We demonstrate the equivalence between (i) the semirelativistic limit (up to second order in the inverse of the speed of light) of the self-consistent Dirac-Maxwell equations and (ii) the Breit-Pauli equations in the mean-field (Hartree-like) approximation. We explain how the charge and current densities that act as sources in the Dirac-Maxwell equations are related to the microscopic two-electron interactions of the Breit-Pauli model (spin orbit, spin-other-orbit, and spin-spin). The key role played by the second-order corrections to the charge density is clarified.

We present an experimental method for rotating a Bose-Einstein condensate trapped in an axisymmetric magnetic potential. This method is based on the anharmonicity of the trapping potential, which couples the center-of-mass motion of the condensate to its internal motion. By circularly shaking the trapping potential, we generate a circular center-of-mass motion of the condensate around the trap center. The circulating condensate undergoes rotating shape deformation and eventually relaxes into a rotating condensate with a vortex lattice. We discuss the vortex nucleation mechanism and, in particular, the role of the thermal cloud in the relaxation process. Finally, we investigate the dependence of the vortex nucleation on the elliptical polarization of the trap shaking. The response of the condensate is asymmetric with respect to the sign of the shaking polarization, demonstrating the gauge-field effect due to the spin texture of the condensate in the magnetic potential.

We study a two-leg fermionic Hubbard ladder model with a state-dependent hopping. We find that, contrary to the case without a state-dependent hopping, for which the system has a superfluid nature regardless of the sign of the interaction at incommensurate filling, in the presence of such a hopping a spin-triplet superfluid, spin-density wave, and charge-density wave phases emerge. We examine our results in the light of recent experiments on periodically driven optical lattices in cold atoms. We give protocols allowing us to realize the spin-triplet superfluid elusive in the cold atoms.

Thermal fluctuations and melting transitions for rotating single-component superfluids have been intensively studied and are well understood. In contrast, the thermal effects on vortex states for two-component superfluids with density-density interaction, which have a much richer variety of vortex ground states, have been much less studied. Here, we investigate the thermal effects on vortex matter in superfluids with $\mathrm{U}\left(1\right)\times \mathrm{U}\left(1\right)$ broken symmetries and intercomponent density-density interactions, as well as the case with a larger $\mathrm{SU}\left(2\right)$ broken symmetry obtainable from the $\left[\mathrm{U}\right(1)\times \mathrm{U}(1\left)\right]$-symmetric case by tuning scattering lengths. In the former case we find that, in addition to first-order melting transitions, the system exhibits thermally driven phase transitions between square and hexagonal lattices. Our main result, however, concerns the case where the condensate exhibits $\mathrm{SU}\left(2\right)$ symmetry, and where vortices are not topological. At finite temperature, the system exhibits effects which do not have a counterpart in single-component systems. Namely, it has a state where thermally averaged quantities show no regular vortex lattice, yet the system retains superfluid coherence along the axis of rotation. In such a state, the thermal fluctuations result in transitions between different (nearly) degenerate vortex states without undergoing a melting transition. Our results apply to multicomponent Bose-Einstein condensates, and we suggest how to detect some of these unusual effects experimentally in such systems.

The quantum Fisher information and quantum correlation parameters are employed to study the application of nonclassical light to the problem of parameter estimation. It is shown that the optimal measurement sensitivity of a quantum state is determined by its intermode correlations (which depends on path entanglement) and intramode correlations (which depends on the photon statistics). In light of these results, we consider the performance of quantum-enhanced optical interferometers. Furthermore, we propose a Heisenberg-limited metrology protocol involving standard elements from passive and active linear optics, for which the quantum Cramér-Rao bound is saturated with an intensity measurement. Interestingly, the quantum advantage for this scheme is derived solely from the nonclassical photon statistics of the probe state and does not depend on entanglement. We study the performance of this scheme in the presence of realistic losses and consequently predict a substantial enhancement over the shot-noise limit with current technological capabilities.

We present an investigation of the temporal correlation of time-energy entangled photon pairs propagating through multi-frequency-channel dispersive media, in which photon spectra spread over multiple discrete frequency channels with dispersions. We have observed more complex coincidence structures including double coincidence envelopes and dependence on frequency detuning that are absent in the single-channel case. Our results on the correlation of the time-energy photonic entanglement in dispersive media with channel divisions would impact the fields of quantum metrology and communication.

Spontaneous synchronization is a fundamental phenomenon, important in many theoretical studies and applications. Recently, this effect has been analyzed and observed in a number of physical systems close to the quantum-mechanical regime. In this work we propose mutual information as a useful order parameter which can capture the emergence of synchronization in very different contexts, ranging from semiclassical to intrinsically quantum-mechanical systems. Specifically, we first study the synchronization of two coupled Van der Pol oscillators in both classical and quantum regimes and later we consider the synchronization of two qubits inside two coupled optical cavities. In all these contexts, we find that mutual information can be used as an appropriate figure of merit for determining the synchronization phases independently of the specific details of the system.

Scattering theory methods make it possible to calculate the Casimir energy of a perfectly conducting elliptic cylinder opposite a perfectly conducting plane in terms of Mathieu functions. In the limit of zero radius, the elliptic cylinder becomes a finite-width strip, which allows for the study of edge effects. However, existing packages for computing Mathieu functions are insufficient for this calculation because none can compute Mathieu functions of both the first and second kind for complex arguments. To address this shortcoming, we have written a general-purpose Mathieu-function package, based on algorithms developed by Alhargan. We use these routines to find edge corrections to the proximity force approximation for the Casimir energy of a perfectly conducting strip opposite a perfectly conducting plane.

State-by-state cross sections for dissociative electron attachment and electron-impact dissociation for molecular oxygen are computed using ab initio resonance curves calculated with the $R$-matrix method. When ${\mathrm{O}}_2$ is in its vibrational ground state, the main contribution for both processes comes from the ${}^2{\Pi }_u$ resonance state of ${\mathrm{O}}_2^{-}$ but with a significant contribution from the ${}^4{\Sigma }_u^{-}$ resonant state. Vibrational excitation leads to an increased contribution from the low-lying ${}^2{\Pi }_g$ resonance, greatly increased cross sections for both processes, and the threshold moving to lower energies. These results provide important input for models of ${\mathrm{O}}_2$-containing plasmas in nonequilibrium conditions.

Lyman-α radiation, $1216\AA$, has been seen from the sun and from various astrophysical sources. This radiation arises from the radiative transition from the $2p{}^{2}P$ state to the $1s{}^{2}S$ state of the hydrogen atom. The ${}^2\mathrm{P}$ state can be excited from the $1s{}^{2}S$ state by electron impact. However, it is possible to produce this excited state by photodetachment of the ${\mathrm{H}}^{-}$ ion, leaving the H atom in the ${}^2\mathrm{P}$ state. We have calculated cross sections for this process using Hylleraas-type functions for the ${\mathrm{H}}^{-}$ ion and using the exchange approximation for the photoelectron in the final continuum states of angular momenta equal to 0 and 2. The photoabsorption cross sections in ${\mathrm{H}}^{-}$ ions or He atoms leaving the hydrogen atom and helium ion in 2 ${}^2\mathrm{S}$ are also calculated. Similar calculations have been carried out for the ${\mathrm{Li}}^{+},{\mathrm{Be}}^{2+}$, and ${\mathrm{C}}^{4+}$ ions.

A time-dependent quantum wave-packet method is employed to investigate the rovibrational dynamics of population transfer in the ground electronic state controlled by two-color ($\omega +2\omega$) pulses analogous to coherently control the processes of ionization and dissociation. The population can be transferred to three target states, $|4,1\rangle ,|0,1\rangle$, and $|4,0\rangle$, at the same time through the ladder $\Lambda$ and multiphoton transitions. With the variation of the relative phase between $\omega$ and $2\omega$ pulses, the population distributions show oscillation behavior with a period of $\pi$. The population variation with relative phase depends on the size of the electric field asymmetry. The probabilities transferred to different target states can be controlled by varying the pulse amplitudes.

Torsional control is studied theoretically using a four-dimensional (4D) model introduced recently [Phys. Rev. Lett. 107, 113004 (2011) and Phys. Rev. A 87, 043403 (2013)] for calculating energy levels and eigenfunctions of nonrigid biphenyl-like molecules undergoing internal rotation and subject to a strong electric field. The time-dependent Schrödinger equation is solved to determine the behavior of the molecule when submitted to a short laser pulse. Torsional alignment is investigated for four limiting hindering potentials and for several peak laser intensities. The results obtained with the 4D model are compared to those from already available 2D and 1D models. Similar results are found with the 4D and 2D model and are consistent with the molecule interacting the most with the electric field for the hindering potential displaying four minima with $D_{2d}$ symmetry staggered equilibrium configurations. Molecular axis alignment is also investigated and it is found that the one arising with the 4D model starts deviating substantially from the one arising with a rigid rotator for a value of the peak laser intensity of $3\times {10}^{13}$ ${\mathrm{W}/\mathrm{cm}}^2$.

The excitation of many-electron atoms and ions by twisted light has been studied within the framework of the density-matrix theory and Dirac's relativistic equation. Special attention is paid to the magnetic sublevel population of excited atomic states as described by means of the alignment parameters. General expressions for the alignment of the excited states are obtained under the assumption that the photon beam, prepared as a coherent superposition of two twisted Bessel states, irradiates a macroscopic target. We demonstrate that for this case the population of excited atoms can be sensitive to both the transverse momentum and the (projection of the) total angular momentum of the incident radiation. While the expressions are general and can be employed to describe the photoexcitation of any atom, independent on its shell structure and number of electrons, we performed calculations for the $3s\to 3p$ transition in sodium. These calculations indicate that the “twistedness” of incoming radiation can lead to a measurable change in the alignment of the excited ${}^{2}P_{3/2}$ state as well as the angular distribution of the subsequent fluorescence emission.

We model the dynamics of condensation in a bimodal trap, consisting of a large reservoir region, and a tight “dimple” whose depth can be controlled. Experimental investigations have found that such dimple traps provide an efficient means of achieving condensation. In our kinetic equations, we include two- and three-body processes. The two-body processes populate the dimple, and lead to loss when one of the colliding atoms is ejected from the trap. The three-body processes produce heating and loss. We explain the principal trends, give a detailed description of the dynamics, and provide quantitative predictions for time scales and condensate yields. From these simulations, we extract optimal parameters for future experiments.

The precision of most compact inertial sensing schemes using trapped- and guided-atom interferometers has been limited by uncontrolled phase errors caused by trapping potentials and interactions. Here we propose an acoustic interferometer that uses sound waves in a toroidal Bose-Einstein condensate to measure rotation, and we demonstrate experimentally several key aspects of this type of interferometer. We use spatially patterned light beams to excite counterpropagating sound waves within the condensate and use in situ absorption imaging to characterize their evolution. We present an analysis technique by which we extract separately the oscillation frequencies of the standing-wave acoustic modes, the frequency splitting caused by static imperfections in the trapping potential, and the characteristic precession of the standing-wave pattern due to rotation. Supported by analytic and numerical calculations, we interpret the noise in our measurements, which is dominated by atom shot noise, in terms of rotation noise. While the noise of our acoustic interferometric sensor, at the level of $\sim \text{rad}{\text{s}}^{-1}/\sqrt{\text{Hz}}$, is high owing to rapid acoustic damping and the small radius of the trap, the proof-of-concept device does operate at the high densities and small volumes of trapped Bose-Einstein condensed gases.

Due to practical reasons, experimental and theoretical continuous-variable (CV) quantum information (QI) has been heavily based on Gaussian states. Nevertheless, many CV-QI protocols require the use of non-Gaussian states and operations. Here, we show that the Einstein-Podolsky-Rosen-steering inequality can be used to obtain a practical witness for the generation of pure bipartite non-Gaussian states. While the scenario requires pure states, we show its broad relevance by reporting the experimental observation of the non-Gaussianity of the CV two-photon state generated in the process of spontaneous parametric down-conversion (SPDC). The observed non-Gaussianity is due only to the intrinsic phase-matching conditions of SPDC.

The derivation of a quantum Markovian model for an optomechanical system consisting of a quantum mechanical mirror interacting with quantum optical input fields via radiation pressure is a difficult problem which ultimately involves the scattering process of quantum stochastic calculus. We show that, while the scattering process may be approximated in a singular limit by regular processes using different schemes, the limit model is highly sensitive to the mathematical interpretation of the approximation scheme. We find two main types of stochastic limits of regular models, and illustrate the origin of this difference at the level of one-particle scattering. As an alternative modeling scheme, we consider models of mirrors as nontrivial dielectric media with boundaries that are themselves quantized. Rather than treating the plane waves for the electromagnetic field, we take the actual physical modes and quantize these. The input-output formalism is then obtained in the far zone where the plane-wave approximation is valid. Several examples are considered, and the quantum stochastic model is derived. We also consider the quantum trajectories problem for continual measurement of the reflected output fields, and derive the stochastic master equations for homodyning and photon-counting detection to estimate the mirror observables.

The negative and positive Goos-Hänchen (GH) shifts in reflected light are revisited for a partial coherent light incident on a cavity. A three-level dilute gaseous atomic medium, which follows two-photon Raman transitions, is considered in a cavity. The anomalous (negative group index) and normal (positive group index) dispersions of the intracavity medium lead to negative and positive GH shifts, respectively. The effects of beam width, spatial coherence, and mode index of partial coherent light fields are studied on the negative and positive GH shifts. It is observed that the amplitude of negative and positive GH shifts are relatively large for a small range of beam width and for a small value of spatial coherence of partial coherent light beams. The amplitude of GH shifts becomes small for large beam width and spatial coherence of incident light. Further, the distortion in the reflected light field increases when the amplitude of the GH shifts increases and vice versa.

We study the dynamics of stimulated Raman scattering in high-$Q$ split-mode microresonators. It is found that Raman lasing preferentially occurs in only one of the two competing split modes, and can therefore be beat-note free. Sweeping the pump wavelength causes the intracavity field pattern of the pump light to rotate, which makes the Raman laser hop between the two split modes. During these hops, both modes lase simultaneously, producing a beat note in the output Raman power. By studying this beat note, we demonstrate that the mode splitting is strongly affected by the Raman intensities in the two modes via the optical Kerr effect.