We use classical field simulations of the homogeneous Bose gas to study the breakdown of superflow due to vortex nucleation past a cylindrical obstacle at finite temperature. Thermal fluctuations modify the vortex nucleation from the obstacle, turning antiparallel vortex lines (which would be nucleated at zero temperature) into wiggly lines, vortex rings, and even vortex tangles. We find that the critical velocity for vortex nucleation decreases with increasing temperature and scales with the speed of sound of the condensate, becoming zero at the critical temperature for condensation.

We present an atomic multiwave interferometer with magnetic sublevels to precisely determine the Aharonov-Casher (AC) geometric phase. Simulations show that this interferometer has sharper fringes than a normal two-wave interferometer, which means a higher phase resolution can be achieved. Moreover, atoms evolving in a single hyperfine structure state make the interferometer insensitive to the dc Stark phase shift. This dc Stark shift is one of the main noise sources in AC phase measurements. The constraint of the photon rest mass is also discussed when using this atomic interferometer to measure the Aharonov-Casher phase.

We determine the size of the critical region of the superfluid transition in the Bardeen-Cooper-Schrieffer–Bose-Einstein condensation (BCS-BEC) crossover of a three-dimensional fermion gas, using a renormalization-group approach to a bosonic theory of pairing fluctuations. For the unitary Fermi gas, we find a sizable critical region $[T_G^{-},T_G^{+}]$, of order $T_c$, around the transition temperature $T_c$ with a pronounced asymmetry: $|T_G^{+}-T_c|/|T_G^{-}-T_c|\sim 8$. The critical region is strongly suppressed on the BCS side of the crossover but remains important on the BEC side.

We demonstrate that the total reflected field produced by the interaction of a moderately relativistic laser with dense plasma is itself an efficient driver of high-order-harmonic generation. A system of two or more successive interactions of an incident laser beam on solid targets may therefore be an experimentally realizable method of optimizing conversion of laser energy to high-order harmonics. Particle-in-cell simulations suggest that attosecond pulse intensity may be increased by up to four orders of magnitude in a multipass system, with decreased duration of the attosecond pulse train. We discuss high-order-harmonic wave-form engineering for enhanced attosecond pulse generation with an electron trajectory model, present the behavior of multipass systems over a range of parameters, and offer possible routes towards experimental implementation of a two-pass system.

This work analyzes the temporal coherence and correlation of twin beams generated in a quasi-phase-matched nonlinear crystal in a counterpropagating configuration, ranging from the low-gain regime, where counterpropagating photon pairs are generated spontaneously, to the regime of stimulated pair production, close to the mirrorless optical parametric oscillator threshold. Here, we show a critical divergence of the correlation time and slowing down of quantum fluctuations originating from the feedback mechanism responsible for the MOPO threshold.

The major barrier to realizing a perfect lens with left-handed materials is perceived to be their intrinsic loss. Here we show that only specific designs of perfect lenses are limited by loss—those in which material loss is translated to internal feedback. The asymptotically uniform transmission required for perfect lensing is hindered by such feedback, which generates resonances that lead to a spatial cutoff in the lens transmission. Moreover, uniform transmission and its resonant deterioration stem from completely separate classes of modal excitations. A perfect lens made of lossy left-handed materials is therefore not forbidden in principle. Pursuing perfect lens designs that avoid internal feedback offers a path towards realization of practical perfect lenses.

The time-dependent fermionic Hartree-Fock equations can be stochastically extended in such a way as to become the exact representation of quantum dynamics. This fact was first observed in the work of Juillet and Chomaz [Phys. Rev. Lett. 88, 142503 (2002)]. During the past decade, this observation has led to the emergence of a whole family of stochastic wave-function methods for fermions. The common feature of all these methods is that they are based on the expansion of the density operator over the dyadic product of the two fermionic Slater determinant states. In this work, we develop a unified and rigorous foundation for this family of methods. We find a general form of stochastic equations and describe the sufficient conditions under which these methods converge towards exact quantum dynamics. To achieve these goals, we employ the representation of quantum dynamics in generalized phase space. In particular, we consider the quasiprobability distributions which emerge in these stochastic methods and their master equations. It is shown that the convergence towards exact quantum dynamics is controlled by the problem of boundary terms. We provide an example of stochastic Hartree-Fock method which is well-defined and free from this problem.

We provide an analytical investigation of the pairwise entanglement dynamics for a system, consisting of an arbitrary number of qubits dissipating into a common and non-Markovian environment for both weak- and strong-coupling regimes. In the latter case, a revival of pairwise entanglement due to the memory depth of the environment is observed. The leakage of photons into a continuum state is assumed to be the source of dissipation. We show that for an initially Werner state, the environment washes out the pairwise entanglement, but a series of nonselective measurements can protect the relevant entanglement. On the other hand, by limiting the number of qubits initially in the superposition of single excitation, a stationary entanglement can be created between qubits initially in the excited and ground states. Finally, we determine the stationary distribution of the entanglement versus the total number of qubits in the system.

We describe the entanglement of two indistinguishable delocalized spin-$\frac{1}{2}$ particles in the simplest spatial configuration of three spatial modes with the constraint that at most one particle occupy each mode. It is shown that this is the only number of modes for which maximally entangled states exist in such a system. The set of entangled states, including the set of maximally entangled states, is described and different types of entanglement in terms of Bell-nonlocal correlations for different partitions of the system are identified. In particular we focus on the entangled states that are Bell local for a tripartition of the system and cannot be described as a superposition of bipartite entangled pairs of localized particles. Two entanglement invariants are constructed and it is shown that all entanglement monotones are functions of these. Furthermore, the system has a generic nontrivial local unitary symmetry with a corresponding $2\pi /3$ fractional topological phase. In addition to this a necessary and sufficient condition for the existence of maximally entangled states in systems of arbitrary numbers of delocalized particles with arbitrary spin, where at most one particle can occupy each mode, is derived.

The quantum-mechanical counterpart of a classical random walk offers a rich dynamics that has recently been shown to include topologically protected bound states (zero modes) at boundaries or domain walls. Here we show that a topological zero mode may acquire a dynamical role in the presence of nonlinearities. We consider a one-dimensional discrete-time quantum walk that combines zero modes with a particle-conserving nonlinear relaxation mechanism. The presence of both particle-hole and chiral symmetry converts two zero modes of opposite chirality into an attractor-repeller pair of the nonlinear dynamics. This makes it possible to steer the walker towards a domain wall and trap it there.

The round-robin differential phase-shift quantum key distribution protocol provides a secure way to exchange private information without monitoring conventional disturbances and still maintains a high tolerance of noise, making it desirable for practical implementations of quantum key distribution. However, photon number resolving detectors are required to ensure that the detected signals are single photons in the original protocol. Here, we adopt the detector-decoy method and give the bounds to the fraction of detected events from single photons. Utilizing the advantages of the protocol, we provide a practical method of performing the protocol with desirable performances requiring only threshold single-photon detectors.

We propose a superconducting circuit comprising a dc superconducting quantum interference device with a mechanically compliant arm embedded in a coplanar microwave cavity that realizes an optomechanical system with a degenerate or nondegenerate parametric interaction generated via the dynamical Casimir effect. For experimentally feasible parameters, this setup is capable of reaching the single-photon ultrastrong-coupling regime while simultaneously possessing a parametric coupling strength approaching the renormalized cavity frequency. This opens up the possibility of observing the interplay between these two fundamental nonlinearities at the single-photon level.

Electron-impact direct double ionization (DDI) of the ground-state $\mathrm{L}{\mathrm{i}}^{+}$ ion is investigated using an approach which takes into account contribution from ionization-ionization, ionization-excitation-ionization, and excitation-ionization-ionization processes. Reasonable agreement with the experimental data is obtained when bound electrons of the $\mathrm{L}{\mathrm{i}}^{+}$ ion are considered as residing on the opposite sides of the nucleus. It is shown that distribution of the excess energy between the scattered and the ejected electrons, which participate in the next step of ionization, has a significant effect on the DDI cross sections. Better agreement with the experiment is obtained when electrons share the excess energy. The DDI study reveals the dominant role of the ionization-ionization process for the $\mathrm{L}{\mathrm{i}}^{+}$ ion.

It is well known that area pulses make Rabi oscillation and chirped pulses in the adiabatic interaction regime induce complete population inversion of a two-state system. Here we show that chirped zero-area pulses could engineer an interplay between the adiabatic evolution and Rabi-like rotations. In a proof-of-principle experiment utilizing spectral chirping of femtosecond laser pulses with a resonant spectral hole, we demonstrate that the chirped zero-area pulses could induce, for example, complete population inversion and return of the cold rubidium atom two-state system. Experimental result agrees well with the theoretically considered overall dynamics, which could be approximately modeled to a Ramsey-like three-pulse interaction, where the $x$ and $z$ rotations are driven by the hole and the main pulse, respectively.

We propose an experimental protocol to directly observe the Kondo effect by scattering ultracold atoms. We propose using an optical Feshbach resonance to engineer Kondo-type spin-dependent interactions in a system with ultracold ${}^6\mathrm{Li}$ and ${}^{87}\mathrm{Rb}$ gases. We calculate the momentum transferred from the ${}^{87}\mathrm{Rb}$ gas to the ${}^6\mathrm{Li}$ gas in a scattering experiment and show that it has a logarithmically enhanced temperature dependence, characteristic of the Kondo effect, and analogous to the resistivity of alloys with magnetic impurities. Experimentally detecting this enhancement will give a different perspective on the Kondo effect, and allow us to explore a rich variety of problems such as the Kondo lattice problem and heavy-fermion systems.

We present a correlated many-body approach to calculate the distribution function and fluctuations for a Bose-Einstein condensate with $N$ interacting atoms in the harmonic confinement. The present formulation uses the recursion relation for the canonical ensemble partition function $\left(Z\right)$. $Z$ is calculated from the energy spectrum of the many-body effective potential, which keeps all possible two-body correlations and uses the realistic interatomic interaction. The condensate statistics are in very good agreement with earlier results of an ideal gas for which exact statistical moments for all temperature are known. We also present the numerical results of condensate statistics for real experimental situations. The calculated moments nicely exhibit the mesoscopic effect for a few hundred atoms, whereas the sharp fall in the variance for the large condensate near the critical temperature shows the possibility of phase transition. We also calculate the critical temperature for the mesoscopic regime. Our present calculation mimics the JILA experiment with ${}^{87}\mathrm{Rb}$ atoms.

We use the finite-difference-time-domain method for the simulation of one-dimensional Raman random lasers. This method enables us to introduce mode competition, as well as self- and cross-saturation effects in our analysis. Our results show that Raman random laser emission is single mode only for the low pump intensities. When pump intensity increases, other orders of Stokes and anti-Stokes lasing modes appear in the emission spectrum. These modes strongly interact with each other and transfer of energy takes place between them. The lasing thresholds of different modes of the Raman random laser are calculated and compared with each other. The spatial distribution of electric field along the length of the disordered structure is calculated corresponding to different pump intensities. As the pump intensity increases, more localization centers appear in the electric field distribution of the laser emission along the system length. These localization centers are attributed to the spatial distribution of lasing modes whose thresholds are being reached and their random positions significantly depend on the pumping intensity value. We also demonstrate that the lasing threshold of different laser modes decreases with increasing the disorder strength due to the improvement of Anderson localization. Furthermore, the time-dependent theory presented here indicates that changing the pump wavelength changes all lasing wavelengths of the Raman random laser, including first-order Stokes and other-order Stokes and anti-Stokes lasing modes. This fast and powerful time-dependent method makes possible the investigation and simulation of two- and three-dimensional Raman random lasers.

Taking into account relaxing Kerr nonlinearity and walk-off effects, the conditions and gain spectra of cross-phase modulation-induced modulational instability (XPM-MI) of two incoherently copropagating optical waves of different frequencies and same polarization are investigated. We devote particular attention to the mixed case in which one pulse propagates under the normal group-velocity dispersion (GVD) regime, while the second one is under an anomalous GVD regime. We unveil that in the limit of an instantaneuous nonlinear response, the typical frequency with maximum gain converges to a finite value in the mixed GDV regime, while it continuously grows with the group-velocity mismatch in the normal GVD regime. As a result, the maximum gain typically decreases with the group-velocity mismatch in the mixed regime, contrasting with the opposite trend in the normal GVD regime. Further, we show that besides the mode having maximum gain at a frequency decaying with $1/{\tau }^{1/3}$ in the slow response limit, there is a second mode having maximum gain with a distinct scaling behavior ${\mathrm{\Omega }}_{\text{max}}\propto 1/\tau$ in the absence of group-velocity mismatch. The associated maximum gains scale, respectively, as $1/{\tau }^{2/3}$ and $1/\tau$, thus signaling the corresponding quadratic and linear dispersion relation of these modes in the low-frequency limit. A detailed analysis of the influence of the nonlinear response time and group-velocity dispersion on the MI gain spectrum is also provided.

The resonant-state-expansion (RSE) Born approximation, a rigorous perturbative method developed for electrodynamic and quantum mechanical open systems, is further developed to treat waveguides with a Sellmeier dispersion. For media that can be described by these types of dispersion over the relevant frequency range, such as optical glass, I show that the perturbed RSE problem can be solved by diagonalizing a second-order eigenvalue problem. In the case of a single resonance at zero frequency, this is simplified to a generalized eigenvalue problem. Results are presented using analytically solvable planar waveguides and parameters of borosilicate BK7 glass, for a perturbation in the waveguide width. The efficiency of using either an exact dispersion over all frequencies or an approximate dispersion over a narrow frequency range is compared. I included a derivation of the RSE Born approximation for waveguides to make use of the resonances calculated by the RSE.