We describe weakly interacting atomic or molecular bosons trapped in harmonically confined optical lattices, which exhibit a wedding cake structure consisting of insulating (Mott) shells. We show that superfluid regions emerge between Mott shells as a result of fluctuations due to finite hopping and find that the order parameter equation in the superfluid regions is not of the standard Gross-Pitaevskii type except near the insulator-to-superfluid boundaries. We obtain the excitation spectra in the Mott and superfluid regions, and we show that the superfluid shells possess low-energy sound modes with spatially dependent sound velocity described by a local index of refraction directly related to the local superfluid density. Furthermore, we discuss the Berezinskii-Kosterlitz-Thouless transition and vortex-antivortex pairs in thin (wide) superfluid shells (rings) limited by three- (two-) dimensional Mott regions. Last, we propose an experiment to detect superfluid shells using Laguerre-Gaussian beams and Bragg spectroscopy.

We present experimental results from an extensive investigation of a Ni-like Mo x-ray laser pumped in the transient regime and GRIP configuration (GRazing Incidence Pumping). The pump laser is a 10 Hz, 1 J, Ti:sapphire laser system. The main diagnostic is a monochromatic near-field imaging system with a 1.7 micron spatial resolution that shows the soft-x-ray laser source size and position relative to the target surface. Changes of those characteristics are observed for different GRIP angles, varied between $15°$ and $21°$, while keeping all other parameters constant. Intense lasing is observed routinely at 18.9 nm with up to 3 microjoule output energy and stable operation is demonstrated at 10 Hz. We have investigated the role of several pumping parameters, in particular, the relative energy and delay between the long and short pulse. We show that this multiparameter scan leads to a well-defined optimal regime of operation and better understanding of the GRIP configuration. Finally, as the GRIP scheme requires careful tailoring of the plasma conditions to the specific soft-x-ray laser under investigation, we add a prepulse before the plasma producing long pulse to generate large-scale preplasmas. This increases the brightness of the soft-x-ray beam and leads to an almost Gaussian near-field spatial profile.

We experimentally study the polarization dynamics in the multi-transverse-mode regime of a vertical-cavity surface-emitting laser under isotropic optical feedback. Simultaneous measurements of orthogonally polarized states are conducted for both the total output and several spatial positions on the beam pattern. When the total output is detected, both slow and fast fluctuations of the two orthogonally polarized states are anticorrelated. For a chosen spatial position, slow fluctuations of the two polarizations are anticorrelated; fast fluctuations at the time scale of the external cavity round-trip time do not show fixed correlation properties when transverse modes have similar strengths.

The dynamics and propagation of ultrashort optical pulses generated in mode-locked lasers are investigated. The mode locking process depends crucially on the gain and loss mechanisms inside the cavity. Analytical models are introduced that include dispersion management and gain-loss terms with energy and power saturation. Comparisons of the pulse dynamics with previously well-known models are discussed. Stable soliton solutions are found for wide ranges of the parameters; the only significant requirement being sufficient gain in the system. The evolution of the system “locks” into the pure soliton solutions obtained independently with mode finding algorithms. Such solutions can be viewed as soliton wave attractors. Finally, it is shown that these solutions satisfy an asymptotic averaged system and can be approximated by elementary, Gaussian-type, functions.

Efficient single-photon frequency up-conversion was demonstrated under strong multi-longitudinal-mode pump, where the incident single-photon state was converted to a superposition state after the nonlinear interaction with the multimode pump field. Through frequency summing with a sufficiently strong multimode pump at $1.06\mu \text{m}$, a single-photon signal at $1.55\mu \text{m}$ was up-converted to the visible replicas near $0.63\mu \text{m}$ with a nearly unity efficiency. This may support tunable multimode photonic quantum-information interface and precise wavelength control on single-photon manipulation.

In earlier work a linear differential equation satified by the Schwartz ground-state electron density $\varrho \left(r\right)$ for (non-relativistic) He-like atomic ions with large atomic number $Z$ has been derived. Here, we utilize the asymptotic expansion at large $r$ given by Amovilli and March for the neutral He atom. We thereby show that a linear differential equation of the same general shape as that satisfied by the Schwartz $\varrho \left(r\right)$ again emerges for the neutral He atom itself, in the asymptotic limit of large $r$. We argue that essential input into the final differential equation for the He ground-state electron density will be the ionization potential plus the atomic polarizability.

We present an efficient approach to continuous-time quantum error correction that extends the low-dimensional quantum filtering methodology developed by van Handel and Mabuchi [e-print arXiv:quant-ph/0511221] to include error recovery operations in the form of real-time quantum feedback. We expect this paradigm to be useful for systems in which error recovery operations cannot be applied instantaneously. While we could not find an exact low-dimensional filter that combined both continuous syndrome measurement and a feedback Hamiltonian appropriate for error recovery, we developed an approximate reduced-dimensional model to do so. Simulations of the five-qubit code subjected to the symmetric depolarizing channel suggests that error correction based on our approximate filter performs essentially identically to correction based on an exact quantum dynamical model.

We demonstrate a multiphoton Rydberg dark resonance where a $\Lambda$ system is coupled to a Rydberg state. This $\mathcal{N}$-type level scheme combines the ability to slow and store light pulses associated with long-lived ground-state superpositions with the strongly interacting character of Rydberg states. For the $n{d}_{5/2}$ Rydberg state in ${}^{87}\text{R}\text{b}$ (with $n=26$ or 44) and a beam size of 1 mm, we observe a resonance linewidth of less than 100 kHz in a room-temperature atomic ensemble limited by transit-time broadening. The resonance is switchable with an electric field of order $1\text{V}{\text{cm}}^{-1}$. Applications in electro-optic switching and photonic phase gates are discussed.

We consider the possibility of using stabilizer states to perform deterministic dense coding among multiple senders and a single receiver. In the model we studied, the utilized stabilizer state is partitioned into several subsystems and then each subsystem is held by a distinct party. We present a sufficient condition for a stabilizer state to be useful for deterministic distributed dense coding with respect to a given partition plan. The corresponding protocol is also constructed. Furthermore, we propose a method to partially solve a more general problem of finding the set of achievable alphabet sizes for an arbitrary stabilizer state with respect to an arbitrary partition plan. Finally, our work provides a perspective from the stabilizer formalism to view the standard dense coding protocol and also unifies several previous results in a single framework.

We consider a spin ladder model which is known to have matrix product states as exact ground states with spin liquid characteristics. The model has two critical-point transitions at the parameter values $u=0$ and $\infty$. We study the variation of entanglement and fidelity measures in the ground states as a function of $u$ and specially look for signatures of quantum phase transitions at $u=0$ and $\infty$. The two different entanglement measures used are $S\left(i\right)$ (the single-site von Neumann entropy) and $S\left(i,j\right)$ (the two-body entanglement). At the quantum critical point (QCP) $u=\infty$, the entanglement measure $E$ $\left[=S\left(i\right),S\left(i,j\right)\right]$ vanishes but remains nonzero at the other QCP $u=0$. The first and second derivatives of $E$ with respect to the parameter $u$ and the entanglement length associated with $S\left(i,j\right)$ are further calculated to identify special features, if any, near the QCPs. We further determine the GS fidelity $F$ and a quantity $\text{ln}\left|D\right|$ related to the second derivative of $F$ and show that these quantities calculated for finite-sized systems are good indicators of QPTs occurring in the infinite system.

A scheme is presented for realizing a quantum phase gate with three-level atoms, solid-state qubits—often called artificial atoms, or ions that share a quantum data bus such as a single-mode field in the cavity quantum electrodynamics system or a collective vibrational state of trapped ions. In this scheme, the conditional phase shift is tunable and controllable via the total effective interaction time. Furthermore, the method can be used to effectively prepare graph states, which are important resources for quantum computation, quantum error correction, studies of multiparticle entanglement, and fundamental tests of nonlocality and decoherence.

We study the reflection and transmission of a homonuclear diatomic molecule incident upon a potential barrier in one dimension. The effect of discrete and continuous unbound molecular states is investigated. We use the method of variable reflection and transmission amplitudes for discrete unbound states and we extend the method to include continuous unbound states. We take into account transitions between the bound and unbound states in the process of tunneling. For the molecule incident in a bound state, we calculate the probabilities of reflection and transmission in bound states as well as in unbound states. We focus on the molecule incident upon a $\delta$ barrier but we also investigate rectangular and Gaussian barriers. We show that transmission resonances are appreciably reduced by the inclusion of unbound states due to the lack of resonant structure in the probabilities of reflection and transmission in unbound states. We also find that much of the behavior of the molecule in the process of tunneling is primarily due to the bound states.

Atomic coherence phenomena are usually investigated using single beam techniques without spatial resolution. Here we demonstrate state-selective imaging of cold ${}^{85}\text{R}\text{b}$ atoms in a three-level ladder system, where the atomic refractive index is sensitive to the quantum coherence state of the atoms. We use a phase-sensitive diffraction contrast imaging (DCI) technique which depends on the complex refractive index of the atom cloud. A semiclassical model allows us to analytically calculate the detuning-dependent refractive index of the system. The predicted Autler-Townes splitting and our experimental measurements are in excellent agreement. DCI provided a quantitative image of the distribution of the excited-state fraction, and compared with on-resonance absorption and blue cascade fluorescence techniques, was found to be experimentally simple and robust.

We demonstrate magnetic field enabled optical forces on a neutral indium atomic beam in a light field consisting of five frequencies. The role of dark magnetic ground state sublevels is studied and enables us to cool the atomic beam transversely to near the Doppler limit with laser frequencies tuned above the atomic resonance. The effect of laser cooling can be explained with transient effects in the light potential created by the standing wave light field where the atoms are optically pumped into the dark states and recycled by Larmor precession.

We numerically study imbalanced two component Fermi gases with attractive interactions in highly elongated harmonic traps. An accurate parametrization formula for the ground state energy is presented for a spin-polarized attractive Gaudin-Yang model. Our studies are based on an accurate microscopic spin-density-functional theory through the Kohn-Sham scheme which employs the one-dimensional homogeneous Gaudin-Yang model with a Luther-Emery-liquid ground-state correlation as a reference system. A Thomas-Fermi approximation is examined incorporating the exchange-correlation interaction. By studying the charge and spin density profiles of the system based on these methods, we gain a quantitative understanding of the role of attractive interactions and polarization on the formation of the two-shell structure, with the coexisted Fulde-Ferrell-Larkin-Ovchinnikov-type phase in the center of the trap and either the BCS superfluid phase or the normal phase at the edges of the trap. Our results are in good agreement with the recent theoretical consequences.

We present detailed numerical and analytical investigations of the nonequilibrium dynamics of spin-polarized ultracold Fermi gases following a sudden switching on of the atom-atom pairing coupling strength. Within a time-dependent mean-field approach we show that on increasing the imbalance it takes longer for pairing to develop, the period of the nonlinear oscillations lengthens, and the maximum value of the pairing amplitude decreases. As expected, dynamical pairing is suppressed by the increase of the imbalance. Eventually, for a critical value of the imbalance the nonlinear oscillations do not even develop. Finally, we point out an interesting temperature-reentrant behavior of the exponent characterizing the initial instability.

We study light emission patterns from stadium-shaped semiconductor (GaAs) microcavity lasers theoretically and experimentally. Performing systematic wave calculations for passive cavity modes, we demonstrate that the averaging by low-loss modes, such as those realized in multimode lasing, generates an emission pattern in good agreement with the ray model’s prediction. In addition, we show that the dependence of experimental far-field emission patterns on the aspect ratio of the stadium cavity is well reproduced by the ray model.

We develop a fully quantum-mechanical approach for the description of spontaneous parametric down-conversion in waveguides. Our method allows us to write an expression for the quantum state easily and directly, even when multiple photon pairs are generated in the process. The role of material dispersion in the normalization of the modes of the system, usually neglected, is properly treated here. The example of an ${\text{Al}}_y{\text{O}}_x/{\text{Al}}_{0.5}{\text{Ga}}_{0.5}\text{As}$ ridge waveguide is discussed to illustrate the application of the formalism.

The generation of optical phase oscillations is investigated in an interferometer using a ${\text{Bi}}_{12}{\text{SiO}}_{20}$ non-steady-state photoelectromotive-force detector. Phase modulation of the signal optical beam is created by the detected signal itself, in contrast to the standard forced regime where such modulation is produced by an external source. The conditions necessary for the self-excitation of the oscillations are obtained using the results of the small-signal approach for the non-steady-state photoelectromotive-force effect. The amplitude and frequency of the oscillations are defined by the photoelectric properties of the detector but not by the feedback loop. The dependencies of the oscillations on the time and gain factor are measured for both the diffusion and drift regimes.