We reexamine the problem of switching off unwanted phase evolution and decoherence in a single two-state quantum system in the light of recent results on random dynamical decoupling methods [L. Viola and E. Knill, Phys. Rev. Lett. 94, 060502 (2005)]. A systematic comparison with standard cyclic decoupling is effected for a variety of dynamical regimes, including the case of both semiclassical and fully quantum decoherence models. In particular, exact analytical expressions are derived for randomized control of decoherence from a bosonic environment. We investigate quantitatively control protocols based on purely deterministic, purely random, as well as hybrid design, and identify their relative merits and weaknesses at improving system performance. We find that for time-independent systems, hybrid protocols tend to perform better than pure random and may improve over standard asymmetric schemes, whereas random protocols can be considerably more stable against fluctuations in the system parameters. Beside shedding light on the physical requirements underlying randomized control, our analysis further demonstrates the potential for explicit control settings where the latter may significantly improve over conventional schemes.

We study a natural notion of decoherence on quantum random walks over the hypercube. We prove that this model possesses a decoherence threshold beneath which the essential properties of the hypercubic quantum walk, such as linear mixing times, are preserved. Beyond the threshold, we prove that the walks behave like their classical counterparts.

We present a technique to resolve a Gaussian density matrix and its time evolution through known expectation values in position and momentum. Further we find the full spectrum of this density matrix and apply the technique to a chain of harmonic oscillators to find agreement with conformal field theory in this domain. We also observe that a nonconformal state has a divergent entanglement entropy.

A dynamical many-body theory is presented which systematically extends beyond mean-field and perturbative quantum-field theoretical procedures. It allows us to study the dynamics of strongly interacting quantum-degenerate atomic gases. The nonperturbative approximation scheme is based on a systematic expansion of the two-particle irreducible effective action in powers of the inverse number of field components. This yields dynamic equations which contain direct scattering, memory, and “off-shell” effects that are not captured by the Gross-Pitaevskii equation. This is relevant to account for the dynamics of, e.g., strongly interacting quantum gases atoms near a scattering resonance, or of one-dimensional Bose gases in the Tonks-Girardeau regime. We apply the theory to a homogeneous ultracold Bose gas in one spatial dimension. Considering the time evolution of an initial state far from equilibrium we show that it quickly evolves to a nonequilibrium quasistationary state and discuss the possibility to attribute an effective temperature to it. The approach to thermal equilibrium is found to be extremely slow.

Extended Gross-Pitaevskii equations for the rotating $F=2$ condensate in a harmonic trap are solved both numerically and variationally using trial functions for each component of the wave function. Axially symmetric vortex solutions are analyzed and energies of polar and cyclic states are calculated. The equilibrium transitions between different phases with changing of the magnetization are studied. We show that at high magnetization the ground state of the system is determined by interaction in “density” channel, and at low magnetization spin interactions play a dominant role. Although there are five hyperfine states, all the particles are always condensed in one, two, or three states. Two interesting types of vortex structures are also discussed.

We apply the formulation developed in a recent paper [Y. Ohashi and A. Griffin, Phys. Rev. A 72, 013601 (2005)] for single-particle excitations in the BCS-BEC crossover to the case of a broad Feshbach resonance. At $T=0$, we solve the Bogoliubov–de Gennes coupled equations taking into account a Bose condensate of bound states (molecules). In the case of a broad resonance, the density profile $n\left(r\right)$, as well as the profile of the superfluid order parameter $\tilde{\Delta }\left(r\right)$, are spatially spread out to the Thomas-Fermi radius, even in the crossover region. This order parameter $\tilde{\Delta }\left(r\right)$ suppresses the effects of low-energy Andreev bound states on the rf tunneling current. As a result, the peak energy in the rf spectrum is found to occur at an energy equal to the superfluid order parameter $\tilde{\Delta }(r=0)$ at the center of the trap, in contrast to the case of a narrow resonance, and in agreement with recent measurements. The local density approximation is found to give a good approximation for the rf-tunneling spectrum.

We present an exact study of the finite-temperature properties of hard-core bosons (HCB’s) confined on one-dimensional optical lattices. Our solution of the HCB problem is based on the Jordan-Wigner transformation and properties of Slater determinants. We analyze the effects of the temperature on the behavior of the one-particle correlations, the momentum distribution function, and the lowest natural orbitals. In addition, we compare results obtained using the grand-canonical and canonical descriptions for systems like the ones recently achieved experimentally. We show that even for such small systems, as small as 10 HCB’s in 50 lattice sites, there are only minor differences between the energies and momentum distributions obtained within both ensembles.

The quantum-mechanical optical theorem in $N$-dimensional space is derived in a simple way from S-matrix theory.

Oscillations of atomic Bose-Einstein condensates in a 1D optical lattice with a two-point basis is investigated. In the low-frequency regime, four branches of modes are resolved, that correspond to the transverse in-phase and out-of-phase breathing modes, and the longitudinal acoustic and optical phonon modes of the condensates. Dispersions of these modes depend intimately on the values of two intersite Josephson tunneling strengths, $J_1$ and $J_2$, and the on-site repulsion $U$ between the atoms. Observation of these mode dispersions is thus a direct way to access them.

Efficient methods for generating pseudorandomly distributed unitary operators are needed for the practical application of Haar-distributed random operators in quantum communication and noise estimation protocols. We develop a theoretical framework for analyzing pseudorandom ensembles generated through a random circuit composition. We prove that the measure over random circuits converges exponentially (with increasing circuit length) to the uniform (Haar) measure on the unitary group, though the rate for uniform convergence must decrease exponentially with the number of qubits. We describe how the rate of convergence for test functions associated with specific randomization tasks leads to weaker convergence conditions that may allow efficient random circuit constructions.

We present a theoretical and experimental investigation of the emission characteristics and the flux of photon pairs generated by spontaneous parametric downconversion in quasi-phase matched bulk crystals for the use in quantum communication sources. We show that, by careful design, one can attain well defined modes close to the fundamental mode of optical fibers and obtain high coupling efficiencies also for bulk crystals, these being more easily aligned than crystal waveguides. We distinguish between singles coupling, ${\gamma }_{\mathrm{s}}$ and ${\gamma }_{\mathrm{i}}$, conditional coincidence, ${\mu }_{\mathrm{i}\mid \mathrm{s}}$, and pair coupling, ${\gamma }_{\mathrm{c}}$, and show how each of these parameters can be maximized by varying the focusing of the pump mode and the fiber-matched modes using standard optical elements. Specifically we analyze a periodically poled KTP-crystal pumped by a $532\mathrm{nm}$ laser creating photon pairs at $810\mathrm{nm}$ and $1550\mathrm{nm}$. Numerical calculations lead to coupling efficiencies above 93% at optimal focusing, which is found by the geometrical relation $L∕z_R$ to be $\approx 1$ to 2 for the pump mode and $\approx 2$ to 3 for the fiber-modes, where $L$ is the crystal length and $z_R$ is the Rayleigh-range of the mode-profile. These results are independent on $L$. By showing that the single-mode bandwidth decreases $\propto 1∕L$, we can therefore design the source to produce and couple narrow bandwidth photon pairs well into the fibers. Smaller bandwidth means both less chromatic dispersion for long propagation distances in fibers, and that telecom Bragg gratings can be utilized to compensate for broadened photon packets—a vital problem for time-multiplexed qubits. Longer crystals also yield an increase in fiber photon flux $\propto \sqrt{L}$, and so, assuming correct focusing, we can only see advantages using long crystals.

In this paper, we consider the generation of a three-qubit Greenberger-Horne-Zeilinger-like thermal state by applying the entanglement swapping scheme of Zukowski et al. [Ann. N. Y. Acad. Sci. 755, 91 (1995)] to three pairs of two-qubit Heisenberg $XY$ chains. The quality of the resulting three-qubit entanglement is studied by analyzing the teleportation fidelity, when it is used as a resource in the teleportation protocol of Karlsson et al. [Phys. Rev. A 58, 4394 (1998)]. We show that even though thermal noise in the original two-qubit states is amplified by the entanglement swapping process, we are still able to achieve nonclassical fidelities for the anisotropic Heisenberg $XY$ chains at finitely higher and higher temperatures by adjusting the strengths of an external magnetic field. This has a positive implication on the solid-state realization of a quantum computer.

We examine correlations in high-energy photoeffect, utilizing a perturbative treatment of the effects beyond the independent particle approximation (IPA) in the high-energy photoionization of states with arbitrary values of the angular momenta $\ell$. The dominant mechanism of IPA breaking is discussed. The dependence of IPA breaking contributions on the parameters $1∕Z$ and $\alpha Z$ is analyzed. In the general case the amplitude is expressed as a linear combination of IPA amplitudes. The development of precise experiments, together with the demonstration that there is substantial cancellation among the nonrelativistic partial correlations amplitudes in many cases, particularly for ground-state atoms, makes a relativistic approach to the problem desirable, even at relatively low values of photon energy.

We study theoretically how hydrogen atoms respond to intense ultrashort laser pulses of duration $\tau$ shorter than the inverse of the initial-state energy ${\epsilon }_i^{-1}$. An analytical expression for the evolution operator $\widehat{S}$ is derived up to the first order of the sudden perturbation approximation. This approximation treats the laser-atom interaction beyond the dipole approximation and yields $\widehat{S}$ as a series in the small parameter ${\epsilon }_i\tau$. It is shown that the effect of realistic laser pulses on atoms begins at the first order of ${\epsilon }_i\tau$. Transitions between atomic $\left(nlm\right)$ states of different $m$ become possible due to the action of the pulse’s magnetic field. Transitions between states of same $m$ and arbitrary $l$ become possible if the static Coulomb potential is taken into account during the pulse.

We report the results of simulations of the many atom wave function when a cold gas is excited to highly excited states. We simulated the many body wave function by direct numerical solution of Schrödinger’s equation. We investigated the fraction of atoms excited and the correlation of excited atoms in the gas for different types of excitation when the blockade region was small compared to the sample size. We also investigated the blockade effect when the blockade region is comparable to the sample size to determine the sensitivity of this system and constraints for quantum information.

The properties of ultracold atomic Bose-Fermi mixtures in external potentials are investigated and the existence of gap solitons of Bose-Fermi mixtures in optical lattices demonstrated. Using a self-consistent approach we compute the energy spectrum and show that gap solitons can be viewed as matter-wave realizations of quantum dots and antidots with the bosonic density playing the role of trapping (expulsive) potential for the fermions. The fermionic states trapped in the condensate are shown to be at the bottom of the Fermi sea and therefore well protected from thermal decoherence. Energy levels, filling factors, and parameters’ dependence of gap soliton quantum dots are also calculated both numerically and analytically.

We study the topological objects in two-component Bose-Einstein condensates. We compare two competing theories of two-component Bose-Einstein condensates, the popular Gross-Pitaevskii theory, and the recently proposed gauge theory of two-component Bose-Einstein condensate which has an induced vorticity interaction. We show that two theories produce very similar topological objects, in spite of the obvious differences in dynamics. Furthermore we show that the gauge theory of two-component Bose-Einstein condensates, with the $U\left(1\right)$ gauge symmetry, is remarkably similar to the Skyrme theory. Just like the Skyrme theory this theory admits the non-Abelian vortex, the helical vortex, and the vorticity knot. We construct the lightest knot solution in two-component Bose-Einstein condensates numerically, and discuss how the knot can be constructed in the spin-$\frac{1}{2}$ condensate of ${}^{87}\mathrm{Rb}$ atoms.

In this paper, we study the theory of spontaneous parametric down-conversion pumped by a short coherent pulse. It is shown that when single spatial mode filters and narrow band optical filters are used to filter the output state of parametric down-conversion, the postselected state of parametric down-conversion can be approximately described by a simple single-mode theory.