We study the dynamics of ultracold atoms trapped in optical double-well potentials in presence of noise generated by an external environment. When prepared in a Fock number state, the system shows phase coherence in the averaged density profile obtained using standard absorption image techniques, that disappears in absence of noise. This effect indicates that also in many-body systems an external environment may enhance quantum coherence, instead of destroying it.

Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudorandom circuits, with the goal of identifying relevant tradeoffs and optimizing convergence. The parameters we explore include the choice of single- and two-qubit gates, the topology of the underlying physical qubit architecture, the probabilistic application of two-qubit gates, as well as circuit size, initialization, and the effect of control constraints. Building on the equivalence between pseudorandom circuits and approximate $t$-designs, a Markov matrix approach is employed to analyze asymptotic convergence properties of pseudorandom second-order moments to a 2-design. Quantitative results on the convergence rate as a function of the circuit size are presented for qubit topologies with a sufficient degree of symmetry. Our results may be useful towards optimizing the efficiency of random state and operator generation.

In current experiments with cold quantum gases in periodic potentials, interference fringe contrast is typically the easiest signal in which to look for effects of nontrivial many-body dynamics. In order better to calibrate such measurements, we analyze the background effect of thermal decoherence as it occurs in the absence of dynamical interparticle interactions. We study the effect of optical lattice potentials, as experimentally applied, on the condensed fraction of a noninteracting Bose gas in local thermal equilibrium at finite temperatures. We show that the experimentally observed decrease of the condensate fraction in the presence of the lattice can be attributed, up to a threshold lattice height, purely to ideal-gas thermodynamics; conversely, we confirm that sharper decreases in first-order coherence observed in stronger lattices are indeed attributable to many-body physics. Our results also suggest that the fringe visibility “kinks” observed in Gerbier et al., Phys. Rev. Lett. 95, 050404 (2005) may be explained in terms of the competition between increasing lattice strength and increasing mean gas density, as the Gaussian profile of the red-detuned lattice lasers also increases the effective strength of the harmonic trap.

We report a series of experimental studies on single-mode fiber coupling of entangled photon pairs in type-II spontaneous parametric down-conversion. We experimentally compare the single-mode coupling efficiencies for three different phase matching regimes of bulk type-II spontaneous parametric down-conversion: collinear, noncollinear, and beamlike. Our experiment shows that the beamlike scheme provides the best single-mode coupling efficiency.

We study the effect of strong radio-frequency (rf) fields on a Bose-Einstein condensate (BEC) of chromium atoms, in a regime where the rf frequency is much larger than the Larmor frequency. We use the modification of the Landé factor by the rf field to bring all Zeeman states to degeneracy, despite the presence of a static magnetic field of up to $100\mathrm{mG}$. This is demonstrated by analyzing the trajectories of the atoms under the influence of dressed magnetic potentials in the strong-field regime. We investigate the problem of adiabaticity of the rf dressing process and relate it to how close the dressed states are to degeneracy. Finally, we measure the lifetime of the rf dressed BECs and identify a rf-assisted two-body loss process induced by dipole-dipole interactions.

Accurate results for nonrelativistic energy, relativistic, QED, and finite nuclear mass corrections are obtained for $2{}^{1}S_{1∕2}$, $3{}^{1}S_{1∕2}$, and $2{}^{1}P_{1∕2}$ states of the Li atom and ${\mathrm{Be}}^{+}$ ion. Our computational approach uses the Hylleraas basis set with the analytic integration and recursion relations. From comparison of experimental results for the isotope shifts to theoretical predictions including nuclear polarizabilities, we obtain nuclear charge radii for Li and Be isotopes.

We present a fully quantum-mechanical calculation of the harmonic spectra from vibrating molecules. By considering $\mathrm{H}_2{}^{+}$ molecules prepared in vibrating motion, we show that the frequency information of the vibrational levels can be extracted from the harmonic yields. The laser-induced dynamics is studied in addition and it is found that the emission efficiency of the harmonics is correlated with the time-varying internuclear separation. We demonstrate that the vibrational dynamics initiated by the pump or by the probe pulse can be investigated simultaneously by the high-order harmonic generation processes.

We analyze the effect of a highly dispersive element placed inside a modulated optical cavity on the frequency and amplitude of the output modulation to determine the conditions for enhanced gyroscopic sensitivities. The element is treated as both a phase and amplitude filter, and the time dependence of the cavity field is considered. Both atomic gases (two level and multilevel) and optical resonators (single and coupled) are considered and compared as dispersive elements. We find that it is possible to simultaneously enhance the gyro scale factor sensitivity and suppress the dead band by using an element with anomalous dispersion that has greater loss at the carrier frequency than at the sideband frequencies, i.e., an element that simultaneously pushes and intensifies the perturbed cavity modes, e.g. a two-level absorber or an undercoupled optical resonator. The sensitivity enhancement is inversely proportional to the effective group index, becoming infinite at a group index of zero. However, the number of round trips required to reach a steady state also becomes infinite when the group index is zero (or two). For even larger dispersions a steady state cannot be achieved, and nonlinear dynamic effects such as bistability and periodic oscillations are predicted in the gyro response.

We propose a general method to induce interference between scattering wave functions in atomic and molecular collisions at ultracold temperatures by using a static magnetic field. The scheme is based on the preparation of collision partners in coherent superpositions of Zeeman states. The magnetic field is used to induce interference between two incoming channels. As an illustrative example, we consider ultracold collisions between ${}^7\mathrm{Li}$ and ${}^{133}\mathrm{Cs}$ atoms, and show that ratios of state resolved collision cross sections can be enhanced by engineering the preparation of the initial coherent superpositions.

Nonequilibrium quantum rings emit circular-polarized subterahertz radiation with a polarization degree controllable on nano- to picosecond time scales. This we conclude using a theory developed here for the time-dependent detection of the circular polarization of polychromatic radiations, valid for time scales comparable to the reciprocal of characteristic emission frequencies. The theory is applied to driven quantum rings whereby the influence of radiative and nonradiative processes on the properties of the emitted light is incorporated.

We introduce a family of Hamiltonians with two degrees of freedom, axial symmetry and complete integrability. The potential function depends on coordinates and one control parameter. A fold catastrophe typically occurs in such a family of potentials and its consequences on the global dynamics are investigated through the energy-momentum map which defines the singular fibration of the four-dimensional phase space. The two inequivalent local canonical forms of the catastrophe are presented: the first case corresponds to the appearance of a second sheet in the image of the energy-momentum map while the second case is associated with the breaking of an already existing second sheet. A special effort is placed on the description of the singularities. In particular, the existence of cuspidal tori is related to a second-order contact point between the energy level set and the reduced phase space. The quantum mechanical aspects of the changes induced by the fold catastrophe are investigated with the quantum eigenstates computed for an octic potential and are interpreted through the quantum-classical correspondence. We note that the singularity exposed in this paper is not an obstruction to a global definition of action-angle variables.

We propose an alternative fidelity measure (namely, a measure of the degree of similarity) between quantum states and benchmark it against a number of properties of the standard Uhlmann-Jozsa fidelity. This measure is a simple function of the linear entropy and the Hilbert-Schmidt inner product between the given states and is thus, in comparison, not as computationally demanding. It also features several remarkable properties such as being jointly concave and satisfying all of Jozsa’s axioms. The trade-off, however, is that it is supermultiplicative and does not behave monotonically under quantum operations. In addition, metrics for the space of density matrices are identified and the joint concavity of the Uhlmann-Jozsa fidelity for qubit states is established.

We formulate a scheme for fault-tolerant quantum computation that works effectively against highly biased noise, where dephasing is far stronger than all other types of noise. In our scheme, the fundamental operations performed by the quantum computer are single-qubit preparations, single-qubit measurements, and conditional-phase (CPHASE) gates, where the noise in the CPHASE gates is biased. We show that the accuracy threshold for quantum computation can be improved by exploiting this noise asymmetry; e.g., if dephasing dominates all other types of noise in the CPHASE gates by four orders of magnitude, we find a rigorous lower bound on the accuracy threshold higher by a factor of 5 than for the case of unbiased noise.

X-ray four-wave mixing signals generated in the ${\mathbf{k}}_1+{\mathbf{k}}_2-{\mathbf{k}}_3$ phase-matching direction are simulated for N $1s$ transitions in paranitroaniline and two-ring hydrocarbons disubstituted with an amine and a nitroso groups. The two-dimensional x-ray correlation spectra (2DXCS) provide background-free probes of couplings between core-electron transitions even for multiple core shells of the same type. Features attributed to couplings between spatially separated core transitions connected by delocalized valence excitations provide information about molecular geometry and electronic structure unavailable from linear near-edge x-ray absorption (XANES).

This paper shows that replacing the usual integration variable $r∊[0,\infty )$ by a reduced radial variable $y\equiv y(r;\vec{\alpha })$ defined analytically on a finite domain $y∊[a,b]$ transforms the conventional radial Schrödinger equation into an equivalent form in which treatment of levels lying extremely close to dissociation becomes just as straightforward and routine as treating levels in the lower part of the potential well. Explicit integral expressions for the eigenvalue error due to the use of a finite step size in finite-difference methods of numerical integration are presented and are used to improve calculated eigenvalues as well as to determine optimal values of the mapping parameters $\vec{\alpha }$. This adaptive mapping procedure is shown to be versatile and efficient for both finite-difference and pseudospectral methods.

Differential cross sections for elastic electron scattering from gaseous water are reported. The measurements are obtained using the relative flow method with He as the standard gas and a thin collimating aperture source of gas instead of a conventional needle source. Differential cross sections were measured at incident energies of 1, 2, 4, 6, 8, 10, 15, 20, 30, 50, and $100\mathrm{eV}$ for scattering angles ranging from 5° to 130° and integrated over angles to obtain integral cross sections. Corresponding calculations of the differential cross section are carried out using the Schwinger multichannel method, employing extensive basis sets and considering polarization and dipole-scattering effects. Whereas excellent qualitative agreement with past measurements of differential cross sections is observed, our measurements are found to be consistently in significant quantitative disagreement with these measurements. The present calculations, on the other hand, generally agree in magnitude with previous results.

Consider $N$ bosons in a finite box $\Lambda ={[0,L]}^3\subset {\mathbb{R}}^3$ interacting via a two-body non-negative soft potential $V=\lambda \tilde{V}$ with $\tilde{V}$ fixed and $\lambda >0$ small. We will take the limit $L,N\to \infty$ by keeping the density $\varrho =N∕L^3$ fixed and small. We construct a variational state, which gives an upper bound on the ground-state energy per particle $\epsilon$, $\epsilon ⩽4\pi \varrho a[1+(128∕15\sqrt{\pi }){\left(\varrho a^3\right)}^{1∕2}{S}_{\lambda }]+O\left({\varrho }^2\mid \ln \varrho \mid \right)$, as $\varrho \to 0$, with a constant satisfying $1⩽S_{\lambda }⩽1+C\lambda$. Here $a$ is the scattering length of $V$ and thus depends on $\lambda$. In comparison, the prediction by Lee and Yang [Phys. Rev. 105, 1119 (1957)] and Lee, Huang, and Yang [Phys. Rev. 106, 1135 (1957)] asserts that $S_{\lambda }=1$ independent of $\lambda$.

We study the dynamical behavior of dissipative solitons in an optical cavity filled with a Kerr medium when a localized beam is applied on top of the homogeneous pump. In particular, we report on the excitability regime that cavity solitons exhibit which is an emergent property since the system is not locally excitable. The resulting scenario differs in an important way from the case of a purely homogeneous pump and now two different excitable regimes, both class I, are shown. The whole scenario is presented and discussed, showing that it is organized by three codimension-2 points. Moreover, the localized beam can be used to control important features, such as the excitable threshold, improving the possibilities for the experimental observation of this phenomenon.

We theoretically and numerically study the effect of backscattering on rotating ring lasers by employing the Maxwell-Bloch equations. We show that frequency shifts due to the Sagnac effect incorporating the effect of backscattering can be observed without lock-in phenomenon, if the strength of backscattering originating in the bumps of the refractive index is larger than a certain value. It is also shown that the experimental results corresponding to the theoretical ones can actually be obtained by using a semiconductor fiber-optic ring laser gyroscope.

We theoretically study and compare the light-induced Fréedericksz transition and above-threshold reorientation in pure and dye-doped nematic liquid crystals embedded into periodic dielectric structures. The presence of optical defect modes is found to significantly alter the effective influence of dyes as compared to the standard case of liquid crystal films without periodic structure, which is due to the overall resonant absorption of the dye-doped liquid crystal layer. Both statics and dynamics are discussed. In particular, it is found that optical response time can be up to several orders of magnitude faster with pure liquid crystals than with dye-doped ones. Thermal effects caused by absorption of dyes are also investigated to gauge whether it may induce nematic-to-isotropic phase transition.