We propose a scheme to implement the simplest and best-studied version of the quantum random walk, the discrete Hadamard walk, in one dimension using a coherent macroscopic sample of ultracold atoms, Bose-Einstein condensate (BEC). Implementation of the quantum walk using a BEC gives access to the familiar quantum phenomena on a macroscopic scale. This paper uses a rf pulse to implement the Hadamard operation (rotation) and stimulated Raman transition technique as a unitary shift operator. The scheme suggests the implementation of the Hadamard operation and unitary shift operator while the BEC is trapped in a long Rayleigh range optical dipole trap. The Hadamard rotation and a unitary shift operator on a BEC prepared in one of the internal states followed by a bit-flip operation, implements one step of the Hadamard walk. To realize a sizable number of steps, the process is iterated without resorting to intermediate measurement. With current dipole trap technology, it should be possible to implement enough steps to experimentally highlight the discrete quantum random walk using a BEC leading to further exploration of quantum random walks and its applications.

The time-independent Schrödinger equation with an isotropic velocity-dependent potential is considered. Treating the velocity-dependent interaction as a small perturbation, we develop analytical formulas for the changes in the scattering phase shifts and wave functions. It is shown that only the zeroth-order solution and the perturbing potential are needed to determine the phase-shift and wave-function corrections. No prior knowledge of the unperturbed scattering-states continuum is required. In order to test the validity of our approach, we applied it to an exactly solvable model for nucleon-nucleon scattering. The results of the perturbation formalism compare quite well with those of the exactly solvable model. The developed formalism can be applied in problems concerning pion-nucleon, nucleon-nucleon, and electron-atom scattering. It may also be useful in studying the scattering of electrons in semiconductor heterostructures.

The phase diagram of a nonrelativistic fermionic system with imbalanced state populations interacting via a short-range $S$-wave attractive interaction is analyzed in the mean-field approximation. We determine the energetically favored state for different values of the mismatch between the two Fermi spheres in the weak- and strong-coupling regimes considering both homogeneous and nonhomogeneous superconductive states. We find that the homogeneous superconductive phase persists for values of the population imbalance that increase with increasing coupling strength. In the strong-coupling regime and for large population differences the energetically stable homogeneous phase is characterized by one gapless mode. We also find that the inhomogeneous superconductive phase characterized by the condensate $\Delta \left(\mathbf{x}\right)\sim \Delta \exp (i\mathbf{q}\bullet \mathbf{x})$ is energetically favored in a range of values of the chemical-potential mismatch that shrinks to zero in the strong-coupling regime.

We present a microscopic laser model for many atoms coupled to a single-cavity mode, including the light forces, which result from atom-field momentum exchange. Within a semiclassical description, we solve the equations for the atomic motion and the internal dynamics to obtain analytic expressions for the optical potential and the friction force seen by each atom. When optical gain is maximum at frequencies where the light field extracts kinetic energy from the atomic motion, the dynamics combines optical lasing and motional cooling. From the corresponding momentum-diffusion coefficient we predict sub-Doppler temperatures in the stationary state. This generalizes the theory of cavity-enhanced laser cooling to active cavity systems. We identify the gain-induced reduction of the effective resonator linewidth as the key origin for the faster cooling and the lower temperatures, which implies that a bad cavity with a gain medium can replace a high-$Q$ cavity. In addition, this shows the importance of light forces for gas lasers in the low-temperature limit, where atoms can arrange in a periodic pattern maximizing gain and counteracting spatial hole burning. Ultimately, in the low-temperature limit, such a setup should allow us to combine optical lasing and atom lasing in a single device.

The Margolus-Levitin lower bound on the minimal time required for a state to be transformed into an orthogonal state is generalized. It is shown that for some initial states the new bound is stronger than the Margolus-Levitin one.

Atoms confined in a magnetic trap can escape by making spin-flip Majorana transitions due to a breakdown of the adiabatic approximation. Several papers have studied this process for atoms with spin $F=1∕2$ or 1. The present paper calculates the escape rate for atoms with spin $F>1$. This problem has new features because the perturbation $\mathrm{\Delta }T$ that allows atoms to escape satisfies a selection rule $\mathrm{\Delta }{F}_z=0,\pm 1,\pm 2$ and multistep processes contribute in leading order. When the adiabatic approximation is satisfied, the leading-order terms can be summed to yield a simple expression for the escape rate.

In this paper, a density-functional exchange potential is proposed. The suggested exchange potential reproduces the correct asymptotic behavior of finite systems: $-1∕r$, without significant increase in computational costs over a local-density approximation. Our model exchange potential, which is an explicit functional of a density and the gradient of the density, is given by a hybridization procedure of a Hartree potential and the homogeneous electron gas limit of the exchange potential. Since the Hartree potential behaves as $N∕r$ in an asymptotic region with $N$ number of electrons, it is utilized for achieving the correct $-1∕r$ asymptotic behavior in our model exchange potential. We found that the suggested exchange potential can yield very good estimates for the ionization potential of atoms and ions from the highest occupied orbital energies.

We discuss a rescattering deflection parameter to gauge the progression from strong- to ultrastrong-field rescattering dynamics. Our analytical and numerical treatments of rescattering quantify the change from nonrelativistic, dipole approximation strong-field dynamics to an ultrastrong-field interaction where $v∕c\ne 0$ and ${\mathbf{B}}_{\text{laser}}\ne 0$. At the threshold between these two regimes the Lorentz deflection reduces the returning electron flux at the core and suppresses rescattering related phenomena. Both radiation and nonsequential ionization from rescattering are studied. We show the ultrastrong-field regime can occur at intensities as low as ${10}^{14}\mathrm{W}∕{\mathrm{cm}}^2$ for mid-IR $\left(2\mu \mathrm{m}\text{to}5\mu \mathrm{m}\right)$ wavelengths or as high as ${10}^{18}\mathrm{W}∕{\mathrm{cm}}^2$ for UV radiation.

We investigate the superfluidity and the associated Nambu-Goldstone modes in a three-flavor atomic Fermi gas with $\mathrm{SU}\left(3\right)$ global symmetry. The $s$-wave pairing occurs in flavor antitriplet channel due to the Pauli principle, and the superfluid state contains both gapped and gapless fermionic excitations. Corresponding to the spontaneous breaking of the $\mathrm{SU}\left(3\right)$ symmetry to a $\mathrm{SU}\left(2\right)$ symmetry with five broken generators, there are only three Nambu-Goldstone modes, one is with linear dispersion law and two are with quadratic dispersion law. The other two expected Nambu-Goldstone modes become massive with a mass gap of the order of the fermion energy gap in a wide coupling range. The abnormal number of Nambu-Goldstone modes, the quadratic dispersion law, and the mass gap have significant effect on the low-temperature thermodynamics of the matter.

The energy spectrum for an ultracold rotating Bose gas in a harmonic trap is calculated exactly for small systems, allowing the atoms to occupy several Landau levels. Two vortexlike states and two strongly correlated states (the Pfaffian and Laughlin) are considered in detail. In particular, their critical rotation frequencies and energy gaps are determined as a function of particle number, interaction strength, and the number of Landau levels occupied (up to three). For the vortexlike states, the lowest-Landau-level (LLL) approximation is justified only if the interaction strength decreases with the number of particles; nevertheless, the constant of proportionality increases rapidly with the angular momentum per particle. For the strongly correlated states, however, the interaction strength can increase with particle number without violating the LLL condition. The results suggest that, in large systems, the Pfaffian and Laughlin states might be stabilized at rotation frequencies below the centrifugal limit for sufficiently large interaction strengths, with energy gaps a significant fraction of the trap energy.

A phenomenological approach is developed that allows one to completely describe the effects of unwanted noise, such as the noise associated with absorption and scattering, in high-$Q$ cavities. This noise is modeled by a block of beam splitters and an additional input-output port. The replacement schemes enable us to formulate appropriate quantum Langevin equations and input-output relations. It is demonstrated that unwanted noise renders it possible to combine a cavity input mode and the intracavity mode in a nonmonochromatic output mode. Possible applications to unbalanced and cascaded homodyning of the intracavity mode are discussed and the advantages of the latter method are shown.

We consider the coherent population trapping effect with a train of ultrashort pulses in a $\Lambda$-type system with two bound states and a continuum replacing the upper state. Population transfer to the continuum can be totally suppressed provided that the splitting between the bound states is a multiple of the pulse repetition rate. Compared to the traditional case with only two laser fields coupling the bound states to the continuum, CPT with a pulse train allows one to avoid incoherent population losses due to interaction of the fields with “wrong” transitions, which results in only partial suppression of ionization. A method of suppression of excited-state absorption of pumping radiation in laser crystals, with pumping in the form of the pulse train, is proposed. As a particular example pumping dynamics of a ${\mathrm{Ti}}^{3+}:{\mathrm{YAlO}}_3$ crystal using this technique is numerically analyzed.

The intracavity phase-modulated laser can work in two distinct stages: 1) phase mode-locking when the applied modulation frequency is equal to the cavity’s fundamental frequency or one of its harmonics, and 2) the FM laser oscillation at a moderate detuned modulation frequency. In this paper, we experimentally studied the noise buildup process in the transition from FM laser oscillation to phase mode-locking in a phase-modulated laser. We found that the relaxation oscillation frequency varies with the modulation frequency detuning and the relaxation oscillation will occur twice in the transition region. Between these two relaxation oscillations, the supermode noise can be significantly enhanced, which is evidence of excess noise in laser systems. All of these results can be explained by the theory of Floquet modes in a phase-modulated laser cavity.

Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time quantum walk. Though the properties of these two walks have shown similarities, it has remained an open problem to find the exact relation between the two. The precise connection of these two processes, both quantally and classically, is presented. Extension to higher dimensions is also discussed.

Necessary and sufficient observable conditions for the non-negativity of all partial transpositions of multimode quantum states are derived. The result is a hierarchy of inequalities for minors in terms of moments of the given state. The violation of any inequality is a sufficient condition for entanglement. Full entanglement can be certified for a manifold of multimode quantum states. A MATHEMATICA package is given for a systematic test of the hierarchy of conditions.

Trellises play an important theoretical and practical role for classical codes. Their main utility is to devise complexity-efficient error estimation algorithms. Here, we describe trellis representations for quantum stabilizer codes. We show that they share the same properties as their classical analogs. In particular, for any stabilizer code it is possible to find a minimal trellis representation. Our construction is illustrated by two fundamental error estimation algorithms.

We present experimental and theoretical studies of the absorption, emission, and photodissociation spectra of ${\mathrm{Rb}}_2$ molecules in solid helium. We have identified 11 absorption bands of ${\mathrm{Rb}}_2$. All laser-excited molecular states are quenched by the interaction with the He matrix. The quenching results in efficient population of a metastable $\left(1\right){}^3\Pi _u$ state, which emits fluorescence at $1042\mathrm{nm}$. In order to explain the fluorescence at the forbidden transition and its time dependence we propose a new molecular exciplex ${\mathrm{Rb}}_2\left({}^3\Pi _u\right){\mathrm{He}}_2$. We have also found evidence for the formation of diatomic bubble states following photodissociation of ${\mathrm{Rb}}_2$.

The use of a complex absorbing potential (CAP) of the form $-i\eta W$ to calculate the Siegert energy of a resonance state rests on a solid mathematical foundation [U. V. Riss and H.-D. Meyer, J. Phys. B 26, 4503 (1993)]. In this paper, in order to facilitate a better understanding of the basic principles underlying the CAP method, a radial one-particle Hamiltonian with a model potential supporting resonances is analyzed. Using a purely quadratic CAP $[W\left(r\right)=r^2]$, the eigenstates of $H=-(1∕2)d^2∕d{r}^2-i\eta W\left(r\right)$ are employed to construct a discrete variable representation. The introduction of this grid method makes it transparent how using a CAP is related to the method of complex scaling, and why, in the limit of an infinite basis set, the exact Siegert energy may emerge in the spectrum as $\eta \to 0^{+}$.

We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for the non-Markovian damped harmonic oscillator. In the general framework, our results demonstrate the possibility to use a closed system as a simulator for open quantum systems. The quantum simulator is based on sets of controlled drives of the closed harmonic oscillator with appropriately tailored electric field pulses. The non-Markovian dynamics of the damped harmonic oscillator is obtained by using the information about the spectral density of the open system when averaging over the drives of the closed oscillator. We consider single trapped ions as a specific physical implementation of the simulator, and we show how the simulator approach reveals physical insight into the open system dynamics, e.g., the characteristic quantum mechanical non-Markovian oscillatory behavior of the energy of the damped oscillator, usually obtained by the non-Lindblad-type master equation, can have a simple semiclassical interpretation.