The superfluid–Mott-insulator phase transition of ultracold spin-1 bosons with ferromagnetic and antiferromagnetic interactions in an optical lattice is theoretically investigated. Two counterpropagating linearly polarized laser beams with the angle $\theta$ between the polarization vectors ($\mathrm{lin}\text{−}\theta \text{−}\mathrm{lin}$ configuration), driving an $F_g=1$ to $F_e=1$ internal atomic transition, create the optical lattice and at the same time couple atomic ground states with magnetic quantum numbers $m=\pm 1$. Due to the coupling the system can be described as a two-component one. At $\theta =0$ the system has a continuous isospin symmetry, which can be spontaneously broken, thereby fixing the number of particles in the atomic components. The phase diagram of the system and the spectrum of collective excitations, which are density waves and isospin waves, are worked out. In the case of ferromagnetic interactions, the superfluid–Mott-insulator phase transition is always second order, but in the case of antiferromagnetic interactions for some values of system parameters it is first order and the superfluid and Mott phases can coexist. Varying the angle $\theta$ one can control the populations of atomic components and continuously turn on and tune their asymmetry.

We examine the possibility of storing and retrieving a single photon using electromagnetically induced transparency. We consider the theory of a proof-of-principle two-photon interference experiment, in which an atomic vapor cell is placed in one arm of a two-photon interferometer. Since the two-photon state is entangled, we can examine the degree to which entanglement survives. We show that while the experiment might be difficult, it should be possible to perform. We also show that the two-photon interference pattern has oscillatory behavior.

A general expression for the semiclassical, nonrelativistic linear polarizability of an arbitrary volume element $V$ has been derived in the long wavelength approximation. The derivation starts from the expectation value of the dipole strength, as in the original Kramers-Heisenberg paper about optical scattering by atoms. The main requirements underlying the present approach are a separate non-Hermitian part of the Hamiltonian and a frequency dependent damping, which is zero for the static case. Resonant and antiresonant exponentials are both found to be necessary to obtain a proper static response. It is concluded that even parity for the damping has to be preferred from the theoretical point of view, although odd and asymmetric parity yield virtually the same polarizability. The electromagnetic response can still be written in terms of a single complex frequency, in agreement with the requirements of electrodynamics. The resulting expression is suited for the treatment of nonisotropic systems.

Noise in optical telecommunication fibers is an important limitation on optical quantum data transmission. Unfortunately, the classically successful amplifiers cannot be used in quantum communication because of the no-cloning theorem. We propose a simple method to reduce quantum noise: the insertion of phase shifters and/or beam splitters at regular distance intervals into a fiber. We analyze in detail the case of qubits encoded into polarization states of low-intensity light, which is of central importance to various quantum information tasks, such as quantum cryptography and communication. We discuss the experimental feasibility of our scheme and propose a simple experiment to test our method.

We study the generation of quantum entanglement in two-particle scattering processes. When two wave packets collide, we discover that entanglement grows appreciably because of the interference between the incident and scattered waves. After the collision, quantum entanglement is mainly governed by the scattering phase shift and the widths of the incident wave packets. For interaction potentials that exhibit scattering resonance, we show that quantum entanglement can be enhanced near resonance energies.

We calculate cross sections for elastic scattering and annihilation in antihydrogen-helium collisions at low energies. The calculations are based on the Born-Oppenheimer approximation, and incorporate the effects of the strong interaction through a scattering length approach. We find that the strong nuclear force not only causes significant annihilation, but also cannot be neglected in the elastic channel. In the zero energy limit we obtain the scattering length $a=-7.69-3.80i\mathrm{a.u.}$ for ground state antihydrogen-helium collisions. Annihilation is found to dominate over elastic scattering up to a temperature about $3\mathrm{K}$. Loosely bound metastable antihydrogen-helium states are also investigated, and it is found that a number of relatively long-lived states with up to three units of angular momentum exist.

The spin polarization parameters of photoelectrons from Xe, Cs, and Ba $3d_{5∕2}$ and $3d_{3∕2}$ levels are calculated using a modified version of the so-called spin-polarized random phase approximation with exchange. The effects of relaxation of excited electrons due to the creation of a $3d$ vacancy are also accounted for. We demonstrate that these parameters that characterize the photoionization process, as a function of the incoming photon frequency $\omega$, acquire additional features when the interaction between electrons that belong to the $3d_{5∕2}$ and $3d_{3∕2}$ components of the spin-orbit doublet is taken into account. We conclude that through spin-orbit interaction polarization can be achieved and correlations probed.

We present a scheme of population transfer between two metastable (ground) states of the $\Lambda$ atom without considerable excitation of the atom using single frequency-chirped laser pulses. The physics of the process is generation of the “trapped” superposition of the ground states by the laser pulse at sufficiently high laser peak intensity. The main conditions for realization of this regime are the following: The width of the transform-limited laser pulse envelope frequency spectrum (without chirp) must be smaller and the peak Rabi frequency of the pulse must be larger than the frequency interval between the two ground states of the $\Lambda$ atom. During the frequency chirp, the laser pulse must first come into resonance with the transition from the initially occupied ground state to the excited state and after that with the transition between the excited and second initially empty ground states. In the case when the envelope frequency spectrum width (without chirp) of the pulse exceeds the frequency interval between the two ground states, we show a possibility of controllable generation of superposition of the ground states with a controllable excitation of the $\Lambda$ atom.

We characterize several equilibrium vortex effects in a rotating Bose-Einstein condensate. Specifically we attempt precision measurements of the vortex-lattice spacing and vortex-core size over a range of condensate densities and rotation rates. These measurements are supplemented by numerical simulations, and both experimental and numerical data are compared to theory. Finally, we study the effect of the centrifugal weakening of the trapping spring constants on the critical temperature for quantum degeneracy and the effects of finite temperature on vortex contrast.

We apply controlled perturbation theory to calculate the spectrum of the Gross-Pitaevskii equation for a system composed of attractive bosons confined in an anisotropic harmonic trap. The energy spectrum is calculated as a function of the coupling parameters for traps going from cigar to pancake shapes. The critical number of particles that ensures real values for the energy spectrum is obtained as a function of the potential anisotropic parameter, showing strong dependence of the critical number on the anisotropy of the trap. For a number of particles above the critical value the metastability of the system is characterized through the calculation of the condensate lifetime, using the imaginary part of the energy values. The obtained results are relevant for experiments where highly anisotropic traps are considered.

It is shown that the ferromagnetic transition takes place always above Bose-Einstein condensation in ferromagnetically coupled spinor Bose gases. We describe the Bose ferromagnet within Ginzburg-Landau theory by a “two-fluid” model below Bose-Einstein condensation. Both the Bose condensate and the normal component are spontaneously magnetized. As a main result we show that spin waves in the two fluids are coupled together so as to produce only one mixed spin-wave mode in the coexisting state. The spin-wave stiffness coefficient of the mixed mode, $c_s$, includes contributions from both the two phases, implying the “two-fluid” feature of the system. $c_s$ can show a sharp bend at the Bose-Einstein condensation temperature.

By using the time average of amplitude products we are able to identify changes in the dynamical complexity and the spatial coherence of a multimode laser. We find that there are cases in which as the pump increases, the dynamical complexity decreases and the spatial coherence improves. In some limiting cases the complexity is reduced to zero and the beam is completely coherent spatially. We show that these phenomena are caused by phase synchronization of the mode amplitudes and that they can be observed using slow detectors.

We suggest a scheme to generate a macroscopic superposition state (“Schrödinger cat state”) of a free-propagating optical field using a beam splitter, homodyne measurement, and a very small Kerr nonlinear effect. Our scheme makes it possible to reduce considerably the required nonlinear effect to generate an optical cat state using simple and efficient optical elements.

We derive the class of covariant measurements that are optimal according to the maximum likelihood criterion. The optimization problem is fully resolved in the case of pure input states, under the physically meaningful hypotheses of unimodularity of the covariance group and measurability of the stability subgroup. The general result is applied to the case of covariant state estimation for finite dimension, and to the Weyl-Heisenberg displacement estimation in infinite dimension. We also consider estimation with multiple copies, and analyze the behavior of the likelihood versus the number of copies. A “continuous-variable” analog of the measurement of direction of the angular momentum with two antiparallel spins by Gisin and Popescu is given.

Quantum Brownian oscillator model (QBM), in the Fock-space representation, can be viewed as a multilevel spin-boson model. At sufficiently low temperature, the oscillator degrees of freedom are dynamically reduced to the lowest two levels and the system behaves effectively as a two-level (E2L) spin-boson model (SBM) in this limit. We discuss the physical mechanism of level reduction and analyze the behavior of E2L-SBM from the QBM solutions. The availability of close solutions for the QBM enables us to study the non-Markovian features of decoherence and leakage in a SBM in the nonperturbative regime (e.g., without invoking the Born approximation) in better details than before. Our result captures very well the characteristic non-Markovian short time low temperature behavior common in many models.

We express the optimization of entanglement witnesses for arbitrary bipartite states in terms of a class of convex optimization problems known as robust semidefinite programs (RSDPs). We propose, using well known properties of RSDPs, several sufficient tests for separability of mixed states. Our results are then generalized to multipartite density operators.

We study the exact dynamics underlying stimulated Raman adiabatic passage (STIRAP) for a particle in a multilevel anharmonic system (the infinite square well) driven by two sequential laser pulses, each with constant carrier frequency. In phase space regions where the laser pulses create chaos, the particle can be transferred coherently into energy states different from those predicted by traditional STIRAP. It appears that a transition to chaos can provide an additional tool to control the outcome of STIRAP.

Symmetrized complex amplitudes for the double photoionization of helium are computed by the time-dependent close-coupling and exterior complex scaling methods, and it is demonstrated that both methods are capable of direct calculation of these amplitudes. The results are found to be in excellent agreement with each other and in very good agreement with results of other ab initio methods and experiments.

The measurement of an electromagnetic radiation field by a linearly accelerated observer is discussed. The nonlocality of this process is emphasized. The nonlocal theory of accelerated observers is briefly described and the consequences of this theory are illustrated using a concrete example involving the measurement of an incident pulse of radiation by an observer that experiences uniform acceleration during a limited interval of time.