Making use of the Bloch density matrix technique, we derive exact analytical expressions for the density profile in Fourier space, for the current density and the so-called integrated current for fermionic systems confined by a two-dimensional harmonic oscillator, in the presence of a magnetic field or in a rotating trap of arbitrary strength. We present numerical, illustrative examples with or without magnetic field (with or without rotation).

We investigate the lowest scattering state of a one-dimensional Bose gas with attractive interactions trapped in a hard-wall trap. By solving the Bethe ansatz equation numerically, we determine the full energy spectrum and the exact wave function for different attractive interaction parameters. The resultant density distribution, momentum distribution, reduced one-body density matrix, and two-body correlation show that a decreased attractive interaction induces rich density profiles and specific correlation properties in the weakly attractive Bose gas.

We report the magnetic merging of ultracold atomic gases of ${}^{85}\mathrm{Rb}$ and ${}^{87}\mathrm{Rb}$ by the controlled overlap of two initially spatially separated magnetic traps. We present a detailed analysis of the combined magnetic-field potential as the two traps are brought together that predicts a clear optimum trajectory for the merging. We verify this prediction experimentally using ${}^{85}\mathrm{Rb}$ and find that the final atom number in the merged trap is maximized with minimal heating by following the predicted optimum trajectory. Using the magnetic-merging approach allows us to create variable-ratio isotopic Rb mixtures with a single laser-cooling setup by simply storing one isotope in a magnetic trap before jumping the laser frequencies to the transitions necessary to laser cool the second isotope.

We study the spin-mixing dynamics of ultracold spin-1 atoms in a weak nonuniform magnetic field with field gradient $G$, which can flip the spin from $+1$ to $-1$ so that the magnetization $m={\rho }_{+}-{\rho }_{-}$ is not a constant anymore. The dynamics of $m_F=0$ Zeeman component ${\rho }_0$, as well as the system magnetization $m$, are illustrated for both ferromagnetic and polar interaction cases in the mean-field theory. We find that the dynamics of system magnetization can be tuned between the Josephson-like oscillation similar to the case of double well and the interesting self-trapping regimes, i.e., the spin-mixing dynamics sustains a spontaneous magnetization. Meanwhile, the dynamics of ${\rho }_0$ may be sufficiently suppressed for initially imbalanced number distribution in the case of polar interaction. A “beat-frequency”oscillation of the magnetization emerges in the case of balanced initial distribution for polar interaction, which vanishes for ferromagnetic interaction.

We study emission from quasi-one-dimensional modes of an asymmetric resonant cavity that are associated with a stable periodic ray orbit confined inside the cavity by total internal reflection. It is numerically demonstrated that such modes exhibit directional emission, which is explained by chaos-assisted emission induced by dynamical tunneling. Fabricating semiconductor microlasers with an asymmetric resonant cavity, we experimentally demonstrate the selective excitation of the quasi-one-dimensional modes by employing the device structure to preferentially inject currents to these modes and observe directional emission in good accordance with the theoretical prediction based on chaos-assisted emission.

We analyze the existence, bifurcations, and shape transformations of one-dimensional gap solitons (GSs) in the first finite band gap induced by a periodic potential built into materials with local self-focusing and nonlocal self-defocusing nonlinearities. Originally stable on-site GS modes become unstable near the upper edge of the band gap with the introduction of the nonlocal self-defocusing nonlinearity with a small nonlocality radius. Unstable off-site GSs bifurcate into a new branch featuring single-humped, double-humped, and flat-top modes due to the competition between local and nonlocal nonlinearities. The mechanism underlying the complex bifurcation pattern and cutoff effects (termination of some bifurcation branches) is illustrated in terms of the shape transformation under the action of the varying degree of the nonlocality. The results of this work suggest a possibility of optical-signal processing by means of the competing nonlocal and local nonlinearities.

An ab initio approach is used to describe the time evolution of the amplitudes of whispering gallery modes in a system of coupled microdisk resonators with Kerr nonlinearity. It is shown that this system demonstrates a transition between Josephson-like nonlinear oscillations and self-trapping behavior. Manifestation of this transition in the dynamics of radiative losses is studied.

Spontaneous Raman emission in atomic gases provides an attractive source of photon pairs with a controllable delay. We show how this technique can be implemented in solid state systems by appropriately shaping the inhomogeneous broadening. Our proposal is eminently feasible with current technology and provides a realistic solution to entangle remote rare-earth-metal-doped solids in a heralded way.

The phase compensation mechanism induced by anomalous dispersion in the reflection process of four-wave mixing (or reflection from a grating) in a three-level system is investigated, where the four wave vectors do not match in vacuum. An efficiency of the reflected signal of as high as 43% from a hot atomic cell of Cs is observed. The maximum reflection occurs when the frequency of the probe beam (and consequently the frequency of the reflected signal) is slightly red detuned from the transition frequency, which is attributed to the phase compensation from the steep anomalous dispersion accompanied with a strong probe absorption. The dependences of the efficiency on the angle between the coupling and probe lights, on the intensity of the coupling, field and on atomic density are studied. A theoretical model is presented and it is in good agreement with the experimental results.

We analyze the nonadiabatic effects on the propagation of a two-mode squeezed field inside a medium of three-level $\Lambda$ atoms that display the dark resonance. We identify the different effects for the two-mode quantum properties: (i) unconditional transparency for the sum squeezing and (ii) induced transparency or spectral narrowing for the difference squeezing depending on the relative widths of the initial correlation spectrum to the transparency window. These effects combine to induce transparency or spectrum narrowing for the bipartite entanglement. The potential applications range from quantum information to laser spectroscopy and frequency standards.

Starting from the derived expression of the Bogoliubov transformation for a broadband pulsed pump, we theoretically characterize the heralded single-photon source, which is based on the signal and idler photon pairs produced in optical fiber via spontaneous four-wave mixing by a pulsed pump. The second-order intensity correlation function, heralding efficiency, indistinguishability, and brightness of the heralded single photons as a function of source parameters, are analyzed and discussed. The validity of the theoretical analysis and calculations are confirmed by the experimental results. The investigations are useful for optimizing the source parameters and for developing a single-photon source suitable for quantum-information processing.

We discuss the dynamics of interacting dark-bright two-dimensional vector solitons in multicomponent immiscible bulk Bose-Einstein condensates. We describe matter-wave molecules without a scalar counterpart that can be seen as bound states of vector objects. We also analyze the possibility of using these structures as building blocks for the design of matter-wave switchers.

We investigate the effect of turbulence on quantum ghost imaging. We use entangled photons and demonstrate that for a specific experimental configuration the effect of turbulence can be greatly diminished. By decoupling the entangled photon source from the ghost-imaging central image plane, we are able to dramatically increase the ghost-image quality. When imaging a test pattern through turbulence, this method increases the imaged pattern visibility from $V=0.15\pm 0.04$ to $0.42\pm 0.04$.

For a two-level system in a time-periodic field we show that in the non-Hermitian $\mathit{PT}$ case the level crossing is of two quasistationary states that have the same dynamical symmetry property. At the field’s parameters where the two levels which have the same dynamical symmetry cross, the corresponding quasienergy states coalesce and a self-orthogonal state is obtained. This situation is very different from the Hermitian case where a crossing of two quasienergy levels happens only when the corresponding two quasistationary states have different dynamical symmetry properties and, unlike the situation in the non-Hermitian case, the spectrum remains complete also when the two levels cross.

We study a device formed by a Bose-Einstein condensate (BEC) coupled to the field of a cavity with a moving end mirror and find a working point such that the mirror-light entanglement is reproduced by the BEC-light quantum correlations. This provides an experimentally viable tool for inferring mirror-light entanglement with only a limited set of assumptions. We prove the existence of tripartite entanglement in the hybrid device, persisting up to temperatures of a few milli-Kelvin, and discuss a scheme to detect it.

We discuss the use of the transverse spatial degrees of freedom of photons propagating in the paraxial approximation for continuous-variable information processing. Given the wide variety of linear optical devices available, a diverse range of operations can be performed on the spatial degrees of freedom of single photons. Here we show how to implement a set of continuous quantum logic gates which allow for universal quantum computation. In contrast with the usual quadratures of the electromagnetic field, the entire set of single-photon gates for spatial degrees of freedom does not require optical nonlinearity and, in principle, can be performed with a single device: the spatial light modulator. Nevertheless, nonlinear optical processes, such as four-wave mixing, are needed in the implementation of two-photon gates. The efficiency of these gates is at present very low; however, small-scale investigations of continuous-variable quantum computation are within the reach of current technology. In this regard, we show how novel cluster states for one-way quantum computing can be produced using spontaneous parametric down-conversion.

Two nonlinear Kerr oscillators mutually coupled by parametric pumping are studied as a source of states entangled in photon numbers. Temporal evolution of entanglement quantified by negativity shows the effects of sudden death and birth of entanglement. Entanglement is preserved even in asymptotic states under certain conditions. The role of reservoirs at finite temperature in entanglement evolution is elucidated. Relation between generation of entangled states and violation of Cauchy-Schwartz inequality for oscillator intensities is found.

We investigate ${}^{129}\mathrm{Xe}$-Cs ($D_1,D_2$) spin exchange optical pumping (SEOP) at high Xe densities ($~$0.12–2.44 amagat) using newly available high-power ($>$40 W) laser diode arrays and compare with ${}^{129}\mathrm{Xe}$-Rb $D_1$ SEOP under similar conditions. At elevated Xe densities, the spin-exchange rate (per alkali-metal atom, ${\gamma }^{\prime }$) for Cs-${}^{129}\mathrm{Xe}$ is $~$1.5-fold greater than that for Rb-${}^{129}\mathrm{Xe}$. Higher spin-exchange rates and lower ${}^{129}\mathrm{Xe}$ spin-destruction rates for Cs-${}^{129}\mathrm{Xe}$ versus Rb-${}^{129}\mathrm{Xe}$ contribute to $~$twofold improvement in ${}^{129}\mathrm{Xe}$ nuclear spin polarization measured at 9.4 T—with the largest gains observed at the highest Xe densities.

We show theoretically and experimentally that two-photon coherent control in a $V$-shape three-level system projects a one-photon coherent transient in a simple two-level system. The second- and third-order spectral phase terms of a shaped laser pulse play the roles of time and quadratic spectral phase, respectively, in conventional coherent transients. In a three-pulse coherent control experiment of atomic rubidium, the phase and amplitude of controlled transition probability is retrieved from a two-dimensional Fourier-transform spectral peak. It is hoped that this control scheme may harness coherent control capability on multidimensional Fourier-transform spectroscopy.