We study the dynamics of a trapped spin-1 condensate in a magnetic field. First, we analyze the homogeneous system, for which the dynamics can be understood in terms of orbits in phase space. We analytically solve for the dynamical evolution of the populations of the various Zeeman components of the homogeneous system. This result is then applied via a local-density approximation to trapped quasi-one-dimensional condensates. Our analysis of the trapped system in a magnetic field shows that both the mean-field and Zeeman regimes are simultaneously realized, and we argue that the border between these two regions is where spin domains and phase defects are generated. We propose a method to experimentally tune the position of this border.

We investigate the generation of two-mode-entangled light from a laser-driven three-level $\mathsf{V}$-type atom inside a cavity by taking into account spontaneously generated quantum interference between two atomic decay channels. We show that under some conditions, the system can reduce to a nondegenerate parametric amplifier which is responsible for the entanglement between the two cavity modes. Compared to the case without the quantum interference, it is found that the entanglement of the cavity field can be significantly enhanced by the interference when the relative phase of the two pumping lasers $\delta \varphi =\pi$.

We apply a kinetic model to predict the existence of an instability mechanism in elongated Bose-Einstein condensates. Our kinetic description, based on the Wigner formalism, is employed to highlight the existence of unstable Bogoliubov waves that may be excited in the counterpropagation configuration. We identify a dimensionless parameter, the Mach number at $T=0$, that tunes different regimes of stability. We also estimate the magnitude of the main parameters at which two-stream instability is expected to be observed under typical experimental conditions.

A Fermi-Fermi mixture of ${}^{40}\text{K}$ and ${}^6\text{L}\text{i}$ does not exhibit the Efimov effect in a free space, but the Efimov effect can be induced by confining only ${}^{40}\text{K}$ in one dimension. Here the Efimov’s three-body parameter is controlled by the confinement length. We show that the three-body recombination rate in such a system in the dilute limit has a characteristic logarithmic-periodic dependence on the effective scattering length with the scaling factor 22.0 and can be expressed by formulas similar to those for identical bosons in three dimensions. The ultracold mixture of ${}^{40}\text{K}$ and ${}^6\text{L}\text{i}$ in the one-dimensional–three-dimensional mixed dimensions is thus a promising candidate to observe the Efimov physics in fermions.

We present the experimental demonstration of nondestructive probing of the ${{}^{1}S}_0\text{−}{{}^{3}P}_0$ clock transition probability in an optical lattice clock with ${}^{87}\text{S}\text{r}$ atoms. It is based on the phase shift induced by the atoms on a weak off-resonant laser beam. The method we propose is a differential measurement of this phase shift on two modulation sidebands with opposite detuning with respect to the ${{}^{1}S}_0\text{−}{{}^{1}P}_1$ transition, allowing a detection limited by the photon shot noise. We have measured an atomic population of ${10}^4$ atoms with a signal-to-noise ratio of 100 per cycle, while keeping more than 95% of the atoms in the optical lattice with a depth of 0.1 mK. The method proves simple and robust enough to be operated as part of the whole clock setup. This detection scheme enables us to reuse atoms for subsequent clock state interrogations, dramatically reducing the loading time and thereby improving the clock frequency stability.

A scheme for generating states of three free electrons entangled with respect to their spins is suggested. It consists of sequential ejection of two Auger electrons ($e_2$ and $e_3$) in the nonradiative decay of an inner-shell vacancy created due to the emission of photoelectron $e_1$ from an atom, say $A$. In the absence of spin-orbit interaction, the entanglement among the spin angular momenta of the flying $\left(e_1,e_2,e_3\right)$ is generated simply by the Coulomb interaction experienced by them inside $A$. Their states are classified according to the hierarchic structure suggested by Dür, Cirac, and Tarrach [Phys. Rev. Lett. 83, 3562 (1999); Dür and Cirac, Phys. Rev. A 61, 042314 (2000)]. The generation of fully separable, 1-electron biseparable, fully inseparable, or “$1\to 2$ entangled” tripartite (in addition to various kinds of bipartite) states is shown to be completely determined only by the spin multiplicities of the electronic states of $A$ and of its ionic species $\left(A^{{+}^{\ast }},A^{2{+}^{\ast }},A^{3+}\right)$ participating in the suggested scheme. The entanglement of three electrons is Greenberger-Horne-Zeilinger type. The experimental characterization of these states is fully achieved merely by the measurements of the energies of $\left(e_1,e_2,e_3\right)$, without requiring any entanglement witness or other similar protocols hitherto developed in quantum information.

Bosonic Josephson junctions can be realized by confining ultracold gases of bosons in multiwell traps and studied theoretically with the $M$-site Bose-Hubbard model. We show that canonical equilibrium states of the $M$-site Bose-Hubbard model may be approximated by mixtures of coherent states, provided the number of atoms is large and the total energy is comparable to $k_{B}T$. Using this approximation, we study thermal fluctuations in bosonic Josephson junctions in the mean-field regime. Statistical estimates of the fluctuations of relative phase and number, obtained by averaging over many replicates of an experiment, can be used to estimate the temperature and the tunneling parameter or to test whether the experimental procedure is effectively sampling from a canonical thermal equilibrium ensemble.

We discuss the thermodynamics of a nonrelativistic gas of bosons with a local repulsive interaction. In particular, we compute the temperature and density dependences of pressure, energy and entropy densities, superfluid and condensate fractions, correlation length, specific heat, isothermal and adiabatic compressibilities, and various sound velocities. The $T\to 0$ limit approaches the quantum phase transition, while the universal critical behavior of a classical second-order phase transition in the O(2) universality class determines the region around the critical temperature. Our nonperturbative flow equations based on exact functional renormalization cover all regions in the phase diagram.

We present a quantum analysis of three-mode optoacoustic parametric interactions in an optical cavity, in which two orthogonal transverse optical-cavity modes are coupled to one acoustic mode through radiation pressure. Due to the optimal frequency matching—the frequency separation of two cavity modes is equal to the acoustic-mode frequency—the carrier and sideband fields simultaneously resonate and coherently build up. This mechanism significantly enhances the optoacoustic couplings in the quantum regime. It allows exploration of quantum behavior of optoacoustic interactions in small-scale table-top experiments. We show explicitly that given an experimentally achievable parameter, three-mode scheme can realize quantum ground-state cooling of milligram scale mechanical oscillators and create robust stationary tripartite optoacoustic quantum entanglements.

We investigate nonautonomous optical soliton dynamics accurately governed by the nonlinear Schrödinger equation with varying fiber loss and/or Raman gain. Based on the Painlevé analysis a Painlevé integrability condition of this equation, which means a balance between the dispersion, nonlinearity, and the fiber loss and/or gain, has been obtained. Under this condition the optical soliton transmission in fibers can be exactly controlled by proper dispersion and nonlinearity managements and the Raman gain. The existing experiments confirm the validity of our result, which provides a general guidance to design a fiber in information transmission using optical solitons.

Nondiffractive and nondispersive localized waves with narrow bandwidth are investigated theoretically as solutions of the linear scalar wave equation for normally dispersive media. By employing a Fourier approach, we study how the features of the linear dispersion relationship, i.e., the transverse wave number as a function of frequency, change as a function of the parameters of the wave and the medium (dispersion). We classify the localized waves accordingly and give their explicit expressions in those special cases which allow us to solve the Fourier-Bessel integral that yields the general representation of such waves.

The key characteristic of an optical mode in a microcavity is its quality factor describing the optical losses. The numerical computation of this quantity can be very demanding for present-day devices. Here we show for a certain class of whispering-gallery cavities that the quality factor is related to dynamical tunneling, a phenomenon studied in the field of quantum chaos. We extend a recently developed approach for determining dynamical tunneling rates to open cavities. This allows us to derive an analytical formula for the quality factor which is in very good agreement with full solutions of Maxwell’s equations.

We present a scheme for entanglement of macroscopic atomic ensembles which are four spatially separate regions of an atomic cloud using cluster-correlated beams. We show that the cluster-type polarization-encoded entanglement could be mapped onto the long-lived collective ground state of the atomic ensembles, and the stored entanglement could be retrieved based on the technique of electromagnetically induced transparency. We also discuss the efficiency of, the lifetime of, and some quantitative restrictions to the proposed quantum memory.

Based on the time-dependent close-coupling method, energy and angular differential probabilities for various ionization processes of He atoms subjected to intense attosecond soft-x-ray pulses with a photon energy of 91.6 eV and a peak intensity of ${10}^{15}\text{W}/{\text{cm}}^2$ are calculated to explore their dependence on the duration and the chirp of the pulse. It is found that the single and the double electron energy distributions for two-photon double ionization are rather sensitive to chirps. That is, both the magnitudes and locations of the sequential peaks in the single electron energy distributions vary strongly with chirps and the two-electron energy distributions being broadened and stretched along the equal energy sharing direction as opposed to the usual total excess energy direction for the case of zero chirp. In addition, our calculation also reveals an unexpected structure formed between the two sequential peaks. In order to better understand the chirp effects on both independent-electron and correlated electron emissions and their relations to the origin of the structure, we analyzed the corresponding probability differential in energy and angle.

We present a simple derivation of the energy formula found by Tan, relative to the single-channel Hamiltonian relevant for ultracold Fermi gases. This derivation is generalized to particles with different masses, to arbitrary mixtures, and to two-dimensional space. We show how in a field-theoretic approach, the $1/k^4$ tail in the momentum distribution and the energy formula arise in a natural way. As a specific example, we consider quantitative calculations of the energy from different formulas within the ladder diagram approximation in the normal state. The comparison of the results provides an indication on the quality of the approximation.

The lifetime of ${}^{87}\text{R}\text{b}$ atoms trapped in a $\mathsf{z}$ wire trap generated by a closed-circuit superconductive current on a ${\text{MgB}}_2$ strip is measured as a function of the distance between the atom and the strip. The lifetime is found to be longer than 10 s at a distance of $40\mu \text{m}$. This value is an order of magnitude longer than the lifetime of a trap generated by a normal current at the same distance. However, it is many orders of magnitude shorter than the theoretical decay rate induced by the spin-flip transition caused by the fluctuation of the current. This shows that for a type-II superconductor the dominant trap loss mechanism is not the spin-flip transition caused by noise as with a normal current atom trap. An analysis of our measurement suggests that magnetic field distortion resulting from flux penetration into the superconductor leads to much faster decay.

We show experimentally that the interaction of two multifilamenting beams in fused silica with incidence angles up to a few degrees results in an increase in the symmetry of the continuum emission from $D_2$ to $C_{\infty }$ around the axis of symmetry between the two beams. We observe an intense white disk between the locations of the individual conical emission patterns, reducing the conical emission in each of them. We attribute this behavior to an enhanced self-phase modulation in the interference region between the two beams. This frequency conversion depletes by more than 40% the energy initially available in the photon bath to feed filaments.

We experimentally and theoretically demonstrate that multioptical signals can be effectively stored and retrieved by fractional stimulated Raman adiabatic passage technique in a tripod-type four-level ${}^{87}\text{R}\text{b}$ atomic system. The optical pulses stored can be controllably released into two of the three different channels. The restored pulses have the same frequency, polarization, and propagation direction as the writing pulses. The experimental results fit very well with the numerical simulations.

We investigate two coupled microdisks with nonidentical radii focusing on the parametric evolution of energy levels and the unidirectional far-field emission. We show that the evolution of energy levels is characterized by the avoided crossing intrinsically associated with the exceptional point or the non-Hermitian degeneracy. These spectral properties explain highly asymmetric near-field intensity pattern of the resonance mode. The observed unidirectional far-field emission is shown to be understood by considering the forbidden interdisk coupling in the ray picture induced by the frustrated total internal reflection near the closest point between two disks when the interdisk distance is small enough.

Gerry, Ma, and Vrscay [Phys. Rev. A 39, 668 (1989)] studied the time evolution of SU(1,1) coherent states for the damped harmonic oscillator by introducing the Kanai-Caldirola Hamiltonian. The purposes of this Brief Report are to demonstrate that there are somewhat serious errors on their results and to correct them. Most of the figures given in their work are reproduced with correction in order to facilitate our explanation of results.