We introduce quantum walks with a time-dependent coin, and show how they include, as a particular case, the generalized quantum walk recently studied by Wojcik et al. [Phys. Rev. Lett. 93, 180601 (2004)] which exhibits interesting dynamical localization and quasiperiodic dynamics. Our proposal allows for a much easier implementation of this particularly rich dynamics than the original one. Moreover, it allows for an additional control on the walk, which can be used to compensate for phases appearing due to external interactions. To illustrate its feasibility, we discuss an example using an optical cavity. We also derive an approximated solution in the continuous limit (long-wavelength approximation) which provides physical insight about the process.

We propose a method for controlling a class of low temperature chemical reactions. Specifically, we show the hydrogen abstraction channel in the reaction of formaldehyde $\left({\mathrm{H}}_2\mathrm{CO}\right)$ and the hydroxyl radical $\left(\mathrm{OH}\right)$ can be controlled through either the molecular state or an external electric field. We also outline experiments for investigating and demonstrating control over this important reaction. To this end, we report the first Stark deceleration of ${\mathrm{H}}_2\mathrm{CO}$. We have decelerated a molecular beam of ${\mathrm{H}}_2\mathrm{CO}$ essentially to rest, producing molecules at $100\mathrm{mK}$ with a density of $\sim {10}^6{\mathrm{cm}}^{-3}$.

In a Bose-Einstein condensate of ${}^{87}\mathrm{Rb}$ $(F=2,m_F=2)$ atoms we have topologically created a quantized vortex with a charge of 4 by reversing the magnetic field of the trap. Experimental conditions of reversal time and initial magnetic field strength for the successful vortex creation were restricted within narrower ranges, compared to those in the case of the ${}^{23}\mathrm{Na}$ condensate. The experimental difficulty was explained in terms of a non-negligible gravitational sag arising from its large atomic mass. We have successfully stabilized the vortex formation by compensating gravity with a blue-detuned laser beam.

We report results of quantum Monte Carlo simulations in the canonical and the grand-canonical ensemble of the two- and three-dimensional Bose-Hubbard model with quadratic and quartic confining potentials. The quantum criticality of the superfluid-Mott insulator transition is investigated both on the boundary layer separating the two coexisting phases and at the center of the traps where the Mott-insulating phase is first established. Recent simulations of systems in quadratic traps have shown that the transition is not in the critical regime due to the finite gradient of the confining potential and that critical fluctuations are suppressed. In addition, it has been shown that quantum critical behavior is recovered in flat confining potentials as they approach the uniform regime. Our results show that quartic traps display a behavior similar to quadratic ones, yet locally at the center of the traps the bulk transition has enhanced critical fluctuations in comparison to the quadratic case. Therefore quartic traps provide a better prerequisite for the experimental observation of true quantum criticality of ultracold bosonic atoms in optical lattices.

We systematically study the BCS-BEC crossover and the quantum phase transition in ultracold ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$ atoms across a wide Feshbach resonance. The background scattering lengths for ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$ have opposite signs, which lead to very different behaviors for these two types of atoms. For ${}^{40}\mathrm{K}$, both the two-body and the many-body calculations show that the system always has two branches of solutions: one corresponds to a deeply bound molecule state; and the other, the one accessed by the current experiments, corresponds to a weakly bound state with population always dominantly in the open channel. For ${}^6\mathrm{Li}$, there is only a unique solution with the standard crossover from the weakly bound Cooper pairs to the deeply bound molecules as one sweeps the magnetic field through the crossover region. Because of this difference, for the experimentally accessible state of ${}^{40}\mathrm{K}$, there is a quantum phase transition at zero temperature from the superfluid to the normal Fermi gas at the positive detuning of the magnetic field where the $s$-wave scattering length passes its zero point. For ${}^6\mathrm{Li}$, however, the system changes continuously across the zero point of the scattering length. For both types of atoms, we also give a detailed comparison between the results from the two-channel and the single-channel model over the whole region of the magnetic field detuning.

We propose a scheme for simultaneously trapping and detecting single atoms near the surface of a substrate using whispering gallery modes of a microdisk resonator. For efficient atom-mode coupling, the atom should be placed within approximately $150\mathrm{nm}$ from the disk. We show that a combination of red and blue detuned modes can form an optical trap at such distances while the backaction of the atom on the field modes can simultaneously be used for atom detection. We investigate these trapping potentials including van-der-Waals and Casimir-Polder forces and discuss corresponding atom detection efficiencies, depending on a variety of system parameters. Finally, we analyze the feasibility of nondestructive detection.

We study nonclassical polarization states characterized by polarization distributions taking negative values. We consider two different families of polarization distributions that include polarization analogs of the Wigner function. We apply different measures of nonclassical behavior such as the nonclassical depth and the distance of the polarization distribution to its modulus. This approach is applied to relevant quantum field states such as one-photon states, SU(2) coherent states, quadrature coherent states, and twin number states. We examine observables allowing the detection of the negativity of the polarization distributions.

Fisher’s measure of information is compared to the usual measure of sensitivity of the SU(2) and SU(1,1) interferometers. The states of optimum Fisher information measure and prescribed mean photon-number difference are defined, and the properties of these states are studied in the SU(2) interferometer.

We study the free expansion of a dilute two-component Fermi gas with attractive interspecies interaction in the Bardeen-Cooper-Schrieffer–Bose-Einstein condensate (BCS-BEC) crossover. We apply a time-dependent parameter-free density-functional theory by using two choices of the equation of state: an analytic formula based on Monte Carlo data and the mean-field equation of state resulting from the extended BCS equations. The calculated axial and transverse radii and the aspect ratio of the expanding cloud are compared to experimental data on vapors of ${}^6\mathrm{Li}$ atoms. Remarkably, the mean-field theory shows a better agreement with the experiments than the theory based on the Monte Carlo equation of state. Both theories predict a measurable dependence of the aspect ratio on expansion time and on scattering length.

We introduce a self-consistent framework for the analysis of both Abelian and non-Abelian geometric phases associated with open quantum systems, undergoing cyclic adiabatic evolution. We derive a general expression for geometric phases, based on an adiabatic approximation developed within an inherently open-systems approach. This expression provides a natural generalization of the analogous one for closed quantum systems, and we prove that it satisfies all the properties one might expect of a good definition of a geometric phase, including gauge invariance. A striking consequence is the emergence of a finite time interval for the observation of geometric phases. The formalism is illustrated via the canonical example of a spin-$1∕2$ particle in a time-dependent magnetic field. Remarkably, the geometric phase in this case is immune to dephasing and spontaneous emission in the renormalized Hamiltonian eigenstate basis. This result positively impacts holonomic quantum computing.

A nonequilibrium, generally time-dependent, environment whose form is deduced by optimal learning control is shown to provide a means for incoherent manipulation of quantum systems. Incoherent control by the environment (ICE) can serve to steer a system from an initial state to a target state, either mixed or in some cases pure, by exploiting dissipative dynamics. Implementing ICE with either incoherent radiation or a gas as the control is explicitly considered, and the environmental control is characterized by its distribution function. Simulated learning control experiments are performed with simple illustrations to find the shape of the optimal nonequilibrium distribution function that best affects the posed dynamical objectives.

Expansion of the solution to the time-dependent Schrödinger equation for a one-channel nonstationary system in terms of Siegert states is discussed. A discrete set of coupled pseudodifferential equations defining time evolution of the coefficients in the expansion is derived, and physical observables (probabilities of transitions to discrete states and the spectrum of ejected particles) are expressed in terms of these coefficients. In contrast to other time-dependent close-coupling methods in atomic and molecular physics, the present approach treats the continuum with no approximation. A price for that is a more involved mathematical structure of the resulting coupled equations. The approach is implemented in terms of Siegert pseudostates and illustrated by calculations for a model time-dependent rectangular potential.

We explore the prospects of optical shaking, a recently suggested generic approach to laser cooling of neutral atoms and molecules. Optical shaking combines elements of Sisyphus cooling and of stochastic cooling techniques and is based on feedback-controlled interaction of particles with strong nonresonant laser fields. The feedback loop guarantees a monotonous energy decrease without a loss of particles. We discuss two types of feedback algorithms and provide an analytical estimation of their cooling rate. We study the robustness of optical shaking against noise and establish minimal stability requirements for the lasers. The analytical predictions are in a good agreement with the results of detailed numerical simulations.

Laser-cooled ${}^{85}\mathrm{Rb}$ atoms were optically excited to $46d_{5∕2}$ Rydberg states. A microwave pulse transferred a fraction of the atoms to the $47p_{3∕2}$ Rydberg state. The resonant electric dipole-dipole interactions between atoms in these two states were probed using the linewidth of the two-photon microwave transition $46d_{5∕2}\text{−}47d_{5∕2}$. The presence of a weak magnetic field $\approx 0.5\mathrm{G}$ reduced the observed line broadening, indicating that the interaction is suppressed by the field. The field removes some of the energy degeneracies responsible for the resonant interaction, and this is the basis for a quantitative model of the resulting suppression. A technique for the calibration of magnetic field strengths using the $34s_{1∕2}\text{−}34p_{1∕2}$ one-photon transition is also presented.

We consider the self-localization of neutral impurity atoms in a Bose-Einstein condensate in a one-dimensional model. Within the strong coupling approach, we show that the self-localized state exhibits parametric soliton behavior. The corresponding stationary states are analogous to the solitons of nonlinear optics and to the solitonic solutions of the Schrödinger-Newton equation (which appears in models that consider the connection between quantum mechanics and gravitation). In addition, we present a Bogoliubov-de Gennes formalism to describe the quantum fluctuations around the product state of the strong coupling description. Our fluctuation calculations yield the excitation spectrum and reveal considerable corrections to the strong coupling description. The knowledge of the spectrum allows a spectroscopic detection of the impurity self-localization phenomenon.

We present a general analysis of the state obtained by subjecting a continuous-wave (cw) Gaussian field to non-Gaussian measurements. The generic multimode state of a cw Gaussian field is fully characterized by the time dependent mean values and variances and the two-time covariances of the field quadrature variables. We present a general theory to extract from this information the results of detection and quantum state reduction within specific temporal output modes. The formalism is applied to schemes for heralded production of propagating light pulses with single photon and Schrödinger kitten states from a cw squeezed beam of light.

We present a theoretical investigation on the open-aperture Gaussian-beam $Z$-scan technique for two dominant saturable absorption models, by using the Adomian decomposition method. Analytic expressions of the $Z$-scan traces are deduced for a cw laser and a pulsed laser, respectively; in particular, for performable simulations, the optimal sum upper limit is found. We give an experimental demonstration, in which a side-chain azobenzene polymer poly [6-[1-(4-(4-nitrophenylazo)phenyl) piperazine] hexyl methacrylate] (Pda) film behaves as a test sample. The results manifest that our theory is reasonable and the Pda film is a good saturable absorber at the wavelength of $532\mathrm{nm}$.

Entanglement of purification was introduced by Terhal et al. [J. Math. Phys. 43, 4286 (2002)] for characterizing the bound of the generation of correlated states from maximally entangled states with sublinear size of classical communication. On the other hand, M. Horodecki [Phys. Rev. A61, 052309 (2000)] obtained the optimal compression rate with a mixed states ensemble in the visible setting. In this paper, we prove that the optimal visible compression rate for mixed states is equal to the limit of the regularized entanglement of purification of the state corresponding to the given ensemble. This result gives a unique interpretation to the entanglement of purification.

We propose a scheme for quantum error correction using robust continuous variable probe modes, rather than fragile ancilla qubits, to detect errors without destroying data qubits. The use of such probe modes reduces the required number of expensive qubits in error correction and allows efficient encoding, error detection, and error correction. Moreover, the elimination of the need for direct qubit interactions significantly simplifies the construction of quantum circuits. We will illustrate how the approach implements three existing quantum error correcting codes: the three-qubit bit-flip (phase-flip) code, the Shor code, and an erasure code.