The popular approach of softening the Coulomb singularity in models with reduced dimensionality leads to uncontrollable discrepancies with numerical results obtained using exact potentials. This is demonstrated for ionization and dissociation probabilities as well as for high-order harmonic generation spectra even of the simple hydrogen molecular ion in aligned geometry. Soft-core models perform better in full dimensions, thereby losing one of their advantages, namely the gain in computation time that is achieved by going to reduced dimensionality. However, the much simpler numerical implementation of soft-core potentials carries over to full dimensions. Moreover, a generalization of the soft-core potential given in previous work [M. Lein, P. P. Corso, J. P. Marangos, and P. L. Knight, Phys. Rev. A 67, 023819 (2003)] is proposed, leading to a tremendous improvement toward the exact results, which is very promising for future calculations without cylindrical symmetry.

Through the introduction of a class of trial wave functions portraying combined rotations and vibrations of molecules formed through particle localization in concentric polygonal rings, a correlated basis is constructed that spans the translationally invariant part of the lowest-Landau-level (LLL) spectra. These trial functions, referred to as rovibrational molecular (RVM) functions, generalize our previous work that focused exclusively on electronic cusp states, describing them as pure vibrationless rotations. From a computational viewpoint, the RVM correlated basis enables controlled and systematic improvements of the original strongly correlated variational wave function. Conceptually, it provides the basis for the development of a quantal molecular description for the full LLL spectra. This quantal molecular description is universal, being valid for both bosons and fermions, for both the yrast and excited states of the LLL spectra, and for both low and high angular momenta. Furthermore, it follows that all other translationally invariant trial functions (e.g., the Jastrow-Laughlin, compact composite-fermion, or Moore-Read functions) are reducible to a description in terms of an excited rotating and vibrating quantal molecule.

By means of analytical and numerical methods, we reveal the main features of nonautonomous matter-wave solitons near the Feshbach resonance in a one-dimensional Bose-Einstein condensate confined by a harmonic potential with a varying-in-time longitudinal trapping frequency. Based on the generalized nonautonomous Gross-Pitaevskii model, we show that solitons in nonautonomous physical systems exist only under certain conditions so that varying-in-time nonlinearity and confining harmonic potential cannot be chosen independently; they satisfy the exact integrability scenarios and complement each other. We focus on the most physically important examples where the applied magnetic field is either a linearly or a periodically varying-in-time function. In the case of periodically varying scattering length, variations of confining harmonic potential are found to be sign-reversible (periodic attractive and repulsive) to support the soliton-management regime. We investigate the losses of validity of one-dimensional (1D) approximation in the cases when, by the joint action of varying-in-time nonlinearity and confining potential, the atom cloud can be compressed from an initially elongated quasi-1D cigar-shaped geometry to a final ball-shaped three-dimensional geometry and the induced soliton collapse may occur.

We compute the critical temperature of Bose-Einstein condensation in dilute three-dimensional homogeneous Bose gases. Our method involves the models of spatial permutations and should be exact to lowest order in the scattering length of the particle interactions. We find that the change in the critical temperature, $\Delta T_{\mathrm{c}}/T_{\mathrm{c}}^{(0)}$, behaves as $ca{\rho }^{1/3}$ with $c=-2.33$. This contradicts the current consensus among physicists.

We study the ground-state properties and quantum dynamics of few-boson mixtures with strong interspecies repulsion in one-dimensional traps. If one species localizes at the center, e.g., due to a very large mass compared to the other component, it represents an effective barrier for the latter, and the system can be mapped onto identical bosons in a double well. For weaker localization, the barrier atoms begin to respond to the light component, leading to an induced attraction between the mobile atoms that may even outweigh their bare intraspecies repulsion. To explain the resulting effects, we derive an effective Hubbard model for the lighter species accounting for the back action of the barrier in correction terms to the lattice parameters. Also the tunneling is drastically affected: by varying the degree of localization of the “barrier” atoms, the dynamics of intrinsically noninteracting bosons can change from Rabi oscillations to effective pair tunneling. For identical fermions (or fermionized bosons), this leads to the tunneling of attractively bound pairs.

Bose-Einstein condensation (BEC) of Feshbach molecules in a homogeneous Bose gas is studied at finite temperatures in a single-channel mean-field approach where the Hartree-Fock energy and pairing gap are determined self-consistently. In the molecular-BEC state, the atomic excitation is gapped and the molecular excitation is gapless. The binding energy of Feshbach molecules is shifted from the vacuum value by many-body effects. When the scattering length $a_s$ of the atoms is negative, the system is subject to mechanical collapse due to negative compressibility. The system is stable in most regions with positive scattering lengths. However, at low temperatures near the resonance, the molecular-BEC state vanishes, and the coherent mixture of atomic and molecular BEC is subject to mechanical collapse.

The standard Klein paradox describes how an incoming electron scatters off a supercritical electrostatic barrier that is so strong that it can generate electron-positron pairs. This fermionic system has been widely discussed in textbooks to illustrate some of the discrepancies between quantum mechanical and quantum field theoretical descriptions for the pair creation process. We compare the fermionic dynamics with that of the corresponding bosonic system. We point out that the direct counterpart of the Pauli exclusion principle (the central mechanism to resolve the fermionic Klein paradox) is stimulated emission, which leads to the resolution of the analogous bosonic paradox.

Motivated by recent realizations of microwave-driven nonlinear resonators in superconducting circuits, the impact of environmental degrees of freedom is analyzed as seen from a rotating frame. A system plus reservoir model is applied to consistently derive in the weak coupling limit the master equation for the reduced density in the moving frame and near the first bifurcation threshold. The concept of an effective temperature is introduced to analyze to what extent a detailed balance relation exists. Explicit expressions are also found for the Lamb-shift. Results for ohmic baths are in agreement with experimental findings, while for structured environments population inversion is predicted that may qualitatively explain recent observations.

We earlier constructed a generalized entropy concept to show the direction of time in an evolution following from a Markov generator. In such a dynamical system the entity found changes in a monotonic way starting from any initial state of the system. In this article, we generalize the treatment to the case when population is pumped into the system from levels not explicitly considered. These populations then pass through the coupled levels and exit by decay to levels outside the system. We derive the form of the equation of motion and relate it to our earlier treatments. It turns out that the formalism can be generalized to the new situation. Its physically relevant features are demonstrated and the behavior obtained is illustrated by a numerical treatment of the standard two-level system with pumping and relaxation included.

A functional integral formulation of quantum mechanics for non-Lagrangian systems is presented. The approach, which we call “stringy quantization,” is based solely on classical equations of motion and is free of any ambiguity arising from Lagrangian and/or Hamiltonian formulation of the theory. The functionality of the proposed method is demonstrated on several examples. Special attention is paid to the stringy quantization of systems with a general $A$-power friction force $-\kappa {\mathrm{q̇}}^A$. Results for $A=1$ are compared with those obtained in the approaches by Caldirola-Kanai, Bateman, and Kostin. Relations to the Caldeira-Leggett model and to the Feynman-Vernon approach are discussed as well.

Closed quantum systems evolve unitarily and therefore cannot converge in a strong sense to an equilibrium state starting out from a generic pure state. Nevertheless for large system size one observes temporal typicality. Namely, for the overwhelming majority of the time instants, the statistics of observables is practically indistinguishable from an effective equilibrium one. In this paper we consider the Loschmidt echo (LE) to study this sort of unitary equilibration after a quench. We draw several conclusions on general grounds and on the basis of an exactly solvable example of a quasifree system. In particular we focus on the whole probability distribution of observing a given value of the LE after waiting a long time. Depending on the interplay between the initial state and the quench Hamiltonian, we find different regimes reflecting different equilibration dynamics. When the perturbation is small and the system is away from criticality the probability distribution is Gaussian. However close to criticality the distribution function approaches a double-peaked, universal form.

The control of the Casimir force between two parallel plates can be achieved through adjusting the frequency-dependent electromagnetic properties of materials of the two plates. We show that, for different plate separations, the main contribution to the Casimir force comes from different frequency regions: For smaller (larger) separation, it comes from the higher (lower) frequency region. When the separation of the plates increases, the Casimir force can vary from attractive to repulsive and/or vice versa, by selecting the two plates with suitable electromagnetic properties. We discuss how a restoring Casimir force, which varies from repulsive to attractive by increasing the separation, can be realized and that the stable equilibrium is formed at zero Casimir force.

We calculate the geometric phase of a bipartite two-level system coupled to an external environment. We analyze the reduced density matrix for an arbitrary initial state of the composite system and compute the correction to the unitary geometric phase through a kinematic approach. In all cases considered, we observe a similar structure as a function of the degree of the entanglement of the initial state. Further, we compute the entanglement entropy and concurrence of the bipartite state and analyze if there is any relation among these quantities and the geometric phase acquired during the nonunitary system’s evolution. Finally, we discuss the results obtained.

We study the evolution of nearest-neighbor entanglement in the one-dimensional Ising model with an external transverse field. The system is initialized as the so-called thermal ground state of the pure Ising model. We analyze properties of the generation of entanglement for different regions of external transverse fields. We find that the derivative of the time at which the entanglement reaches its first maximum with respect to the reciprocal transverse field has a minimum at the critical point. This is an indicator of quantum phase transition.

We discuss both theoretically and experimentally elementary two-photon polarization entanglement localization after break of entanglement caused by linear coupling of environmental photon with one of the system photons. The localization of entanglement is based on simple polarization measurement of the surrounding photon after the coupling. We demonstrate that nonzero entanglement can be localized back irrespectively to the distinguishability of coupled photons. Further, it can be increased by local single-copy polarization filters up to an amount violating Bell inequalities. The present technique allows restoration of entanglement in those cases, when the entanglement distillation produces no entanglement from the coupling.

Under two-party deterministic dense coding, Alice communicates (perfectly distinguishable) messages to Bob via a qudit from a pair of entangled qudits in pure state $|\Psi \rangle$. If $|\Psi \rangle$ represents a maximally entangled state (i.e., each of its Schmidt coefficients is $\sqrt{1/d}$), then Alice can convey to Bob one of $d^2$ distinct messages. If $|\Psi \rangle$ is not maximally entangled, then Ji et al. [Phys. Rev. A 73, 034307 (2006)] have shown that under the original deterministic dense-coding protocol, in which messages are encoded by unitary operations performed on Alice’s qudit, it is impossible to encode $d^2-1$ messages. Encoding $d^2-2$ messages is possible; see, for example, the numerical studies by Mozes et al. [Phys. Rev. A 71, 012311 (2005)]. Answering a question raised by Wu et al. [Phys. Rev. A 73, 042311 (2006)], we show that when $|\Psi \rangle$ is not maximally entangled, the communications limit of $d^2-2$ messages persists even when the requirement that Alice encode by unitary operations on her qudit is weakened to allow encoding by more general quantum operators. We then describe a dense-coding protocol that can overcome this limitation with high probability, assuming the largest Schmidt coefficient of $|\Psi \rangle$ is sufficiently close to $\sqrt{1/d}$. In this protocol, $d^2-2$ of the messages are encoded via unitary operations on Alice’s qudit, and the final $(d^2-1)$-th message is encoded via a non-trace-preserving quantum operation.

With the help of the spin-orbit interaction, we propose a scheme to perform holonomic single-qubit gates on the electron spin confined to a quantum dot. The manipulation is done in the absence (or presence) of an applied magnetic field. By adiabatic changing the position of the confinement potential, one can rotate the spin state of the electron around the Bloch sphere in semiconductor heterostructures. The dynamics of the system is equivalent to employing an effective non-Abelian gauge potential whose structure depends on the type of the spin-orbit interaction. As an example, we find an analytic expression for the electron spin dynamics when the dot is moved around a circular path (with radius $R$) on the two dimensional electron gas (2DEG) and show that all single-qubit gates can be realized by tuning the radius and orientation of the circular paths. Moreover, using the Heisenberg exchange interaction, we demonstrate how one can generate two-qubit gates by bringing two quantum dots near each other, yielding a scalable scheme to perform quantum computing on arbitrary $N$ qubits. This proposal shows a way of realizing holonomic quantum computers in solid-state systems.

One of the simplest security proofs of quantum key distribution is based on the so-called complementarity scenario, which involves the complementarity control of an actual protocol and a virtual protocol [M. Koashi, e-print arXiv:0704.3661 (2007)]. The existing virtual protocol has a limitation in classical postprocessing, i.e., the syndrome for the error-correction step has to be encrypted. In this paper, we remove this limitation by constructing a quantum circuit for the virtual protocol. Moreover, our circuit with a shield system gives an intuitive proof of why adding noise to the sifted key increases the bit error rate threshold in the general case in which one of the parties does not possess a qubit. Thus, our circuit bridges the simple proof and the use of wider classes of classical postprocessing.

We present calculations of contact potential surface patch effects that simplify previous treatments. It is shown that, because of the linearity of Laplace’s equation, the presence of patch potentials does not affect an electrostatic calibration of a two-plate Casimir measurement apparatus. Using models that include long-range variations in the contact potential across the plate surfaces, a number of experimental observations can be reproduced and explained. For these models, numerical calculations show that if a voltage is applied between the plates which minimizes the force, a residual electrostatic force persists, and that the minimizing potential varies with distance. The residual force can be described by a fit to a simple two-parameter function involving the minimizing potential and its variation with distance. We show the origin of this residual force by use of a simple parallel capacitor model. Finally, the implications of a residual force that varies in a manner different from $1/d$ on the accuracy of previous Casimir measurements is discussed.

Binding energies of 23 Rydberg fine-structure levels of Ni with n $=$ 9 and $L⩾5$ were measured using resonant excitation Stark ionization spectroscopy. From this spectrum, the quadrupole moment and the scalar and tensor dipole polarizability of the ${}^2{D}_{5/2}$ ground state of Ni${}^{+}$ were determined to be $Q=-0.474(2)$, ${\alpha }_{d,0}=7.92(6)$, and ${\alpha }_{d,2}=1.15(14)$ a.u. The electric hexadecapole moment was determined to be $-0.33(21)$ a.u.