Characteristic functions are shown to be useful for highly sensitive measurements. Redistributions of motional Fock states of a trapped atom can be directly monitored via the most fragile nonclassical part of the characteristic function. The method can also be used for decoherence measurements in optical quantum-information systems.

A radially polarized beam focused by a high-numerical-aperture (NA) objective has a strong longitudinal and nonpropagating electric field in the focal region, which implies that it is suitable for axial optical trapping. In this paper, we use the vectorial diffraction integral to represent the field distribution of the radially polarized beam focused by a high-NA objective and then employ the $T$-matrix method to compute the radiation forces on spherical particles. Effects of different parameters, such as the size of the sphere, the inner radius of the radially polarized beam, and the NA of the objective, on the radiation forces are presented.

Subnatural linewidth in an optical transition in Cs was obtained by the suppression and recovery of the trapping of atoms. Cold Cs atoms in a magneto-optical trap (MOT) were irradiated using a weak probe laser to suppress MOT loading. When a counterpropagating coupling laser was directed to be resonant with the upper transition, the probe laser was induced to transmit and the MOT loading was recovered. This work investigates quantitatively this behavior by applying simulated electromagnetically induced transparency, taking into account the linewidth of the lasers as a decoherence source.

Using the local-density approximation and mean-field method, ultracold fermionic gases are studied under a nonuniform gradient magnetic field $\vec{B}=\left(B_0+\alpha z+\lambda z^2\right)\overrightarrow{e_x}$, where $B_0$ is the Feshbach resonant magnetic field, $\alpha$ and $\lambda$ are external parameters, $z$ is the spatial coordinate, and $\overrightarrow{e_x}$ is a unit vector pointing in the $x$ direction. In the case of thermal and chemical equilibrium, coexistence of the regimes of molecular Bose-Einstein condensation (BEC), Bardeen-Cooper-Schrieffer superfluid, and the unitarity limit is obtained. The relations between the particle density distribution in each state of matter and the magnetic field parameters are discussed. In particular, the effect of magnetic field on the molecular density distribution in the BEC state is analyzed. As a result, it is found that the range of BEC can be controlled by changing the parameter values of the magnetic field.

In a recent work [Phys. Rev. Lett. 98, 140402 (2007)] we defined “steering,” a type of quantum nonlocality that is logically distinct from both nonseparability and Bell nonlocality. In the bipartite setting, it hinges on the question of whether Alice can affect Bob’s state at a distance through her choice of measurement. More precisely and operationally, it hinges on the question of whether Alice, with classical communication, can convince Bob that they share an entangled state under the circumstances that Bob trusts nothing that Alice says. We argue that if she can, then this demonstrates the nonlocal effect first identified in the famous Einstein-Podolsky-Rosen paper [Phys. Rev. 47, 777 (1935)] as a universal effect for pure entangled states. This ability of Alice to remotely prepare Bob’s state was subsequently called steering by Schrödinger, whose terminology we adopt. The phenomenon of steering has been largely overlooked, and prior to our work had not even been given a rigorous definition that is applicable to mixed states as well as pure states. Armed with our rigorous definition, we proved that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. In this work we expand on these results and provide further examples of steerable states. We also elaborate on the connection with the original EPR paradox.

We study the analytically solvable Ising model of a single qubit system coupled to a spin bath. The purpose of this study is to analyze and elucidate the performance of Markovian and non-Markovian master equations describing the dynamics of the system qubit, in comparison to the exact solution. We find that the time-convolutionless master equation performs particularly well up to fourth order in the system-bath coupling constant, in comparison to the Nakajima-Zwanzig master equation. Markovian approaches fare poorly due to the infinite bath correlation time in this model. A recently proposed post-Markovian master equation performs comparably to the time-convolutionless master equation for a properly chosen memory kernel, and outperforms all the approximation methods considered here at long times. Our findings shed light on the applicability of master equations to the description of reduced system dynamics in the presence of spin baths.

In this paper we solve the following problem. Let ${\mathcal{H}}_{nm}$ be a Hilbert space of dimension $nm$, and let $A$ be a positive semidefinite self-adjoint linear operator on ${\mathcal{H}}_{nm}$. Under which conditions on the spectrum has $A$ a positive partial transpose (is PPT) with respect to any partition ${\mathcal{H}}_n\otimes {\mathcal{H}}_m$ of the space ${\mathcal{H}}_{nm}$ as a tensor product of an $n$-dimensional and an $m$-dimensional Hilbert space? We show that the necessary and sufficient conditions can be expressed as a set of linear matrix inequalities (LMIs) on the eigenvalues of $A$.

Doubly dressed states in a ladder-type two-photon, three-level coupling system are observed. The electromagnetically induced transparency (EIT) doublet signal is interpreted as arising from the absorption and gain components of the Mollow spectrum. The separation of the EIT doublet matches the theoretical prediction. A numerical simulation demonstrates that the Doppler velocity group may perturb the light shift from the symmetric center of the EIT doublet. The quantum nature of the EIT system significantly suppresses Doppler broadening.

Ultracold fermionic atomic gas with Bardeen-Cooper-Schrieffer pairing between hyperfine states is studied. It is shown that a $\pi$-Josephson contact [superfluid–normal-gas–superfluid $(S∕N∕S)$] can be realized in systems where the left and right banks $S$ are superfluids and the weak link $N$ is a normal gas with the finite mismatch in chemical potentials ${\delta }_{{\mu }_N}\ne 0$. If such a $\pi$-junction is part of a closed superfluid ring the superfluid mass-current flows spontaneously—the ultracold atomic $\pi$–superconducting quantum interference device ($\pi$-SQUID). This situation is realized if the radius of the ring $R$ is larger than the critical one $R_c$. The same effect will be realized also for ${\delta }_{{\mu }_N}⪢\Delta$, where $\Delta$ is the superfluid gap in S. The sensitivity of the $\pi$-SQUID to inertial effects is discussed in the case of rotational motion.

We use numerical optimization to study the properties of (1) the class of one-dimensional potential energy functions and (2) systems of point nuclei in two dimensions that yield the largest intrinsic hyperpolarizabilities, which we find to be within 30% of the fundamental limit. In all cases, we use a one-electron model. It is found that a broad range of optimized potentials, each of very different character, yield the same intrinsic hyperpolarizability ceiling of 0.709. Furthermore, all optimized potential energy functions share common features such as (1) the value of the normalized transition dipole moment to the dominant state, which forces the hyperpolarizability to be dominated by only two excited states and (2) the energy ratio between the two dominant states. All optimized potentials are found to obey the three-level ansatz to within about 1%. Many of these potential energy functions may be implementable in multiple quantum well structures. The subset of potentials with undulations reaffirm that modulation of conjugation may be an approach for making better organic molecules, though there appear to be many others. Additionally, our results suggest that one-dimensional molecules may have larger diagonal intrinsic hyperpolarizability ${\beta }_{xxx}^{\mathrm{int}}$ than higher-dimensional systems.

With a strongly nonlocal model, we present an analytical solution of the coherent interaction of two Gaussian beams with an arbitrary phase difference and arbitrary incident angles. Numerical simulations show that the analytical solution can describe the interaction of two Gaussian beams very well in the strongly nonlocal case. It is theoretically shown that one can steer lights in strongly nonlocal media by tuning the incident conditions of coherently interacting beams like the phase difference between beams and their relative amplitude.

Approximate solutions of $\left(1+2\right)$-dimensional strongly nonlocal solitons (SNSs) are presented. It is shown that the power of a SNS in a nematic liquid crystal is in direct proportion to the second power of the degree of nonlocality, the power of a SNS in a nonlocal medium with a logarithmic nonlocal response is in inverse proportion to the second power of its beamwidth, and the power of a SNS in a nonlocal medium with an $s\text{th}$-power decay nonlocal response is in direct proportion to the $\left(s+2\right)\text{th}$ power of the degree of nonlocality.

Numerical simulations have revealed that by adding a second harmonic field to a laser field with a time-dependent ellipticity, single isolated attosecond pulses can be generated as a result of the combined power of the two-color gating and the polarization gating. The duration of the pump laser applicable to this double optical gating scheme is a factor of 2 longer than that for the conventional polarization gating. Pulses with 200 attosecond duration can be generated from argon gas even with $10\mathrm{fs}$ lasers. It was discovered that the number of attosecond pulses and their intensities could be controlled by either the relative phase between the two color fields or the carrier-envelope phase.

We prove that it is possible to modify the stationary states of a quantum dynamical semigroup, describing the irreversible evolution of a two-level system, by means of an auxiliary two-level system, a quantum probe that can be suitably prepared. The target system and the probe can be initially entangled or uncorrelated. We find that this indirect control of the stationary states is possible, even if there are no initial correlations, under suitable conditions on the dynamical parameters characterizing the evolution of the joint system.

We propose a method to generate entangled coherent states between two spatially separated atomic Bose-Einstein condensates (BECs) via the technique of electromagnetically induced transparency (EIT). Two strong coupling laser beams and two entangled probe laser beams are used to cause two distant BECs to be in EIT states and to generate an atom-photon entangled state between probe lasers and distant BECs. The two BECs are initially in unentangled product coherent states while the probe lasers are initially in an entangled state. Entangled states of two distant BECs can be created through the performance of projective measurements upon the two outgoing probe lasers under certain conditions. Concretely, we propose two protocols to show how to generate entangled coherent states of the two distant BECs. One is a single-photon scheme in which an entangled single-photon state is used as the quantum channel to generate entangled distant BECs. The other is a multiphoton scheme where an entangled coherent state of the probe lasers is used as the quantum channel. Additionally, we also obtain some atom-photon entangled states of particular interest such as entangled states between a pair of optical Bell states (or quasi-Bell-states) and a pair of atomic entangled coherent states (or quasi-Bell-states).

We investigate cooling mechanisms in magneto-optically and magnetically trapped erbium. We find efficient sub-Doppler cooling in our trap, which can persist even in large magnetic fields due to the near degeneracy of two Landé $g$ factors. Furthermore, a continuously loaded magnetic trap is demonstrated where we observe temperatures below $25\mu \mathrm{K}$. These favorable cooling and trapping properties suggest a number of scientific possibilities for rare-earth-metal atomic physics, including narrow linewidth laser cooling and spectroscopy, unique collision studies, and degenerate bosonic and fermionic gases with long-range magnetic dipole coupling.

We study in detail coherent phase control of femtosecond resonance-mediated $\left(2+1\right)$ three-photon absorption and its dependence on the spectral bandwidth of the excitation pulse. The regime is the weak-field regime of third perturbative order. The corresponding interference mechanism involves a group of three-photon excitation pathways that are on resonance with the intermediate state and a group of three-photon excitation pathways that are near resonant with it. The model system of the study is atomic sodium (Na), for which experimental and numerical-theoretical results are obtained. Prominent among the results is our finding that with simple proper pulse shaping an increase in the excitation bandwidth leads to a corresponding increase in the enhancement of the three-photon absorption over the absorption induced by the (unshaped) transform-limited pulse. For example, here, a 40 nm bandwidth leads to an order-of-magnitude enhancement over the transform-limited absorption.

Bose-Einstein-condensed gases in external spatially random potentials are considered in the frame of a stochastic self-consistent mean-field approach. This method permits the treatment of the system properties for the whole range of the interaction strength, from zero to infinity, as well as for arbitrarily strong disorder. Besides a condensate and superfluid density, a glassy number density due to a spatially inhomogeneous component of the condensate occurs. For very weak interactions and sufficiently strong disorder, the superfluid fraction can become smaller than the condensate fraction, while at relatively strong interactions, the superfluid fraction is larger than the condensate fraction for any strength of disorder. The condensate and superfluid fractions, and the glassy fraction always coexist, being together either nonzero or zero. In the presence of disorder, the condensate fraction becomes a nonmonotonic function of the interaction strength, displaying an antidepletion effect caused by the competition between the stabilizing role of the atomic interaction and the destabilizing role of the disorder. With increasing disorder, the condensate and superfluid fractions jump to zero at a critical value of the disorder parameter by a first-order phase transition.

A coherence loss of an atomic wave scattered from the optical potential in an interferometer is observed. A Talbot-Lau atom interferometer is developed for that measurement using a laser-cooled lithium atomic beam. The long de Broglie wavelength of slow lithium atoms gives a short Talbot length and makes it possible to construct a small and stable atom interferometer.