In this work we compare the results of the Gross-Pitaevskii and modified Gross-Pitaevskii equations with ab initio variational Monte Carlo calculations for Bose-Einstein condensates of atoms in axially symmetric traps. We examine both the ground state and excited states having a vortex line along the $z$ axis at high values of the gas parameter and demonstrate an excellent agreement between the modified Gross-Pitaevskii and ab initio Monte Carlo methods, both for the ground and vortex states.

We study the magnetic soliton dynamics of spinor Bose-Einstein condensates in an optical lattice which results in an effective Hamiltonian of anisotropic pseudospin chain. A modified Landau-Lifshitz equation is derived and exact magnetic soliton solutions are obtained analytically. Our results show that the time oscillation of the soliton size can be controlled in practical experiment by adjusting of the light-induced dipole-dipole interaction. Moreover, the elastic collision of two solitons is investigated.

We have demonstrated the operation of a quantum eraser based on a polarization interferometer. Which-path information is erased not by modifying the interferometer apparatus, but instead by modifying the information obtained from measurements performed on a second beam, whose polarization is correlated with that of the interferometer beam. We compare the results obtained when the two beams are in an entangled state (quantum correlations) and in a mixed state (classical correlations). We find that classical correlations can mimic most, but not all, of the quantum-mechanical behavior.

The zero-range potential model, widely used in nonrelativistic quantum mechanics, is extended to continuum problems involving Dirac particles. A bispinor wave function of a Dirac particle scattered from a system of zero-range potentials is sought in the form of an incident wave superposed with waves emerging from points where targets are located. Interactions between the particle and individual targets are described by imposing certain limiting conditions, relating linearly upper and lower components of the wave function at target locations. This yields an inhomogeneous algebraic system for superposition coefficients appearing in the expression for the wave function. After preliminary considerations, admitting a quite general form of the incident wave, the case of the monochromatic plane-wave scattering is considered in detail. Expressions for $2\times 2$ and $4\times 4$ matrix scattering amplitudes and scattering kernels, as well as for various kinds of differential and total cross sections, are given. An eigenchannel formalism for the model is developed in the manner analogous to that presented in the author’s recent work [R. Szmytkowski, Ann. Phys. (N.Y.) 311, 503 (2004)] on scattering from short-range potentials. Eigenchannel representations of the scattering wave function, of a “final-state” wave function for photodetachment, as well as of outgoing and ingoing matrix Green functions, are derived. Formulas for matrix scattering amplitudes, scattering kernels, and cross sections expressed in terms of eigenphase shifts and eigenchannel spinor harmonics are presented. A possibility to formulate the zero-range potential model for Dirac particles in an alternative way is also discussed.

The dynamics of the outgoing electrons, from the separated fine-structure ionic states of the $4p$ valence shell of krypton atoms, are observed for the single ionization process by incident electrons with energies from 5 to 50 eV above threshold. Triple differential $(e,2e)$ ionization cross sections are deduced from observations made in the “perpendicular-plane” scattering geometry using the same toroidal electrostatic electron energy analyzer for both outgoing electrons. For equal energy outgoing electrons, single and double scattering mechanisms account for the major characteristics of the cross sections. The double scattering becoming increasingly dominant as the excess energy increases; the behavior otherwise is very different from helium.

We have measured the trap frequency as well as the damping coefficient of a magneto-optical trap by using a transient oscillation method. The dependence of such trap properties on the various experimental parameters such as the cooling laser intensity, detuning, and magnetic field gradient is investigated. We find that the measured trap frequency is in excellent agreement with the simple rate-equation analysis based on the Doppler cooling theory. In contrast, the damping coefficient is about twice as large as the calculated one, which is attributed to the existence of the sub-Doppler trap near the trap center.

We propose a scheme for parametric amplification and phase conjugation of an atomic Bose-Einstein condensate (BEC) via stimulated dissociation of a BEC of molecular dimers consisting of bosonic atoms. This can potentially be realized via coherent Raman transitions or using a magnetic Feshbach resonance. We show that the interaction of a small incoming atomic BEC with a (stationary) molecular BEC can produce two counterpropagating atomic beams - an amplified atomic BEC and its phase-conjugate or “time-reversed” replica. The two beams can possess strong quantum correlation in the relative particle number, with squeezed number-difference fluctuations.

We present a detailed analysis of the impact on quantum modular exponentiation of architectural features and possible concurrent gate execution. Various arithmetic algorithms are evaluated for execution time, potential concurrency, and space trade-offs. We find that to exponentiate an $n\text{−}\text{bit}$ number, for storage space $100n$ (20 times the minimum $5n$), we can execute modular exponentiation 200–700 times faster than optimized versions of the basic algorithms, depending on architecture, for $n=128$. Addition on a neighbor-only architecture is limited to $O\left(n\right)$ time, whereas non-neighbor architectures can reach $O\left(\log n\right)$, demonstrating that physical characteristics of a computing device have an important impact on both real-world running time and asymptotic behavior. Our results will help guide experimental implementations of quantum algorithms and devices.

The monogamous nature of entanglement has been illustrated by the derivation of entanglement-sharing inequalities—bounds on the amount of entanglement that can be shared among the various parts of a multipartite system. Motivated by recent studies of decoherence, we demonstrate an interesting manifestation of this phenomena that arises in system-environment models where there exists interactions between the modes or subsystems of the environment. We investigate this phenomenon in the spin-bath environment, constructing an entanglement-sharing inequality bounding the entanglement between a central spin and the environment in terms of the pairwise entanglement between individual bath spins. The relation of this result to decoherence will be illustrated using simplified system-bath models of decoherence.

In this paper, we investigate spin entanglement in the $XXZ$ model defined on a $d$-dimensional bipartite lattice. The concurrence, a measure of the entanglement between two spins, is analyzed. We prove rigorously that the ground-state concurrence reaches maximum at the isotropic point. For dimensionality $d⩾2$, the concurrence develops a cusp at the isotropic point and we attribute it to the existence of magnetic long-range order.

The application of time-dependent wave operator theory to the development of a quantum adiabatic perturbation theory is treated both theoretically and numerically, with emphasis on the description of field-matter interactions which involve short laser pulses. It is first shown that the adiabatic limit of the time-dependent wave operator corresponds to a succession of instantaneous static Bloch wave operators. Wave operator theory is then shown to be compatible with the two-time Floquet theory of light-matter interaction, thus allowing the application of Floquet theory to cases which require the use of a degenerate active space. A numerical study of some problems shows that the perturbation strength associated with nonadiabatic processes can be reduced by using multidimensional active spaces and illustrates the capacity of the wave operator approach to produce a quasiadiabatic treatment of a nominally nonadiabatic Floquet dynamical system.

The transmission of a nonsymmetric potential barrier is a two-channel quantum problem. In this aspect it is analogous to the two-channel radial problem. The analytical properties of the $S$ matrix are similar for both generic quantum-mechanical systems. We here develop an explicit mapping between the two problems. It allows us to formulate barrier transmission in terms of the Siegert pseudostates similarly to the approach developed recently for the two-channel radial case. This results in an efficient method of treating barrier transmission including on equal footing both resonance effects and smooth background behavior.

The exact macroscopic wave functions of two-species Bose-Einstein condensates in an optical lattice beyond the tight-binding approximation are studied by solving the coupled nonlinear Schrödinger equations. The phase diagram for superfluid and insulator phases of the condensates is determined analytically according to the macroscopic wave functions of the condensates, which are seen to be traveling matter waves.

We develop the probabilistic implementation of a nonlocal gate $\exp \left[i\xi {\sigma }_{n_A}{\sigma }_{n_B}\right]$ and $\xi ∊[0,(\pi ∕4)]$, by using a single nonmaximally entangled state. We prove that nonlocal gates can be implemented with a fidelity of $>79.3\%$ and a consumption of $<0.969\mathrm{ebits}$ and two classical bits, when $\xi ⩽0.353$. This provides a higher bound for the feasible operation compared to the former techniques. Besides, gates with $\xi ⩾0.353$ can be implemented with the probability 79.3% and a consumption of 0.969 ebits, which is the same efficiency as the distillation-based protocol, while our method saves extra classical resources. Gates with $\xi \to 0$ can be implemented with nearly unit probability and a small entanglement. We also generalize some applications to the multiple system, where we find it is possible to implement certain nonlocal gates between many nonentangled partners using a nonmaximally multiple entangled state.

We describe criteria for implementation of quantum computation in qudits. A qudit is a -dimensional system whose Hilbert space is spanned by states ∣0⟩, ∣1⟩, …, . An important earlier work [] describes how to exactly simulate an arbitrary unitary on multiple qudits using a parameter family of single qudit and two qudit gates. That technique is based on the spectral decomposition of unitaries. Here we generalize this argument to show that exact universality follows given a discrete set of single qudit Hamiltonians and one two-qudit Hamiltonian. The technique is related to the -matrix decomposition of numerical linear algebra. We consider a generic physical system in which the single qudit Hamiltonians are a small collection of and . A coupling graph results taking nodes 0, …, and edges are allowed Hamiltonians. One qudit exact universality follows iff this graph is connected, and complete universality results if the two-qudit Hamiltonian is also allowed. We discuss implementation in the eight dimensional ground electronic states of and construct an optimal gate sequence using Raman laser pulses.

Paralleling our recent computationally intensive (quasi-Monte Carlo) work for the case $N=4$ (e-print quant-ph/0308037), we undertake the task for $N=6$ of computing to high numerical accuracy, the formulas of Sommers and Życzkowski (e-print quant-ph/0304041) for the $(N^2-1)$-dimensional volume and $(N^2-2)$-dimensional hyperarea of the (separable and nonseparable) $N\times N$ density matrices, based on the Bures (minimal monotone) metric—and also their analogous formulas (e-print quant-ph/0302197) for the (nonmonotone) flat Hilbert-Schmidt metric. With the same seven ${10}^9$ well-distributed (“low-discrepancy”) sample points, we estimate the unknown volumes and hyperareas based on five additional (monotone) metrics of interest, including the Kubo-Mori and Wigner-Yanase. Further, we estimate all of these seven volume and seven hyperarea (unknown) quantities when restricted to the separable density matrices. The ratios of separable volumes (hyperareas) to separable plus nonseparable volumes (hyperareas) yield estimates of the separability probabilities of generically rank-6 (rank-5) density matrices. The (rank-6) separability probabilities obtained based on the 35-dimensional volumes appear to be—independently of the metric (each of the seven inducing Haar measure) employed—twice as large as those (rank-5 ones) based on the 34-dimensional hyperareas. (An additional estimate—33.9982—of the ratio of the rank-6 Hilbert-Schmidt separability probability to the rank-4 one is quite clearly close to integral too.) The doubling relationship also appears to hold for the $N=4$ case for the Hilbert-Schmidt metric, but not the others. We fit simple exact formulas to our estimates of the Hilbert-Schmidt separable volumes and hyperareas in both the $N=4$ and $N=6$ cases.

Anomalous behavior of the saturated absorption resonance line shape on the $1s_5-2p_8(J=2-J=2)$ transition in the Ne atom is experimentally observed. The shape of the saturation resonance on transitions with degenerate excited states of atoms is numerically analyzed. The reasons and conditions for the anomalous behavior of the resonance line shape and the formation of its doublet spectral structure are established. The influence of the resonant light pressure force on the amplitude and the frequency properties of the saturated resonance is investigated. It is shown, that the asymmetry of the doublet splitting of the resonance is caused by the effect of resonant light pressure.

In this paper we show that the superfluidity of cold spin-1 Bose atoms of weak interactions in an optical lattice can be realized according to the excitation energy spectrum which is derived by means of Bogliubov transformation. The characteristic of the superfluid-phase spectrum is explained explicitly in terms of the nonvanishing critical velocity, i.e., the Landau criterion. It is observed that critical velocities of superfluid are different for three spin components and, moreover, can be controlled by adjusting the lattice parameters in practical experiments to detect the superfluid phase.

The high-harmonic generation in a plasma or gas under conditions when the single-atom response is affected by neighboring ions or atoms of the medium is studied theoretically. We solve numerically the three-dimensional Schrödinger equation for a single-electron atom in the combined fields of the neighboring particles and the laser, and average the results over different random positions of the particles using the Monte Carlo method. Harmonic spectra are calculated for different medium densities and laser intensities. We observe a change of the harmonic properties due to a random variation of the harmonic phase induced by the field of the medium, when the medium density exceeds a certain transition density. The transition density is found to depend on the harmonic order, but it is almost independent of the fundamental intensity. It also differs for the two (shorter and longer) quantum paths. The latter effect leads for ionic densities in the transition regime to a narrowing of the harmonic lines and a shortening of the attosecond pulses generated using a group of harmonics.

We suggest a protocol for perfect quantum communication through spin-chain channels. By combining a dual-rail encoding with measurements only at the receiving end, we can get conclusively perfect state transfer, whose probability of success can be made arbitrarily close to unity. As an example of such an amplitude-delaying channel, we show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than $P$ in a Heisenberg chain of $N$ spin-$\frac{1}{2}$ particles can be achieved in a timescale of the order of $(0.33\hslash ∕J)N^{1.7}\mid \ln P\mid$. We demonstrate that our scheme is more robust to decoherence and nonoptimal timing than any scheme using single spin chains.