We investigate whether the force and torque exerted by light pressure on an irregularly shaped dielectric resonator allow to detect resonant frequencies, delivering information complemental to the scattering cross section by mechanical means. The peak-to-valley ratio in the torque signal can be many times larger than in the scattering cross section, and, furthermore, depends on the structure of the resonance wave pattern. The far-field emission pattern of the associated quasibound states can be tested by the angular dependence of the mechanical mechanical probes at finite amplification rate. We relate the force and torque to the scattering matrix and present numerical results for an annularly shaped dielectric resonator.

We report theoretical investigations pertaining to spectroscopy of pendular-state molecules, which are subjected to the large electrostatic interaction between the molecular dipole and a strong external field. After an appropriate coordinate transformation and a power-series expansion with an order parameter $\lambda$ that represents the degree of pendular condition, the zeroth-order Hamiltonian for the pendular limit has been derived. Motions of asymmetric tops in a high field are well described as two-dimensional anisotropic harmonic oscillations, and pendular-state quantum numbers have been introduced to label the energy levels. By using perturbative treatments, energies up to the ${\lambda }^0$ order are represented analytically with the pendular-state quantum numbers. Symmetry considerations are also accomplished by using the group theory appropriate to dipolar rigid bodies of symmetric and asymmetric tops in a uniform electric field. Energy levels and wave functions are classified into irreducible representations of the groups and selection rules for optical transitions are described. Energy-level correlations between the field-free and pendular conditions are also discussed on the basis of the group theoretical considerations. For symmetric and asymmetric tops, pendular-limit selection rules on the quantum numbers are derived by expanding the transition-dipole operators on $\lambda$, and transition strengths are analytically evaluated for all the excitation configurations with each of the transition types. Utilities of the present formulation have been verified by the comparison with exact model calculations based on the matrix diagonalization with a free-rotation basis set.

The kinetic theory of evaporative cooling developed by Luiten et al. [Phys. Rev. A 53, 381 (1996)] is extended to include the dependence of the elastic scattering cross section on collision energy. We introduce a simple approximation by which the transition range between the low-temperature limit and the unitarity limit is described as well. Applying the modified theory to our measurements on evaporative cooling of metastable helium, we find a scattering length $\mid a\mid =10\left(5\right)\mathrm{nm}$.

We study the equilibrium states of a vortex in a Bose-Einstein condensate in a one-dimensional optical lattice. We find that quantum effects can be important and that it is even possible for the vortex to be strongly squeezed, which reflects itself in a different quantum-mechanical uncertainty of the vortex position in two orthogonal directions. The latter is observable by measuring the atomic density after an expansion of the Bose-Einstein condensate in the lattice.

The group velocity of a light pulse propagating through a four-level system exhibiting electromagnetically induced transparency can be manipulated by a pump laser. The pump laser induces the large optical nonlinearities with steep normal or anomalous dispersion. We present experimental measurements that demonstrate both slow and superluminal light propagation in cold Rb atoms.

Ground-state quantum computers mimic quantum-mechanical time evolution within the amplitudes of a time-independent quantum state. We explore the principles that constrain this mimicking. A no-cloning argument is found to impose strong restrictions. It is shown, however, that there is flexibility that can be exploited using quantum teleportation methods to improve ground-state quantum computer design.

We pointed out that the nonadiabatic orientation of quantum rotors, produced by ultrashort laser pulses, is remarkably enhanced by introducing dipolar interaction between the rotors. This enhanced orientation of quantum rotors is in contrast with the behavior of classical paired rotors, in which dipolar interactions prevent the orientation of the rotors. We demonstrate also that a specially designed sequence of pulses can most efficiently enhance the orientation of quantum paired rotors.

In recent experiments on ultracold matter, molecules have been produced from ultracold atoms by photoassociation, Feshbach resonances, and three-body recombination. The created molecules are translationally cold, but vibrationally highly excited. This will eventually lead them to be lost from the trap due to collisions. We propose shaped laser pulses to transfer these highly excited molecules to their ground vibrational level. Optimal control theory is employed to find the light field that will carry out this task with minimum intensity. We present results for the sodium dimer. The final target can be reached to within $99\%$ provided the initial guess field is physically motivated. We find that the optimal fields contain the transition frequencies required by a good Franck-Condon pumping scheme. The analysis identifies the ranges of intensity and pulse duration which are able to achieve this task before any other competing processes take place. Such a scheme could produce stable ultracold molecular samples or even stable molecular Bose-Einstein condensates.

We build up simple models of quantum evolution showing that nonlinearity does not necessarily imply either the possibility of faster-than-light communications or the violation of the second law of thermodynamics. We offer counterexamples proving that conditions of no supraluminal communication considered in the literature as necessary and sufficient are actually only necessary. We formulate conditions and show that this preclusion only entails the linearity of reduced dynamics, thus reopening the possibility to unexplored nonlinear joint evolutions. We make constant use of the Bloch representation of finite-dimensional quantum systems to express our results.

The dynamics of linear and nonlinear excitations in a Bose gas in the Tonks-Girardeau regime with longitudinal confinement are studied within a mean-field theory of quintic nonlinearity. A reductive perturbation method is used to demonstrate that the dynamics of shallow dark solitons, in the presence of an external potential, can effectively be described by a variable-coefficient Korteweg–de Vries equation. The soliton oscillation frequency is analytically obtained to be equal to the axial trap frequency, in agreement with numerical predictions obtained by Busch et al. [J. Phys. B 36, 2553 (2003)] via the Bose-Fermi mapping. We obtain analytical expressions for the evolution of both soliton and emitted radiation (sound) profiles.

The existence of a possible connection between spin and statistics is explored within the framework of Galilean covariant field theory. To this end fields of arbitrary spin are constructed and admissible interaction terms introduced. By explicitly solving such a model in the two-particle sector it is shown that no spin and statistics connection can be established.

We calculated the charge-transfer cross sections for ${\mathrm{O}}^{8+}+\mathrm{H}$ collisions for energies from $1\mathrm{eV}∕\mathrm{amu}$ to $2\mathrm{keV}∕\mathrm{amu}$, using the recently developed hyperspherical close-coupling method. In particular, the discrepancy for electron capture to the $n=6$ states of ${\mathrm{O}}^{7+}$ from the previous theoretical calculations is further analyzed. Our results indicate that at low energies (below $100\mathrm{eV}∕\mathrm{amu}$) electron capture to the $n=6$ manifold of ${\mathrm{O}}^{7+}$ becomes dominant. The present results are used to resolve the long-standing discrepancies from the different elaborate semiclassical calculations near $100\mathrm{eV}∕\mathrm{amu}$. We have also performed the semiclassical atomic orbital close-coupling calculations with straight-line trajectories. We found the semiclassical calculations agree with the quantal approach at energy above $100\mathrm{eV}∕\mathrm{amu}$, where the collision occurs at large impact parameters. Calculations for ${\mathrm{Ar}}^{8+}+\mathrm{H}$ collisions in the same energy range have also been carried out to analyze the effect of the ionic core on the subshell cross sections. By using diabatic molecular basis functions, we show that converged results can be obtained with small numbers of channels.

We propose to utilize density-density correlations in the image of an expanding gas cloud to probe complex many-body states of trapped ultracold atoms. In particular, we show how this technique can be used to detect superfluidity of fermionic gases and to study spin correlations of multicomponent atoms in optical lattices. The feasibility of the method is investigated by analysis of the relevant signal to noise ratio including experimental imperfections.

We analytically show that it is possible to perform coherent imaging by using the classical correlation of two beams obtained by splitting incoherent thermal radiation. A formal analogy is demonstrated between two such classically correlated beams and two entangled beams produced by parametric down-conversion. Because of this analogy, the classical beams can mimic qualitatively all the imaging properties of the entangled beams, even in ways which up to now were not believed possible. A key feature is that these classical beams are spatially correlated both in the near field and in the far field. Using realistic numerical simulations the performances of a quasithermal and a parametric down-conversion source are shown to be closely similar, both for what concerns the resolution and statistical properties. The results of this paper provide a scenario for the discussion of what role the entanglement plays in correlated imaging.

We investigate the effects of spontaneous scattering on the evolution of entanglement of two atomic samples, probed by phase-shift measurements on optical beams interacting with both samples. We develop a formalism of conditional quantum evolutions and present a wave function analysis implemented in numerical simulations of the state vector dynamics. This method allows us to track the evolution of entanglement and to compare it with the predictions obtained when spontaneous scattering is neglected. We provide numerical evidence that the interferometric scheme to entangle atomic samples is only marginally affected by the presence of spontaneous scattering and should thus be robust even in more realistic situations.

A compete orthonormal basis of $N$-qutrit unitary operators drawn from the Pauli group consists of the identity and $9^N-1$ traceless operators. The traceless ones partition into $3^N+1$ maximally commuting subsets (MCS’s) of $3^N-1$ operators each, whose joint eigenbases are mutually unbiased. We prove that Pauli factor groups of order $3^N$ are isomorphic to all MCS’s and show how this result applies in specific cases. For two qutrits, the 80 traceless operators partition into 10 MCS’s. We prove that 4 of the corresponding basis sets must be separable, while 6 must be totally entangled (and Bell-like). For three qutrits, 728 operators partition into 28 MCS’s with less rigid structure, allowing for the coexistence of separable, partially entangled, and totally entangled (GHZ-like) bases. However a minimum of $16\mathrm{GHZ}$-like bases must occur. Every basis state is described by an $N$-digit trinary number consisting of the eigenvalues of $N$ observables constructed from the corresponding MCS.

A method of purification, purification through Zeno-like measurements [H. Nakazato, T. Takazawa, and K. Yuasa, Phys. Rev. Lett. 90, 060401 (2003)], is discussed extensively and applied to a few simple qubit systems. It is explicitly demonstrated how it works and how it is optimized. As possible applications, schemes for initialization of multiple qubits and entanglement purification are presented, and their efficiency is investigated in detail. Simplicity and flexibility of the idea allow us to apply it to various kinds of settings in quantum information and computation, and would provide us with useful and practical methods of state preparation.

The off-diagonal hyperfine interaction between the $6p_{1∕2}$ and $6p_{3∕2}$ states in ${}^{133}\mathrm{Cs}$ is evaluated in third-order MBPT giving $37.3$ and $48.3\mathrm{Hz}$, respectively, for second-order energies of the $6p_{3∕2}$ $F=3$ and $F=4$ levels. This result is a factor of 10 smaller than one obtained from an uncorrelated first-order Dirac–Hartree–Fock calculation and used in the analysis of a recent high-precision $(⩽2\mathrm{kHz})$ measurement of the $6p_{3∕2}$ hyperfine structure [Gerginov et al. Phys. Rev. Lett. 91, 72301 (2003)]. The factor of 10 difference has negligible effect on the conclusions of the recent experiment but will become important for experiments carried out at a precision of better than $1\mathrm{kHz}$.

Feshbach resonances are commonly described by a single-resonance Feshbach model, and open-channel resonances are not taken into account explicitly. However, an open-channel resonance near threshold limits the range of validity of this model. Such a situation exists when the background scattering length is much larger than the range of the interatomic potential. The open-channel resonance introduces strong threshold effects not included in the single-resonance description. We derive an easy-to-use analytical model that takes into account both the Feshbach resonance and the open-channel resonance. We apply our model to ${}^{85}\mathrm{Rb}$, which has a large background scattering length, and show that the agreement with coupled-channel calculations is excellent. The model can be readily applied to other atomic systems with a large background scattering length, such as ${}^6\mathrm{Li}$ and ${}^{133}\mathrm{Cs}$. Our approach provides full insight into the underlying physics of the interplay between open-channel (or potential) resonances and Feshbach resonances.

We construct a many-body Gaussian variational approach for the two-dimensional trapped Bose gas in the condensate phase. Interaction between particles is modelized by a generalized pseudopotential of zero range that allows recovering perturbative results in the ultradilute limit, while back action of noncondensate particles on the condensate part is taken into account for higher density. As an application, we derive the equation of state and solve stability problems encountered in similar mean-field formalisms for a single vortex configuration.