We discuss a general mean field plus random phase approximation (RPA) for describing composite systems at zero and finite temperature. We analyze in particular its implementation in finite systems invariant under translations, where for uniform mean fields it requires just the solution of simple local-type RPA equations. As test and application, we use the method for evaluating the entanglement between two spins in cyclic spin–1/2 chains with both long- and short-range anisotropic $XY$-type couplings in a uniform transverse magnetic field. The approach is shown to provide an accurate analytic description of the concurrence for strong fields, for any coupling range, pair separation, or chain size, where it predicts an entanglement range which can be at most twice that of the interaction. It also correctly predicts the existence of a separability field together with full entanglement range in its vicinity. The general accuracy of the approach improves as the range of the interaction increases.

The decoherence of two initially entangled qubits in anisotropic band-gap photonic crystal has been studied analytically without Born or Markovian approximation. It is shown that the decoherence dynamics of two qubits in a photonic crystal is greatly different from that of two qubits in vacuum or that subjected to the usual non-Markovian reservoir. The results also show that the finite-time decoherence invoked by spontaneous emission could be suppressed efficiently and the entanglement of the Bell state possessing odd parity is more easily preserved in a photonic crystal than that of the Bell state possessing even parity under the same condition. A store scheme for the entangled particle pair is proposed.

We report on measurements of total cross sections for positron scattering from the fundamental molecule formic acid (HCOOH). In this case, the energy range of our experimental work is $0.3–50.2\mathrm{eV}$. Our interpretation of these data was somewhat complicated by the fact that at room temperature, formic acid vapor consists of about 95% monomer and 5% dimer forms, so that the present cross sections represent an average for that ensemble. To assist us in interpreting the data, rigorous Schwinger multichannel level calculations for positron elastic scattering from the formic acid monomer were also undertaken. These calculations, incorporating an accurate model for the target polarization, are found to be in good qualitative agreement with our measured data, particularly when allowance is made for the target beam mixture (monomer versus dimer) in the experiment.

We study dissipative transport of spontaneously emitting atoms in a one-dimensional (1D) standing-wave laser field in the regimes where the underlying deterministic Hamiltonian dynamics is regular and chaotic. A Monte Carlo stochastic wave-function method is applied to simulate semiclassically the atomic dynamics with coupled internal and translational degrees of freedom. It is shown in numerical experiments and confirmed analytically that chaotic atomic transport can take the form either of ballistic motion or a random walking with specific statistical properties. The character of spatial and momentum diffusion in the ballistic atomic transport is shown to change abruptly in the atom-laser detuning regime where the Hamiltonian dynamics is irregular in the sense of dynamical chaos. We find a clear correlation between the behavior of the momentum diffusion coefficient and Hamiltonian chaos probability which is a manifestation of chaoticity of the fundamental atom-light interaction in the diffusivelike dissipative atomic transport. We propose to measure a linear extent of atomic clouds in a 1D optical lattice and predict that, beginning with those values of the mean cloud’s momentum for which the probability of Hamiltonian chaos is close to 1, the linear extent of the corresponding clouds should increase sharply. A sensitive dependence of statistical characteristics of dissipative transport on the values of the detuning allows us to manipulate the atomic transport by changing the laser frequency.

We show that the statistical properties of a Coulomb crystal can be measured by means of a standard interferometric procedure performed on the spin of one ion in the chain. The ion spin, constituted by two internal levels of the ion, couples to the crystal modes via spatial displacement induced by photon absorption. The loss of contrast in the interferometric signal allows one to measure the autocorrelation function of the crystal observables. Close to the critical point, where the chain undergoes a second-order phase transition to a zigzag structure, the signal gives the behavior of the correlation function at the critical point.

We investigate the dynamics of Rydberg electrons excited from the ground state of ultracold atoms trapped in an optical lattice. We first consider a lattice comprising an array of double-well potentials, where each double well is occupied by two ultracold atoms. We demonstrate the existence of molecular states with equilibrium distances of the order of experimentally attainable interwell spacings and binding energies of the order of ${10}^3\mathrm{GHz}$. We also consider the situation whereby ground-state atoms trapped in an optical lattice are collectively excited to Rydberg levels, such that the charge-density distributions of neighboring atoms overlap. We compute the hopping rate and interaction matrix elements between highly excited electrons separated by distances comparable to typical lattice spacings. Such systems have tunable interaction parameters and a temperature $\sim {10}^4$ times smaller than the Fermi temperature, making them potentially attractive for the study and simulation of strongly correlated electronic systems.

We reconsider the geometry of pure and mixed states in a finite quantum system. The ranges of eigenvalues of the density matrices delimit a regular symplex (hypertetrahedron $T_N$) in any dimension $N$; the polytope isometry group is the symmetric group $S_{N+1}$, and splits $T_N$ in chambers, the orbits of the states under the projective group $\mathrm{PU}(N+1)$. The type of states correlates with the vertices, edges, faces, etc., of the polytope, with the vertices making up a base of orthogonal pure states. The entropy function as a measure of the purity of these states is also easily calculable; we draw and consider some isentropic surfaces. The Casimir invariants acquire then also a more transparent interpretation.

We show that oscillations of a homogeneous medium with constant material coefficients produce pairs of photons. Classical analysis of an oscillating medium reveals regions of parametric resonance where the electromagnetic waves are exponentially amplified. The quantum counterpart of parametric resonance is an exponentially growing number of photons in the same parameter regions. This process may be viewed as another manifestation of the dynamical Casimir effect. However, in contrast to the standard dynamical Casimir effect, photon production here takes place in the entire volume and is not due to time dependence of the boundary conditions or material constants.

We calculate the Casimir interaction between parallel planar crystals of Au and the anisotropic cuprate superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2\mathrm{Ca}{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ (BSCCO), with BSCCO’s optical axis either parallel or perpendicular to the crystal surface, using suitable generalizations of the Lifshitz theory. We find that the strong anisotropy of the BSCCO permittivity gives rise to a difference in the Casimir force between the two orientations of the optical axis, which depends on distance and is of order 10–20 % at the experimentally accessible separations $10\text{to}5000\mathrm{nm}$.

We construct a practically implementable classical processing for the Bennett-Brassard 1984 (BB84) protocol and the six-state protocol that fully utilizes the accurate channel estimation method, which is also known as the quantum tomography. Our proposed processing yields at least as high a key rate as the standard processing by Shor and Preskill. We show two examples of quantum channels over which the key rate of our proposed processing is strictly higher than the standard processing. In the second example, the BB84 protocol with our proposed processing yields a positive key rate even though the so-called error rate is higher than the 25% limit.

A procedure is developed to construct improved wave functions for the bound states in various four-electron atoms and ions. The bound state wave functions are improved in the sense that our trial wave functions are compact and accurate. We employ two independent four-electron spin functions ${\chi }_1=\alpha \beta \alpha \beta +\beta \alpha \beta \alpha -\beta \alpha \alpha \beta -\alpha \beta \beta \alpha$ and ${\chi }_2=2\alpha \alpha \beta \beta +2\beta \beta \alpha \alpha -\beta \alpha \alpha \beta -\alpha \beta \beta \alpha -\beta \alpha \beta \alpha -\alpha \beta \alpha \beta$ in each trial wave function. Optimization of the nonlinear parameters is performed for each radial function. Our procedure is applied to obtain the total energies of the ground ${}^{1}S^e$ states in the following four-electron berylliumlike systems: ${\mathrm{Li}}^{-}$, Be, ${\mathrm{B}}^{+}$, ${\mathrm{C}}^{2+}$, ${\mathrm{N}}^{3+}$, ${\mathrm{O}}^{4+}$, ${\mathrm{F}}^{5+}$, ${\mathrm{Ne}}^{6+}$, ${\mathrm{Na}}^{7+}$, and ${\mathrm{Mg}}^{8+}$. All our trial wave functions used in this study are very compact. In fact, each of these functions contains only 300 basis (radial) functions which are constructed from ten-dimensional gaussoids of the five-body relative coordinates $r_{12}$, $r_{13}$, $r_{14}$, $r_{15}$, $r_{23}$, $r_{24}$, $r_{25}$, $r_{34}$, $r_{35}$, and $r_{45}$.

We present a combined experimental and theoretical study of cold collisions between bismuth and helium atoms in strong magnetic fields and demonstrate that the spin-orbit interaction coupling between different nonrelativistic states of Bi leads to rapid Zeeman relaxation. The Zeeman relaxation of Bi in the ground electronic state is found to be very efficient due to the admixture of electronic excited states which show an interaction anisotropy due to their nonzero electronic orbital angular momentum. Our results indicate that dense ensembles of heavy relativistic atoms will generally be unstable in magnetic traps due to significant spin relaxation induced by spin-orbit interactions.

We study theoretically light beam propagation in one-dimensional periodic media with intensity-resonant nonlinearity. The phenomenon of discrete modulational instability is investigated in detail as well as the conditions for the existence and stability of fundamental lattice and surface soliton modes. According to the linear stability analysis, only on-site solitons are stable. The mobility of lattice solitons is analyzed by both free energy and mapping concepts. Only broad solitons may freely traverse the lattice.

We consider stimulated Brillouin scattering excited in a “feedback-free” optical fiber by continuous wave monochromatic pump radiation. We show the Stokes signal displays stochastic dynamic behavior from its onset. On increase of the pump signal a window of periodicity emerges from and subsequently subsides into the stochastic emission, the period of which corresponds to the round-trip time in the fiber. We show this feature arises from coherent regenerative amplification of the stochastic spontaneous Brillouin scattering due to minute residual feedback.

We propose a strategies not only to protect but also to enhance and revive the entanglement in a double Jaynes-Cummings model. We show that such surprising features arise when Zeno-like measurements are performed during the dynamical process.

The low-energy scattering properties of two aligned identical bosonic and identical fermionic dipoles are analyzed. Generalized scattering lengths are determined as functions of the dipole moment and the scattering energy. Near resonance, where a new bound state is being pulled in, all nonvanishing generalized scattering lengths diverge, with the $a_{00}$ and $a_{11}$ scattering lengths being dominant for identical bosons and identical fermions, respectively. Implications for the energy spectrum and the eigenfunctions of trapped two-dipole systems and for pseudopotential treatments are discussed.

We classify, up to local unitary equivalence, the set of $n$-qubit states that is stabilized by the diagonal subgroup of the local unitary group. We exhibit a basis for this set, parametrized by diagrams of nonintersecting chords connecting pairs of points on a circle, and give a criterion for when the stabilizer is precisely the diagonal subgroup and not larger. This investigation is part of a larger program to partially classify entanglement type (local unitary equivalence class) via analysis of stabilizer structure.

With a single-photon representation of the quantum states and a multirail optical network for performing the unitary transformation, we give a scheme for an optical implementation of the universal programmable quantum state discriminator that unambiguously discriminates between two unknown states with optimal probability of success.

A many-body Green’s function approach to the microscopic theory of surface-enhanced Raman scattering is presented. Interaction effects between a general molecular system and a spatially anisotropic metal particle supporting plasmon excitations in the presence of an external radiation field are systematically included through many-body perturbation theory. Reduction of the exact effects of molecular-electronic correlation to the level of Hartree-Fock mean-field theory is made for practical initial implementation, while description of collective oscillations of conduction electrons in the metal is reduced to that of a classical plasma density; extension of the former to a Kohn-Sham density-functional or second-order Møller-Plesset perturbation theory is discussed; further specialization of the latter to the random-phase approximation allows for several salient features of the formalism to be highlighted without need for numerical computation. Scattering and linear-response properties of the coupled system subjected to an external perturbing electric field in the electric-dipole interaction approximation are investigated. Both damping and finite-lifetime effects of molecular-electronic excitations as well as the characteristic fourth-power enhancement of the molecular Raman scattering intensity are elucidated from first principles. It is demonstrated that the presented theory reduces to previous models of surface-enhanced Raman scattering and leads naturally to a semiclassical picture of the response of a quantum-mechanical molecular system interacting with a spatially anisotropic classical metal particle with electronic polarization approximated by a discretized collection of electric dipoles.