We investigate the asymmetric Gaussian cloning of coherent states which produces $M$ copies from $N$ input replicas in such a way that the fidelity of each copy may be different. We show that the optimal asymmetric Gaussian cloning can be performed with a single phase-insensitive amplifier and an array of beam splitters. We obtain a simple analytical expression characterizing the set of optimal asymmetric Gaussian cloning machines and prove the optimality of these cloners using the formalism of Gaussian completely positive maps and semidefinite programming techniques. We also present an alternative implementation of the asymmetric cloning machine where the phase-insensitive amplifier is replaced with a beam splitter, heterodyne detector, and feedforward.

We consider a dilute gas of neutral unpolarized fermionic atoms at zero temperature. The atoms interact via a short-range (tunable) attractive interaction. We demonstrate analytically a curious property of the gas at unitarity. Namely, the correlation energy of the gas, evaluated by second-order perturbation theory, has the same density dependence as the first-order exchange energy, and the two almost exactly cancel each other at a Feshbach resonance irrespective of the shape of the potential, provided $\left(\mu r_s\right)\gg 1$. Here $(\mu {)}^{-1}$ is the range of the two-body potential, and $r_s$ is defined through the number density, $n=3∕\left(4\pi r_s^3\right)$. The implications of this result for universality are discussed.

The effect of the dipole-dipole interaction on the far-off-resonance optical dipole trapping scheme is calculated by a mean-field approach. The trapping laser field polarizes the atoms and the accompanying dipole-dipole energy shift deepens the attractive potential minimum in a pancake-shaped cloud. At high density the thermal motion cannot stabilize the gas against self-contraction and an instability occurs. We calculate the boundary of the stable and unstable equilibrium regions on a two-dimensional phase diagram of the atom number and the ratio of the trap depth to the temperature. We discuss the limitations imposed by the dipole-dipole instability on the parameters needed to reach Bose-Einstein condensation in an optical dipole trap.

When a Rydberg atom is slowly swept through a dipole allowed resonance with an oscillating field adiabatic rapid passage (ARP) from one state to the other can occur. By measuring the time resolved momentum of a Rydberg electron with a half cycle pulse we demonstrate that during ARP the classical oscillating dipole due to the orbital motion of the electron becomes phase locked to the microwave field driving the resonance. Depending on the direction of the sweep through resonance, the atom is in one or the other of the two Floquet eigenstates in which the electron is phase locked in or $\pi$ out of phase with the driving field. In contrast, in Rabi oscillations the electron motion oscillates between leading and lagging the driving microwave field.

A toroidal trap combined with external time-dependent electric field can be used for implementing different dynamical regimes of matter waves. In particular, we show that dynamical and stochastic acceleration, localization, and implementation of the Kapitza pendulum can be originated by means of proper choice of the external force.

We investigate an ultracold Bose-Fermi mixture with a Feshbach resonance between two hyperfine states of fermions. Using a functional integral method, we calculate collective modes associated with fermion pairs and bosons in the superfluid phase. We derive a stability condition of the mixtures that is valid in the entire region of the BCS-BEC crossover. This stability condition, which smoothly connects the well-known results obtained in both the BCS and Bose-Einstein Condensate (BEC) limits, shows that sufficiently strong fermion-boson (FB) interactions destabilize the mixtures. In order to investigate the consequence of this instability, we study the ground-state energy of both the uniformly mixed and the phase-separated states. We find that FB repulsion induces a phase separation, whereas FB attraction should cause a collapse of the mixture. The possibilities for the experimental observation of such instabilities are also discussed.

A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the translational (ray) and intrinsic (polarization) degrees of freedom are derived ab initio. The ray equations take into account the optical Magnus effect (spin Hall effect of photons) as well as trajectory variations owing to the medium anisotropy. Polarization evolution is described by the precession equation for the Stokes vector. In the generic case, the evolution of wave turns out to be non-Abelian: it is accompanied by mutual conversion of the normal modes and periodic oscillations of the ray trajectories analogous to electron zitterbewegung. The general theory is applied to examples of wave evolution in media with circular and linear birefringence.

An extended medium driven in a double Raman configuration generates Stokes and anti-Stokes fields that are described by coupled parametric oscillator equations with solutions that depend on input boundary operators and quantum noise operators. We identify the conditions where the boundary operators can be the substitute to the noise operators for describing two-photon cross correlation in forward and backward geometries. These conditions include short sample and small decoherence between ground states ${\gamma }_{bc}$, and they are fulfilled by the spontaneous Raman electromagnetic induced transparency scheme (weak pump with large detuning). We verify the correspondence between the results from boundary and noise operators analytically and show that the correlation due to the boundary operators is typically smaller than that due to the noise operators. In general the noise operators are required to obtain the correct correlation, especially when the control laser field is weak and ${\gamma }_{bc}$ is finite. Explanations for the findings are given based on the physics represented by the boundary operators and noise operators. Similar conclusions are obtained for the Stokes and anti-Stokes intensities.

We have performed a quantum-dynamical study of vibrational deexcitation and elastic scattering at ultralow collision energies for the bosonic system ${}^7\mathrm{Li}+{}^7\mathrm{Li}_2$ and for the fermionic system ${}^6\mathrm{Li}+{}^6\mathrm{Li}_2$ with diatomic molecules in high vibrational states. Inelastic rates show a strong and irregular dependence on the vibrational state of the diatomic molecule. For the highest vibrational state which lies near the dissociation limit, vibrational deexcitation processes are not suppressed, but rather depleted, for both bosonic and fermionic systems.

Complete experiments in inner-shell photoionization of linear molecules are achieved by combining the velocity vector correlation method, based on imaging and time-of-flight-resolved electron-ion-ion coincidence technique, with the use of elliptically polarized light. We report here on the molecular frame photoelectron angular distributions (MFPADs) obtained using this method in a single experiment performed with elliptically polarized light, for a site selective $K$-shell ionization of the NO molecule in the region of the $\mathrm{N}{\left(1s\right)}^{-1}$ and $\mathrm{O}{\left(1s\right)}^{-1}$ shape resonances. For a comparable photoelectron energy the $\mathrm{N}{\left(1s\right)}^{-1}$ and $\mathrm{O}{\left(1s\right)}^{-1}$ MFPADs display a remarkable symmetry in the inversion with respect to the emission center of the NO molecule, while revealing common features such as, in particular, the dominant role of $p$ and $f$ partial-wave channels in the photoelectron emission. A large molecular frame circular dichroism is observed. These results are well predicted by multichannel Schwinger configuration interaction calculations (MCSCI), which provide additional information for $\mathrm{N}{\mathrm{O}}^{+}\left({}^3\Pi \right)$ and $\mathrm{N}{\mathrm{O}}^{+}\left({}^1\Pi \right)$ multiplet specific photoionization reactions. The analysis of the photoelectron-ion-ion kinetic energy correlation characterizes the ionic fragmentation channels populated after Auger decay of the $\mathrm{N}{\mathrm{O}}^{+}{\left(1s_{\mathrm{N}∕\mathrm{O}}\right)}^{-1}$ ionic states.

We study the influence of cooperative effects such as superradiance and subradiance on the scattering properties of dilute atomic gases. We show that cooperative effects lead to an effective potential between two atoms that decays as $1∕r$. In the case of superradiance, this potential is attractive for close enough atoms and can be interpreted as a coherent mesoscopic effect. We consider a model of multiple scattering of a photon among superradiant pairs and calculate the elastic mean free path and the group velocity. We study first the case of a scalar wave which allows us to obtain and to understand basic features of cooperative effects and multiple scattering. We then turn to the general problem of a vector wave. In both cases, we obtain qualitatively similar results and derive, for the case of a scalar wave, analytic expressions for the elastic mean free path and for the group velocity for an arbitrary detuning (near resonance).

We have experimentally studied the parametric excitation of ${}^{87}\mathrm{Rb}$ atoms in a quadrupole-Ioffe-configuration trap. The temperature of an atomic cloud and number of trapped atoms versus time and modulation frequency of the parametric excitation field have been measured. We also noticed that the contribution of atomic collisions to the energy distributions can not be ignored in the case of weak excitation, which results in a lower temperature of the atomic cloud than by Gehm et al. [Phys. Rev. A 58, 3914 (1998)] predicted.

We report an unusual phenomenon, peculiar sign reversals of the ground-state magnetic resonances and of the zero-dip resonance (Zeeman resonance at zero field) of optically pumped, alkali-metal vapors. These anomalies occur when a weak circularly polarized $D1$ laser light is tuned to pump atoms predominantly from the lower ground-state hyperfine multiplet. One can understand the signal reversals in a simple, semiquantitative way with reference to the spin-temperature distribution. Quantitative computer simulations are in excellent agreement with observations.

We examine single-frequency optical schemes for species-selective trapping of ultracold alkali-metal atoms. Independently addressing the elements of a binary mixture enables the creation of an optical lattice for one atomic species with little or no effect on the other. We analyze a “tune-in” scheme, using near-resonant detuning to create a strong potential for one specific element. A “tune-out” scheme is also developed, in which the trapping wavelength is chosen to lie between two strong transitions of an alkali-metal atom such that the induced dipole moment is zero for that species but is nonzero for any other. We compare these schemes by examining the trap depths and heating rates associated with both. We find that the tune-in scheme is preferable for $\mathrm{Li}\text{−}\mathrm{Na}$, $\mathrm{Li}\text{−}\mathrm{K}$, and $\mathrm{K}\text{−}\mathrm{Na}$ mixtures, while the tune-out scheme is preferable for $\mathrm{Li}\text{−}\mathrm{Cs}$, $\mathrm{K}\text{−}\mathrm{Rb}$, $\mathrm{Rb}\text{−}\mathrm{Cs}$, $\mathrm{K}\text{−}\mathrm{Cs}$, and ${}^{39}\mathrm{K}\text{−}{}^{40}\mathrm{K}$ mixtures. Several applications of species-selective optical lattices are explored, including the creation of a lattice for a single species in the presence of a phononlike background, the tuning of relative effective mass, and the isothermal increase of phase-space density.

We analyze the Mott-insulator phases of dipolar bosonic gases placed in neighboring but unconnected one-dimensional (1D) traps. Whereas for short-range interactions the 1D systems are independent, the non-local dipole-dipole interaction induces a direct Mott-insulator to pair-superfluid transition which significantly modifies the boundaries of the lowest Mott-insulator phases. The lowest boundary of the lowest Mott regions becomes progressively constant as a function of the hopping rate, eventually inverting its slope, leading to a reentrant configuration which is retained in two dimensions. We discuss the consequences of this effect on the spatial Mott-insulator plateaux in experiments with additional harmonic confinement, showing that counterintuitively the plateaux may become wider for increasing hopping. Our results are also applicable to nondipolar boson-boson mixtures.

The magnetic field due to the photon rest mass $m_{ph}$ modifies the standard results of the Aharonov-Bohm effect for electrons, and of other recent quantum effects. For the effect involving a coherent superposition of beams of particles with opposite electromagnetic properties, by means of a tabletop experiment, the limit $m_{ph}\simeq {10}^{-51}\text{g}$ is achievable, improving by 6 orders of magnitude that derived by Boulware and Deser for the Aharonov-Bohm effect.

We find an interesting relationship between multipartite bound entangled states and the stabilizer formalism. We prove that, if a set of commuting operators from the generalized Pauli group on $n$ qudits satisfy certain constraints, then the maximally mixed state over the subspace stabilized by them is an unlockable bound entangled state. Moreover, the properties of this state, such as symmetry under permutations of parties, undistillability, and unlockability, can be easily explained from the stabilizer formalism without tedious calculation. In particular, the four-qubit Smolin state [Smolin, Phys. Rev. A 63, 032306 (2001)] and its recent generalization to even numbers of qubits [Bandyopadhyay et al., Phys. Rev. A 71, 062317 (2005); Augusiak et al., ibid 73, 012318 (2006)] can be viewed as special examples of our results. Finally, we extend our results to arbitrary multipartite systems in which the dimensions of all parties may be different.

Entanglement witnesses (EWs) are nonpositive Hermitian operators which can detect the presence of entanglement. In this paper, we prove that for a given pair of entangled states ${\rho }_1$ and ${\rho }_2$ an EW, $W$, common to both of them exists if and only if for all $0⩽\lambda ⩽1$, $\lambda {\rho }_1+(1-\lambda ){\rho }_2$ is an entangled state. Based on this result, we find a sufficient condition for the presence of entanglement. We then show that an EW which can detect all bell states simultaneously does not exist.

It is shown that the security, against known-plaintext attacks, of the Yuen 2000 (Y00) quantum-encryption protocol can be considered via the wire-tap channel model assuming that the heterodyne measurement yields the sample for security evaluation. Employing the results reported on the wire-tap channel, a generic framework is proposed for developing secure Y00 instantiations. The proposed framework employs a dedicated encoding which together with inherent quantum noise at the attacker’s side provides Y00 security.