We investigate the effect of anisotropic and long-range dipole-dipole interaction (DDI) on the center motions of nonoverlapping Bose-Einstein condensates in bilayer and multilayer stacks. In the bilayer, it is shown analytically that while DDI plays no role in the in-phase modes of center motions of condensates, out-of-phase mode frequency (${\omega }_o$) depends crucially on the strength of DDI ($a_d$). At the small-$a_d$ limit, ${\omega }_o^2(a_d)-{\omega }_o^2(0)\propto a_d$. In the multilayer stack, transverse modes associated with center motions of coupled condensates are found to be optical-phonon-like. At the long-wavelength limit, phonon velocity is proportional to $\sqrt{a}{}_d$.

The mechanism and intrinsic conditions of high-energy wave-breaking-free pulse generation in fiber lasers mode-locked by a nonlinear polarization rotation technique are investigated numerically and experimentally. Both numerical and experimental results show that the pulses along the two orthogonal polarization axes of the fiber have a large difference in pulse energy. The numerical simulations show that the ratio of the energy of two components is limited and ranges from about 8 to about 65. The slope of the instantaneous frequency at the central position of the pulse decreases rapidly with the increase of the pulse duration and energy, whereas the slope at the pulse edge changes slightly. The accumulation of instantaneous frequency throughout the pulse width approaches a constant in a higher pulse energy regime. Understanding the mechanism and intrinsic conditions of the wave-breaking-free pulse generation could be useful in generating high-energy pulses delivered from fiber lasers.

We propose a scheme of generating four-qubit hyperentangled states between a pair of remote noninteracting atomic ions with a $\Lambda$ configuration that are confined in Paul traps. These hyperentangled states, different from the normal entangled states that are entangled in a single degree of freedom, are entangled in both spin and motion degrees of freedom. In our proposal, the entanglement is first generated in spin degrees of freedom using linear optics and then transferred to the motion degree of freedom using a sequence of laser pluses, including the stimulated Raman carrier transitions and sideband transitions. The proposal is completed with regenerating entanglement in spin degrees of freedom using linear optics.

We investigate discrete-time quantum-walk evolution under the influence of periodic measurements in position subspace. The undisturbed survival probability of the particle at the position subspace $P(0,t)$ is compared with the survival probability after frequent ($n$) measurements at interval $\tau =t/n$, $P(0,\tau ){}^n$. We show that $P(0,\tau ){}^n>P(0,t)$ leads to the quantum Zeno effect in position subspace when a parameter $\theta$ in the quantum coin operations and frequency of measurements is greater than the critical value, $\theta >{\theta }_c$ and $n>n_c$. This Zeno effect in the subspace preserves the dynamics in coin Hilbert space of the walk dynamics and has the potential to play a significant role in quantum tasks such as preserving the quantum state of the particle at any particular position, and to understand the Zeno dynamics in a multidimensional system that is highly transient in nature.

Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance yet is often poorly understood. We study the dynamics of a continuous time, adiabatic quantum search algorithm and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: The error decreases exponentially for short times and then decreases polynomially for longer times. We show that the well-known quadratic speedup over classical search is associated only with the exponential error regime. We illustrate the results through examples of evolution paths derived by minimization of the adiabatic error. We also discuss specific strategies for controlling the adiabatic error and run time.

It is shown that the conventional Born series for relativistic electron scattering in the Coulomb field cannot be used for calculating the scattering characteristics. The differential cross section at small scattering angles is found on the basis of the Furry-Sommerfeld-Maue solution of the Dirac equation. Propagation of the electron wave packet is considered in order to separate the incident and scattered fluxes. It is shown that the total scattering cross section proves to be finite but depends on the distance $r$ between the scattering center and the observation point. It is also shown that the polarization characteristics of the scattered beam are changed due to the long-range character of the Coulomb potential. The results can be important because Coulomb scattering is often used for normalization of experimental data in high-energy physics.

A laser-cooling scheme for molecules is presented based on repeated cycle of zero-velocity selection, deceleration, and irreversible accumulation. Although this scheme also employs a single spontaneous emission as in [Raymond Ooi, Marzlin, and Audretsch, Eur. Phys. J. D 22, 259 (2003)], in order to circumvent the difficulty of maintaining closed pumping cycles in molecules, there are two distinct features which make the cooling process of this scheme faster and more practical. First, the zero-velocity selection creates a narrow velocity-width population with zero mean velocity, such that no further deceleration (with many stimulated Raman adiabatic passage (STIRAP) pulses) is required. Second, only two STIRAP processes are required to decelerate the remaining hot molecular ensemble to create a finite population around zero velocity for the next cycle. We present a setup to realize the cooling process in one dimension with trapping in the other two dimensions using a Stark barrel. Numerical estimates of the cooling parameters and simulations with density matrix equations using OH molecules show the applicability of the cooling scheme. For a gas at temperature $T=1$ K, the estimated cooling time is only $2$ ms, with phase-space density increased by about 30 times. The possibility of extension to three-dimensional cooling via thermalization is also discussed.

Results of numerical Monte Carlo simulations for the Stark-tuned $\mathrm{F}\stackrel{\mathrm{··}}{\mathrm{o}}$rster resonance and dipole blockade between two to five cold rubidium Rydberg atoms in various spatial configurations are presented. The effects of the atoms’ spatial uncertainties on the resonance amplitude and spectra are investigated. The feasibility of observing coherent Rabi-like population oscillations at a $\mathrm{F}\stackrel{\mathrm{··}}{\mathrm{o}}$rster resonance between two cold Rydberg atoms is analyzed. Spectra and the fidelity of the Rydberg dipole blockade are calculated for various experimental conditions, including nonzero detuning from the $\mathrm{F}\stackrel{\mathrm{··}}{\mathrm{o}}$rster resonance and finite laser linewidth. The results are discussed in the context of quantum-information processing with Rydberg atoms.

We show anisotropy of the dipole interaction between magnetic atoms or polar molecules can stabilize new quantum phases in an optical lattice. Using a well-controlled numerical method based on the tensor network algorithm, we calculate the phase diagram of the resultant effective Hamiltonian in a two-dimensional square lattice—an anisotropic Hubbard model of hard-core bosons with attractive interaction in one direction and repulsive interaction in the other direction. Besides the conventional superfluid and the Mott insulator states, we find the striped and the checkerboard charge-density-wave states and the supersolid phase that interconnect the superfluid and the striped solid states. The transition to the supersolid phase has a mechanism different from the case of the soft-core Bose-Hubbard model.

We report a theoretical study of Anderson localization of nonclassical light in an array of waveguides in which neighboring waveguides are evanescently coupled and in which the disorder can be added in a controlled manner. We use squeezed light at the input to investigate the effects of nonclassicality and compare the results with those obtained by using conventional classical fields, such as a coherent field and a Gaussian field. Our results show that there is an enhancement in fluctuations of localized light due to the medium’s disorder. We find superbunching of the localized light, which may be useful for enhancing the interaction between radiation and matter. Another important consequence of sub-Poissonian statistics of the incoming light is to quench the total fluctuations at the output. Finally, we show that as a result of the multiplicative noise in the problem, the output field is far from Gaussian even if the input is a coherent field.

An optomechanical interface that converts quantum states between optical fields with distinct wavelengths is proposed. A mechanical mode couples to two optical modes via radiation pressure and mediates the quantum state mapping between the two optical modes. A sequence of optomechanical $\pi /2$ pulses enables state-swapping between optical and mechanical states, as well as the cooling of the mechanical mode. Theoretical analysis shows that high-fidelity conversion can be realized for states with small photon numbers in systems with experimentally achievable parameters. The pulsed conversion process also makes it possible to maintain high conversion fidelity at elevated bath temperatures.

We present a slow-light system based on dual Raman absorption resonances in warm rubidium vapor. Each Raman absorption resonance is produced by a control beam in an off-resonant $\Lambda$ system. This system combines all optical control of the Raman absorption and the low-dispersion broadening properties of the double Lorentzian absorption slow light. The bandwidth, group delay, and central frequency of the slow-light system can all be tuned dynamically by changing the properties of the control beam. We demonstrate multiple pulse delays with low distortion and show that such a system has fast switching dynamics and thus fast reconfiguration rates.

We investigate local contents in $N$-qubit generalized Greenberger-Horne-Zeilinger (GHZ) states. We suggest a decomposition for correlations in the GHZ states into a nonlocal and fully local part, and find a lower and upper bound on the local content. Our lower bound reproduces the previous result for $N=2$ [V. Scarani, Phys. Rev. A 77, 042112 (2008)] and decreases rapidly with $N$.

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group $\mathcal{G}$, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group $\mathcal{G}$. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.

A quantum system in a given resonance state has different open channels for decay. Partial widths are the decay rates of the resonance (metastable) state into the different open channels. Here we present a rigorous derivation of the partial widths from the solution of a time-dependent Schrödinger equation with outgoing boundary conditions. We show that the sum of the partial widths obtained from the resonance wave function is equal to the total width. The difference with respect to previous studies on partial widths and branching ratios is discussed.

We develop a technique for finding the dynamical evolution in time of an averaged density matrix. The result is an equation of evolution that includes an effective Hamiltonian, as well as decoherence terms in Lindblad form. Applying the general equation to harmonic Hamiltonians, we confirm a previous formula for the effective Hamiltonian together with a additional decoherence term which should, in general, be included and whose vanishing provides the criteria for validity of the effective Hamiltonian approach. Finally, we apply the theory to examples of the ac Stark shift and three-level Raman transitions, recovering a decoherence effect in the latter.

We find a class of open-system models in which individual quantum trajectories may depend on parameters that are undetermined by the full open-system evolution. This dependence is imprinted in the geometric phase associated with such trajectories and persists after averaging. Our findings indicate a potential source of ambiguity in the quantum trajectory approach to open quantum systems.

We have computed numerically the Casimir force between two identical pistons inside a very long cylinder, considering different shapes for the pistons. The pistons can be considered quantum billiards, whose spectrum determines the vacuum force. The smooth part of the spectrum fixes the force at short distances and depends only on geometric quantities like the area or perimeter of the piston. However, correcting terms to the force, coming from the oscillating part of the spectrum which is related to the classical dynamics of the billiard, could be qualitatively different for classically integrable or chaotic systems. We have performed a detailed numerical analysis of the corresponding Casimir force for pistons with regular and chaotic classical dynamics. For a family of stadium billiards, we have found that the correcting part of the Casimir force presents a sudden change in the transition from regular to chaotic geometries. This suggests that there could be signatures of quantum chaos in the Casimir effect.

The copper $K\alpha$ photoemission spectra is one of the most widely studied. Recent Dirac-Fock calculations have produced transition energies in good agreement with experiment, though they have relied on approximations that may not be transferable to other complex atoms in which uncertainties in theoretical results are dominated by poor convergence. Through a detailed examination of convergence issues in the copper spectrum, we consider the accuracy obtainable with the multiconfiguration Dirac-Fock (MCDF) method, provide the first determination of fine structure contributions to the spectrum, and demonstrate reliable techniques for modeling spectator states with vacancies in the $3p$, $3d$, and $4s$ shells.

We study the single-particle density of states of a one-dimensional speckle potential, which is correlated and non-Gaussian. We consider both the repulsive and the attractive cases. The system is controlled by a single dimensionless parameter determined by the mass of the particle, the correlation length, and the average intensity of the field. Depending on the value of this parameter, the system exhibits different regimes, characterized by the localization properties of the eigenfunctions. We calculate the corresponding density of states using the statistical properties of the speckle potential. We find good agreement with the results of numerical simulations.