Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. 88, 017901 (2001)], is a measure of the discrepancy between two natural yet different quantum analogs of the classical mutual information. This notion characterizes and quantifies quantumness of correlations in bipartite states from a measurement perspective, and is fundamentally different from the various entanglement measures in the entanglement vs separability paradigm. The phenomenon of nonzero quantum discord is a manifestation of quantum correlations due to noncommutativity rather than due to entanglement, and has interesting and significant applications in revealing the advantage of certain quantum tasks. We will evaluate analytically the quantum discord for a large family of two-qubit states, and make a comparative study of the relationships between classical and quantum correlations in terms of the quantum discord. We furthermore compare the quantum discord with the entanglement of formation, and illustrate that the latter may be larger than the former, although for separable states, the entanglement of formation always vanishes and thus is less than the quantum discord.

We present a solution of the problem of the optimal unambiguous comparison of two ensembles of unknown quantum states ${|{\psi }_1⟩}^{\otimes k}$ and ${|{\psi }_2⟩}^{\otimes l}$. We consider two cases: (1) The two unknown states $|{\psi }_1⟩$ and $|{\psi }_2⟩$ are arbitrary states of qudits. (2) Alternatively, they are coherent states of a harmonic oscillator. For the case of coherent states we propose a simple experimental realization of the optimal “comparison” machine composed of a finite number of beam splitters and a single photodetector.

We develop the strong-field approximation for high-order harmonic generation in hydrogen molecules, including the vibrational motion and the laser-induced coupling of the lowest two Born-Oppenheimer states in the molecular ion that is created by the initial ionization of the molecule. We show that the field dressing becomes important at long laser wavelengths $\left(\approx 2\mu \text{m}\right)$, leading to an overall reduction of harmonic generation and modifying the ratio of harmonic signals from different isotopes.

Using three precisely timed laser pulses, we experimentally demonstrated that a strong femtosecond laser pulse can manipulate a coherent rotational wave packet. In the experiment, the first strong laser pulse created a coherent rotational wave packet from an initial thermal ensemble of ${\text{N}}_2\text{O}$ at room temperature. The second strong laser pulse manipulated the rotational wave packet. The third weak laser pulse probed the time evolution of the rotational wave packet by measuring the time-dependent alignment parameter. The pure heterodyne alignment signal and its Fourier transform spectrum were experimentally obtained and compared with the theoretical calculations. These results illustrated that the relative populations between even and odd rotational states can be controlled in the final rotational wave packet by precisely controlling the time delay between the first and the second laser pulses.

Resonant inelastic x-ray scattering accompanied by core-hole hopping induced by a strong infrared-laser field is studied for the nitrogen molecule. This process involves a strong laser-field-induced promotion of ungerade core holes created by a weak x-ray pulse to a gerade core level, which opens symmetry-forbidden scattering channels and gives rise to new features in the x-ray scattering spectrum. The core-hole hopping within the short lifetime of the core-excited state required for observation of the described process can be achieved at moderate intensities of the infrared field $\left(\sim {10}^{12}\text{W}/{\text{cm}}^2\right)$ because of the large transition dipole moment between the relevant core levels. The dynamics of resonant inelastic x-ray scattering assisted by change of core-hole parity is studied in detail versus the intensity, detuning, phase, and duration of the incident infrared-laser and x-ray pulses.

Most of the literature on quantum vortices predicting various states of vortex matter in three dimensions at finite temperatures in quantum fluids is based on the assumption of an extended and homogeneous system. This is well known not to be the case in actual Bose-Einstein condensates in traps, which are finite systems with nonuniform density. This raises the question to what extent one can speak of different aggregate states of vortex matter (vortex lattices, liquids, and tensionless vortex tangles) in these systems. To address this point, in the present work we focus on the finite-size, boundaries and density inhomogeneity effects on thermal vortex matter in a Bose-Einstein condensate. To this end we perform Monte Carlo simulations on a model system describing trapped Bose-Einstein condensates. Throughout the paper, we draw on analogies with results for vortex matter obtained for extended systems. We also consider, for comparison, the cylindrical confinement geometry with uniform density profile from the center out to the edge of the trap. The trapping potential is taken to be generically of an anharmonic form in such a way as to interpolate between a harmonic trap and a cylindrical confinement geometry. It also allows for a dip in the density profile at the center. We find distinct thermal equilibrium properties of the vortex system as the qualitative characteristics of the trapping potential are varied. For a uniform cylindrical confinement geometry, we find a vortex lattice at the center of the trap as well as ringlike thermal fluctuations of the vortex system as the trap edge is approached. For a harmonic trap, we find a distinct region at the edge of the trap where the vortex lines appear to have lost their line tension. Due to the steep density gradient, this crosses directly over to a vortex-line lattice at the center of the trap at low temperatures. At higher temperatures, an intermediate tensionful vortex liquid may exist. For an anharmonic trap where the ground state condensate density features a local minimum at the center of the trap, we find a corresponding region which appears to feature a tensionless vortex-line liquid phase. This work suggests that, finiteness and intrinsic inhomogeneity of the system notwithstanding, one nonetheless can approximately invoke the notion of distinct aggregate states of vortex matter realized at certain length scales. This might be helpful, in particular, in the search for possible new states of vortex matter in Bose-Einstein condensates with multiple components and different symmetries.

Nonlinear effects in pulse propagation through a medium consisting of four-level double-$\Lambda$-type systems are studied theoretically. We apply three continuous-wave driving fields and a pulsed probe field such that they form a closed interaction loop. Due to the closed loop and the finite frequency width of the probe pulses, the multiphoton resonance condition cannot be fulfilled, such that a time-dependent analysis is required. By identifying the different underlying physical processes we determine the parts of the solution relevant to calculate the linear and nonlinear response of the system. We find that the system can exhibit a strong intensity-dependent refractive index with small absorption over a range of several natural linewidths. For a realistic example we include Doppler and pressure broadening and calculate the nonlinear self-phase modulation in a gas cell with sodium vapor and argon buffer gas. We find that a self-phase modulation of $\pi$ is achieved after the propagation of a few centimeters through the medium while the absorption and pulse shape distortion in the corresponding spectral range is small.

The excitations of a two-dimensional (2D) Bose-Einstein condensate in the presence of a soliton are studied by solving the Kadomtsev-Petviashvili equation which is valid when the velocity of the soliton approaches the speed of sound. The excitation spectrum is found to contain states which are localized near the soliton and have a dispersion law similar to the one of the stable branch of transverse oscillations of a 1D gray soliton in a 2D condensate. By using the stabilization method we show that these localized excitations behave as resonant states coupled to the continuum of free excitations of the condensate.

We present a theoretical study of the collective excitations of a trapped imbalanced fermion gas at unitarity, when the system consists of a superfluid core and a normal outer shell. We formulate the relevant boundary conditions and treat the normal shell both hydrodynamically and collisionlessly. For an isotropic trap, we calculate the mode frequencies as a function of trap polarization. Out-of-phase modes with frequencies below the trapping frequency are obtained for the case of a hydrodynamic normal shell. For the collisionless case, we calculate the monopole mode frequencies and find that all but the lowest mode may be damped.

We study Delbrück scattering in a Coulomb field in the presence of a laser field. The amplitudes are calculated in the Born approximation with respect to the Coulomb field and exactly in the parameters of the laser field having arbitrary strength, spectral content, and polarization. The case of high initial photon energy is investigated in detail for a monochromatic circularly polarized laser field. It is shown that the angular distribution of the process substantially differs from that for Delbrück scattering in a pure Coulomb field. The value of the cross section under discussion may exceed the latter at realistic laser parameters that essentially simplify the possibility of the experimental observation of the phenomenon. The effect of high order terms in the quantum intensity parameter $\chi$ of the laser field is found to be very important already at relatively small $\chi$.

The influence of the relativistic covariance requirement on the optimality of the symmetric state-dependent $1\to 2$ cloning machine is studied. Namely, given a photonic qubit whose basis is formed from the momentum-helicity eigenstates, the change to the optimal cloning fidelity is calculated taking into account the Lorentz covariance unitarily represented by Wigner’s little group. Among other, we found states for which the optimal fidelity of the cloning process drops to 2/3 which corresponds to the fidelity of the optimal classical cloner. Also, an implication for the security of the Bennett-Brassard 1984 protocol is analyzed.

A random-phase approximation with exchange method has been developed for the photoionization of atoms (ions) with an inner open shell. The method allows for the inclusion of both intrashell and intershell correlations in the calculation and has been used to study the photoelectron asymmetry parameter and the cross sections of the Sc $4s$ photoionization in which the Sc $3p\text{−}3d$ transitions have been successfully included. The results demonstrate that the inclusion of the $3p\text{−}3d$ transitions is extremely important in the intershell coupling, which significantly influences the calculated asymmetry parameter and the cross sections of the Sc $4s$ photoionization. Comparison of our calculated asymmetry parameter and the cross sections with the measured data and available calculation is made and discussed. Possible improvements to the present calculated data are offered as well.

The local electric field enhancement generated by radiating fluorophores near a metallic surface results in lifetime variations observable at the single molecule level. Image theory, for dipoles located above flat surfaces, accounts for the results of ensemble experiments and is extensively used to interpret single molecule results. Nonetheless, smooth local surface inhomogeneities give rise to deviations of the single fluorophore properties from the image theory predictions. For this reason, we compute the effects of leading order corrections to the reflected fields of vertical dipoles located above locally curved perfectly conducting surfaces by invoking a small slope approximation.

We examine the properties of a quantum reflection trap when particle interaction is included. We explore the influence of the particle interaction on the trapping for different regimes: repulsive particle interaction and attractive particle interactions in its stable and unstable limit. With variational techniques, we calculate the phase diagram of the quantum reflection trap and determine the stable and unstable regimes of the system.

The operation of a BEC based atom interferometer, where the atoms are held in a weakly confining magnetic trap and manipulated with counterpropagating laser beams, is analyzed. A simple analytic model is developed to describe the dynamics of the interferometer. It is used to find the regions of parameter space with high and low contrast of the interference fringes for both single and double reflection interferometers. We demonstrate that for a double reflection interferometer the coherence time can be increased by shifting the recombination time. The theory is compared with recent experimental realizations of these interferometers.

We introduce an analytical expression for the dynamics of light propagation in a two-dimensional waveguide lattice including general long range coupling. Additionally, the diffraction properties in such general systems are investigated in detail. Using these very general results, particular geometries are discussed, including the possibility of diffraction-free propagation in the center of the Brillouin zone. Furthermore, the transition from the discrete to the continuum limit is analyzed.

We show that the probability distribution of tunneling time can be defined, although the decoherence functional does not satisfy the weak decoherence condition. However, the weak decoherence condition holds whenever the measuring device as defined by von Neumann exists as a part of the system. The resultant tunneling time probability distribution does not contain any information on the height of the potential.

A positive-energy-space-projected relativistic Hylleraas configuration-interaction method has been formulated. The projection procedure is based on the complex coordinate rotation method and may be applied independently of the specific form of the trial function.

We have investigated the behavior of an optical dipole force trap realized using a mode-locked Nd:YAG laser and have compared performance to a continuous-wave (cw) trap built using the same laser but running in a cw mode. The traps are used to confine ultracold ${}^{85}\text{R}\text{b}$ atoms which are loaded from a magneto-optical trap (MOT). In most respects, the two traps behave similarly over a wide range of laser parameters provided that the average potential well depth is the same; however, there is a notable difference in the dipole trap loading efficiency dependence on the detuning of the MOT trap laser frequency during the loading stage.

We investigate atomic magnetometry based on the rotation of a collective spin of atomic ensemble in a magnetic field. The rotation is monitored by a quantum nondemolition interaction of the atomic cloud with a probe light beam. We derive the optimal shape of the light pulse that for a given fixed measurement time and pulse energy minimizes the measurement error. We show that the error can be somewhat reduced by using a properly shaped pulse, but the asymptotic scaling of the error cannot be improved with respect to the scheme with constant intensity of the light beam.