We analyze the amplification by the Aharonov-Albert-Vaidman weak quantum measurement on a Sagnac interferometer [Dixon et al., Phys. Rev. Lett. 102, 173601 (2009)] up to all orders of the coupling strength between the measured system and the measuring device. The amplifier transforms a small tilt of a mirror into a large transverse displacement of the laser beam. The conventional analysis has shown that the measured value is proportional to the weak value, so that the amplification can be made arbitrarily large in the cost of decreasing output laser intensity. It is shown that the measured displacement and the amplification factor are in fact not proportional to the weak value and rather vanish in the limit of infinitesimal output intensity. We derive the optimal overlap of the pre- and postselected states with which the amplification become maximum. We also show that the nonlinear effects begin to arise in the performed experiments so that any improvements in the experiment, typically with an amplification greater than 100, should require the nonlinear theory in translating the observed value to the original displacement.

We consider the effects of plane-wave states scattering off finite graphs as an approach to implementing single-qubit unitary operations within the continuous-time quantum walk framework of universal quantum computation. Four semi-infinite tails are attached at arbitrary points of a given graph, representing the input and output registers of a single qubit. For a range of momentum eigenstates, we enumerate all of the graphs with up to $n=9$ vertices for which the scattering implements a single-qubit gate. As $n$ increases, the number of new unitary operations increases exponentially, and for $n>6$ the majority correspond to rotations about axes distributed roughly uniformly across the Bloch sphere. Rotations by both rational and irrational multiples of $\pi$ are found.

We analyze the efficiency and scalability of the Duan-Lukin-Cirac-Zoller (DLCZ) protocol for quantum repeaters focusing on the behavior of the experimentally accessible measures of entanglement for the system, taking into account crucial imperfections of the stored entangled states. We calculate then the degradation of the final state of the quantum-repeater linear chain for increasing sizes of the chain, and characterize it by a lower bound on its concurrence and the ability to violate the Clausner-Horne-Shimony-Holt inequality. The states are calculated up to an arbitrary number of stored excitations, as this number is not fundamentally bound for experiments involving large atomic ensembles. The measurement by avalanche photodetectors is modeled by “ON/OFF” positive operator-valued measure operators. As a result, we are able to consistently test the approximation of the real fields by fields with a finite number of excitations, determining the minimum number of excitations required to achieve a desired precision in the prediction of the various measured quantities. This analysis finally determines the minimum purity of the initial state that is required to succeed in the protocol as the size of the chain increases. We also provide a more accurate estimate for the average time required to succeed in each step of the protocol. The minimum purity analysis and the new time estimates are then combined to trace the perspectives for implementation of the DLCZ protocol in present-day laboratory setups.

The Casimir interactions in solid-liquid-solid systems as a function of separation distance have been studied by the Lifshitz theory. The dielectric permittivity functions for a wide range of materials are described by Drude, Drude-Lorentz, and oscillator models. We find that the Casimir forces between gold and silica or MgO materials are both repulsive and attractive. We also find the stable forms for the systems. Our studies would provide good guidance for future experimental studies on dispersion interactions.

A mechanism for three-photon double ionization of atoms by extreme-ultraviolet free-electron laser pulses is revealed, where in a sequential process the second ionization step, proceeding via resonant two-photon ionization of ions, is strongly enhanced by the excitation of ionic autoionizing states. In contrast to the conventional model, the mechanism explains the observed relative intensities of photoelectron peaks and their angular dependence in three-photon double ionization of argon.

We present experimental and numerical results on high-order-harmonic generation with a flat-top laser beam. We show that a simple binary tunable phase plate, made of two concentric glass plates, can produce a flat-top profile at the focus of a Gaussian infrared beam. Both experiments and numerical calculations show that there is a scaling law between the harmonic generation efficiency and the increase of the generation volume.

We study the stability region of the topological superfluid phase in a trapped two-dimensional polarized Fermi gas with spin-orbit coupling and across a BCS-BEC crossover. Due to the competition between polarization, pairing interaction, and spin-orbit coupling, the Fermi gas typically phase-separates in the trap. Employing a mean-field approach that guarantees the ground-state solution, we systematically study the structure of the phase separation and investigate in detail the optimal parameter region for the preparation of the topologically nontrivial superfluid phase. We then calculate the momentum space density distribution of the topological superfluid state and demonstrate that the existence of the phase leaves a unique signature in the trap integrated momentum space density distribution which can survive the time-of-flight imaging process.

Realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates are discussed. It is shown that, contrary to common intuition, rotation of the trap containing a spin-orbit condensate does not lead to an equilibrium state with static vortex structures but gives rise instead to nonequilibrium behavior described by an intrinsically time-dependent Hamiltonian. We propose here the following alternative methods to induce thermodynamically stable static vortex configurations: (i) to rotate both the lasers and the anisotropic trap and (ii) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. Effective Hamiltonians for spin-orbit condensates under such perturbations are derived for most currently known realistic laser schemes that induce synthetic spin-orbit couplings. The Gross-Pitaevskii equation is solved for several experimentally relevant regimes. The new interesting effects include spatial separation of left- and right-moving spin-orbit condensates, the appearance of unusual vortex arrangements, and parity effects in vortex nucleation where the topological excitations are predicted to appear in pairs. All these phenomena are shown to be highly nonuniversal and depend strongly on a specific laser scheme and system parameters.

We study an effect of rotation on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of two-component Fermi superfluid gases in a toroidal trap. We investigate the stability of the FFLO states in the quasi-one-dimensional regime on the basis of the Bogoliubov–de Gennes equation. We find that two FFLO phases, i.e., the half-quantum-vortex state and the intermediate state of the Fulde-Ferrell (FF) state and the Larkin-Ovchinnikov (LO) state, are stabilized by the rotation. The phase diagram for the FF state, LO state, intermediate state, and half-quantum-vortex state is shown in both the $T$-$P$ plane and the $T$-$h$ plane. We demonstrate characteristic features of these states, such as the order parameter, flux quantization, and local polarization. Several related works are discussed, and the advantages of cold Fermi gases are indicated.

We consider dipolar interactions between heteronuclear molecules in low-dimensional geometries. The setup consists of two one-dimensional tubes. We study the stability of possible few-body complexes in the regime of repulsive intratube interaction, where the binding arises from intertube attraction. The stable dimers, trimers, and tetramers are found and we discuss their properties for both bosonic and fermionic molecules. To observe these complexes we propose an optical nondestructive detection scheme that enables in situ observation of the creation and dissociation of the few-body complexes. A detailed description of the expected signal of such measurements is given using the numerically calculated wave functions of the bound states. We also discuss implications on the many-body physics of dipolar systems in tubular geometries, as well as experimental issues related to the external harmonic confinement along the tube and the prospect of applying an in-tube optical lattice to increase the effective dipole strength.

We investigate theoretically the time evolution of a one-dimensional system of spin-1/2 fermions in a harmonic trap after, initially, a spiral spin configuration far from equilibrium is created. We predict a spin segregation building up in time already for weak interaction under realistic experimental conditions. The effect relies on the interplay between exchange interaction and the harmonic trap, and it is found for a wide range of parameters. It can be understood as a consequence of an effective, dynamically induced long-range interaction that is derived by integrating out the rapid oscillatory dynamics in the trap.

We study the role of dephasing on entanglement evolution in a two-photon quantum-beat laser. We rigorously derived the pertinent master equation by taking into account dephasing, spontaneous emission, and cavity losses. The dephasing rate, in general, is lager than the rates of other dissipation processes and might influence the realizable quantum properties of the cavity field. We investigate the extent to which the dephasing rate affects the transient as well as steady-state entanglement between the cavity modes. We show that the coherence induced by initial coherent superposition of atomic levels leads to transient as well as steady-state entanglement, which turns out to be susceptible to decoherence. However, the entanglement created via coherence induced by a strong laser field exists for only short times and is relatively robust against decoherence.

We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.

We investigate theoretically the coupling of a cavity mode to a continuous distribution of emitters. We discuss the influence of the emitters’ inhomogeneous broadening on the existence and on the coherence properties of the polaritonic peaks. We find that their coherence depends crucially on the shape of the distribution and not only on its width. Under certain conditions the coupling to the cavity protects the polaritonic states from inhomogeneous broadening, resulting in a longer storage time for a quantum memory based on emitter ensembles. When two different ensembles of emitters are coupled to the resonator, they support a peculiar collective dark state, which is also very attractive for the storage of quantum information.

Propagation of an electromagnetic pulse through a dielectric slab doped with three-level ladder-type atomic systems is discussed. It is shown that the group velocity of the reflected and transmitted pulses can be switched from subluminal to superluminal light propagation by the thickness of the slab or the intensity of the coupling field. Furthermore, it is found that, in the presence of quantum interference, the reflected and transmitted pulses are completely phase dependent. So, the group velocity of the reflected and transmitted pulses can only be switched from subluminal to superluminal by adjusting the relative phase of the applied fields.

We study a five-level double-tripod system of cold atoms for efficiently manipulating the dynamic propagation and evolution of a quantum probe field by modulating four classical control fields. Our numerical results show that it is viable to transform the quantum probe field into a pair of two-color stationary light pulses mutually coupled through two wave packets of atomic spin coherence. The pair of stationary light pulses can be released either from the sample entrance and exit synchronously or just from the sample exit with a controlled time delay. In addition, the two-color stationary light pulses are immune to the fast decay originating from the higher-order Fourier components of atomic spin and optical coherence, and may exhibit the quantum limited beating signals with their characteristic frequency determined by detunings of the four classical control fields. These results could be explored to design novel photonic devices, such as optical routing, beam splitter, and beat generator, for manipulating a quantum light field.

We explore the potential of direct spectroscopy of ultranarrow optical transitions of atoms localized in an optical cavity. In contrast to stabilization against a reference cavity, which is the approach currently used for the most highly stabilized lasers, stabilization against an atomic transition does not suffer from Brownian thermal noise. Spectroscopy of ultranarrow optical transitions in a cavity operates in a very highly saturated regime in which nonlinear effects such as bistability play an important role. From the universal behavior of the Jaynes-Cummings model with dissipation, we derive the fundamental limits for laser stabilization using direct spectroscopy of ultranarrow atomic lines. We find that, with current lattice clock experiments, laser linewidths of about 1 mHz can be achieved in principle, and the ultimate limitations of this technique are at the 1 $\mu$Hz level.

We numerically study the dynamics of pairs of cavity solitons in a laser. We show that the solitons interact even at distances much greater than their sizes in the intensity and carrier-densities profile. The interaction is mediated by the phase. In a certain range of initial values of the distance, the solitons adjust their position until they form bound states. There are two such bound states, corresponding to different equilibrium distances, in which the solitons display partial phase locking, that is, their relative phase slowly oscillates as in a phase-entrained state. In those states, the two solitons can be switched on and off independently. For smaller initial distances, only one soliton survives. For larger initial distances, the solitons lock in phase and repel each other up to a distance of about ten soliton diameters.

In nonrelativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge $Z$ and two-three electrons: $(Z,e,e)$ and $(Z,e,e,e)$. It is shown that in both cases the total energy curve in $Z$ is smooth, without any visible irregularities. Thus, for both systems the physical integer charges $Z=1,2,...$ do not play a distinguished role as would be associated with charge quantization. By definition, a critical charge $Z_{\text{cr}}$ is a charge which separates a domain of the existence of bound states from a domain of unbound ones (continuum). For both systems the critical charges are found, $Z_{\text{cr},2e}=0.910850$ and $Z_{\text{cr},3e}=2.0090$, respectively. Based on numerical analysis, the Puiseux expansion in fractional powers of $(Z-Z_{\text{cr}})$ is constructed for both systems. Our results indicate the existence of a square-root branch point singularity at $Z_{\text{cr}}$ with exponent 3/2. A connection between the critical charge and the radius of convergence of $1/Z$ expansion is briefly discussed.