We present an analytical study of the response of cold atoms in an optical lattice to a weak time- and space-asymmetric periodic driving signal. In the noninteracting limit, and for a finite set of resonant frequencies, we show how a coherent, long-lasting ratchet current results from the interference between first- and second-order processes. In those cases, a suitable three-level model can account for the entire dynamics, yielding surprisingly good agreement with numerically exact results for weak and moderately strong driving.

We investigate the dynamics of matter and optical waves at the early stage of superradiant Rayleigh scattering from Bose-Einstein condensates. Our analysis is within a spatially dependent quantum model which is capable of providing analytic solutions for the operators of interest. The predictions of the present model are compared to the predictions of a closely related mean-field model, and we provide a procedure that allows one to calculate quantum expectation values by averaging over semiclassical solutions. The coherence properties of the outgoing scattered light are also analyzed, and it is shown that the corresponding correlation functions may provide detailed information about the internal dynamics of the system.

We investigate spatial optical solitons propagating in a medium with a saturable but adjustable nonlinearity and a fixed degree of nonlocality. We employ nematic liquid crystals in a planar cell with optical properties tuned by an external voltage and solitons excited in the near infrared. We also demonstrate soliton self-bending versus excitation due to nonlinear variations in walk-off. A theoretical model accounting for the longitudinal derivatives is employed to compute the refractive index distribution and is found in excellent agreement with the experimental data.

The use of a dynamic “accordion” lattice with ultracold atoms is demonstrated. Ultracold atoms of ${}^{87}\mathrm{Rb}$ are trapped in a two-dimensional optical lattice, and the spacing of the lattice is then increased in both directions from 2.2 to 5.5 $\mu$m. Atoms remain bound for expansion times as short as a few milliseconds, and the experimentally measured minimum ramp time is found to agree well with numerical calculations. This technique allows an experiment such as quantum simulations to be performed with a lattice spacing smaller than the resolution limit of the imaging system, while allowing imaging of the atoms at individual lattice sites by subsequent expansion of the optical lattice.

We study the non-Markovian entanglement dynamics of two qubits in a common squeezed bath. We see a remarkable difference between the non-Markovian entanglement dynamics and its Markovian counterpart. We show that a non-Markovian decoherence-free state is also decoherence free in the Markovian regime, but all the Markovian decoherence-free states are not necessarily decoherence free in the non-Markovian domain. We extend our calculation from a squeezed vacuum bath to a squeezed thermal bath, where we see the effect of finite bath temperatures on the entanglement dynamics.

Anholonomies in eigenstates are studied through time-dependent variations of a magnetic flux in an Aharonov-Bohm ring. The anholonomies in the eigenenergy and the expectation values of eigenstates are shown to persist beyond the adiabatic regime. The choice of the gauge of the magnetic flux is shown to be crucial to clarify the relationship of these anholonomies to the eigenspace anholonomy, which is described by a non-Abelian connection in the adiabatic limit.

A momentum representation treatment of the hydrogen atom problem with a generalized uncertainty relation, which leads to a minimal length $\left(\Delta X_i\right){}_{min}=\hslash \sqrt{3\beta +{\beta }^{\prime }}$, is presented. We show that the distance squared operator can be factorized in the case ${\beta }^{\prime }=2\beta$. We analytically solve the $s$-wave bound-state equation. The leading correction to the energy spectrum caused by the minimal length depends on $\sqrt{\beta }$. An upper bound for the minimal length is found to be about ${10}^{-9}\hspace{0.5em}\mathrm{fm}$.

Recently it was pointed out that transition frequencies in certain diatomic molecules have an enhanced sensitivity to variations in the fine-structure constant $\alpha$ and the proton-to-electron mass ratio $m_p/m_e$ due to a near cancellation between the fine structure and vibrational interval in a ground electronic multiplet [V. V. Flambaum and M. G. Kozlov, Phys. Rev. Lett. 99, 150801 (2007)]. One such molecule possessing this favorable quality is silicon monobromide. Here we take a closer examination of SiBr as a candidate for detecting variations in $\alpha$ and $m_p/m_e$. We analyze the rovibronic spectrum by employing the most accurate experimental data available in the literature and perform ab initio calculations to determine the precise dependence of the spectrum on variations in $\alpha$. Furthermore, we calculate the natural linewidths of the rovibronic levels, which place a fundamental limit on the accuracy to which variations may be determined.

We consider an atomic frequency comb based quantum memory inside an asymmetric optical cavity. In this configuration it is possible to absorb the input light completely in a system with an effective optical depth of one, provided that the absorption per cavity round trip exactly matches the transmission of the coupling mirror (“impedance matching”). We show that the impedance matching results in a readout efficiency only limited by irreversible atomic dephasing, whose effect can be made very small in systems with large inhomogeneous broadening. Our proposal opens up an attractive route toward quantum memories with close to unit efficiency.

Effective multimode photon echo quantum memory on multiatomic ensemble in the QED cavity is proposed. We obtain the analytical solution for the quantum memory efficiency that can be equal to unity when optimal conditions for the cavity and atomic parameters are held. Detailed analysis of the optimal conditions is performed. Numerical estimation for realistic atomic and cavity parameters demonstrates the high efficiency of the quantum memory for an optically thin resonant atomic system that opens a door for real applications.

The dynamical creation of entanglement between three-level atoms coupled to the common vacuum is investigated. For the class of bound entangled initial states, we show that the dynamics of closely separated atoms generates stationary distillable entanglement of asymptotic states. We also find that the effect of delayed sudden birth of distillable entanglement occurs in the case of atoms separated by a distance comparable with the radiation wavelength.

We investigate the conditions under which a set $\mathcal{S}$ of pure bipartite quantum states on a $D\times D$ system can be locally cloned deterministically by separable operations, when at least one of the states is full Schmidt rank. We allow for the possibility of cloning using a resource state that is less than maximally entangled. Our results include that: (i) all states in $\mathcal{S}$ must be full Schmidt rank and equally entangled under the $G$-concurrence measure, and (ii) the set $\mathcal{S}$ can be extended to a larger clonable set generated by a finite group $G$ of order $\left|G\right|=N$, the number of states in the larger set. It is then shown that any local cloning apparatus is capable of cloning a number of states that divides $D$ exactly. We provide a complete solution for two central problems in local cloning, giving necessary and sufficient conditions for (i) when a set of maximally entangled states can be locally cloned, valid for all $D$; and (ii) local cloning of entangled qubit states with nonvanishing entanglement. In both of these cases, we show that a maximally entangled resource is necessary and sufficient, and the states must be related to each other by local unitary “shift” operations. These shifts are determined by the group structure, so need not be simple cyclic permutations. Assuming this shifted form and partially entangled states, then in $D=3$ we show that a maximally entangled resource is again necessary and sufficient, while for higher-dimensional systems, we find that the resource state must be strictly more entangled than the states in $\mathcal{S}$. All of our necessary conditions for separable operations are also necessary conditions for local operations and classical communication (LOCC), since the latter is a proper subset of the former. In fact, all our results hold for LOCC, as our sufficient conditions are demonstrated for LOCC, directly.

Recent progress in theories of quantum information has determined nonclassical correlation defined differently from the widely used entanglement as an important property to evaluate computation and communication with mixed quantum states. We introduce an operational method to detect nonclassical correlation of bipartite systems. In this method, we use particular maps analogous to the well-established entanglement witnesses. Thus, the maps are called nonclassical correlation witness maps. Furthermore, it is proved that such a map can be generally decomposed so that a single-run experiment is feasible for implementation in bulk-ensemble systems.

In this work, Rydberg energy levels of the triatomic hydrogen molecule (${\mathrm{H}}_3$) are studied with multichannel quantum-defect theory. We extract the body-frame $p$-wave quantum defects from highly accurate ab initio electronic potential surfaces and calculate the quantum defects of higher angular-momentum states in a long-range multipole potential model. Laboratory-frame quantum-defect matrices emerge from a rovibrational-frame transformation carried out with accurate rovibrational states of ${\mathrm{H}}_3^{+}$. Finally, we use the laboratory-frame quantum defects to calculate Rydberg energy levels for the fundamental neutral triatomic molecule ${\mathrm{H}}_3$.

We introduce the second Born dipole corrections in our recently developed ab initio procedure based on the driven Schrödinger equation formalism and the external scaling method for the determination of the multifold differential cross sections of the single and double ionization of molecular hydrogen by electron impact. To test our procedure, we first apply it to the excitation-ionization process of a He atom and compare the results to those of equivalent theoretical results, which are available. We then show that the introduction of the second Born correction including only dipole terms improves the agreement with the experimental results only in the case of the simple ionization. We think that the introduction of nondipole contributions in the second Born term which are not taken into account in the present work is necessary in the case of the double ionization process.

We demonstrate the strong dependence of the Pancharatnam phase and the excited-state population of a single trapped ion on the laser intensity and phase shift. The simulation demonstrates that there is an enhancement of the Pancharatnam phase sensitivity to the phase shift compared with imposition of population behavior, suggesting a method of controlling qubit dynamics. Moreover, we investigate how the Stark shift influences the behavior of both the Pancharatnam phase and the population.

Motivated by recent progress in trapping Bose-Einstein-condensed atoms in toroidal potentials, we examine solitary-wave solutions of the nonlinear Schrödinger equation subject to periodic boundary conditions. When the circumference of the ring is much larger than the size of the wave, the density profile is well approximated by that of an infinite ring; however, the density and the velocity of propagation cannot vanish simultaneously. When the size of the ring becomes comparable to the size of the wave, the density variation becomes sinusoidal and the velocity of propagation saturates to a constant value.

We examine the dynamics of counterpropagating self-induced transparency solitons in three-level media. In a multilevel system, self-induced transparency gives rise to soliton solutions if the propagation is unidirectional, but the collision of counterpropagating pulses destroys the integrability of the underlying equations. We consider the collision of a rightward and a leftward moving self-induced transparency solitary wave by solving the full Maxwell-Bloch equations numerically using a finite-difference time-domain approach. Depending on pulse duration, amplitude and relative polarizations of the initial solitary waves we observe different regimes of interaction. For high group velocities and orthogonal polarizations, secondary solitary waves are born during the interaction, whereas the collision of solitary waves with the same polarization never produces secondary solitary waves but leaves behind a population grating in the interaction region. Because the crucial parameters can be controlled, an experimental confirmation of the predicted interaction regimes should be feasible.

Recently, the finite-number effect of initial atoms in coherent atom-molecule conversion was investigated by Zhao et al. [Phys. Rev. Lett. 101, 010401 (2008)]. Here, by extending to the atom-heteronuclear molecule dark state, we find that the initial populations imbalance of the atoms plays a significant role in quantum conversion rate and adiabatic fidelity. In particular, even for the finite total number of imbalanced two-species atoms, the mean-field conversion rate, contrary to the general belief, still can be remarkably close to the exact quantum results.