schmitt-Rink (NSR), where the effect of superfluid fluctuations is included within the Gaussian level. As a result, the NSR-GRPA formalism can be used to study collective modes in the BCS-BEC crossover region in a manner which is consistent with Kohn’s theorem. We also include the effect of a Feshbach resonance and a condensate of the associated molecular bound states. A detailed discussion is given of the unusual nature of the Kohn mode eigenfunctions in a Fermi superfluid, in the presence and absence of a Feshbach resonance. When the molecular bosons feel a different trap frequency from the Fermi atoms, the dipole frequency is shown to depend on the strength of effective interaction associated with the Feshbach resonance.

We discuss cooling efficiency for different-species Fermi-Bose mixtures in magnetic traps. A better heat capacity matching between the two atomic species is achieved by a proper choice of the Bose cooler and the magnetically trappable hyperfine states of the mixture. When a partial spatial overlap between the two species is also taken into account, the deepest Fermi degeneracy is obtained for an optimal value of the trapping frequency ratio between the two species. This can be achieved by assisting the magnetic trap with a deconfining light beam, as shown in the case of fermionic ${}^6\mathrm{Li}$ mixed with ${}^{23}\mathrm{Na}$, ${}^{87}\mathrm{Rb}$, and ${}^{133}\mathrm{Cs}$, with optimal conditions found for the not yet explored ${}^6\mathrm{Li}‐{}^{87}\mathrm{Rb}$ mixture.

We present a photon-echo quantum memory technique for manipulating quantum states of photons interacting with an atomic gas medium. The technique offers vast potential for the complete nonlocal-in-time multipulse reconstruction of a stored light as a superposition of echo fields, irradiated from the medium at different moments of time. Using this technique the dynamic control of quantum states is effectively possible by simply varying the laser parameters.

A general prescription is presented for the semiclassical calculation of quantized energy levels of a class of parametric quantum systems. Starting with the Bohr-Sommerfeld quantization conditions of an exactly solvable system in parabolic coordinates, the calculation evolves the classical equations of motion while adiabatically introducing a nonzero parameter. We present accurate results for the quadratic Stark effect in addition to the linear Stark effect, an improvement over previous semiclassical studies.

We propose a way of universal quantum computation by doing joint measurements on distributed singlets. We show how these joint measurements become local measurements when the singlets are interpreted as the virtual components of a large valence-bond state. This proves the equivalence of the cluster-state-based quantum computational model and the teleportation-based model, and we discuss several features and possible extensions. We show that all stabilizer states have a very simple interpretation in terms of valence-bond solids, which allows to understand their entanglement properties in a transparent way.

Momentum distributions of electrons emitted from the $\mathrm{H}\left(1s\right)$ atom by linearly polarized, strong low-frequency laser pulses are studied. The origin of the double-peak structure observed in the distribution of the momentum parallel to the laser field polarization axis is investigated using a quasiclassical trajectory method including tunneling. We show that the double peak originates from the influence of the Coulomb force on the outgoing trajectories rather than from rescattering. Quasiclassical and quantum results agree qualitatively while differences resulting from interference effects are observed.

We present an all-electron ab initio study of multiphoton ionization (MPI) of diatomic molecules in intense laser pulses using the example of ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and ${\mathrm{F}}_2$, and the theoretical approach of time-dependent density-functional theory with correct long-range potential. The results reveal the importance of the electronic structure and correlated multielectron responses in the ionization mechanism, and make evident inner valence electron contributions to the molecular MPI in strong laser fields.