We observe magnetic trapping of atomic nitrogen $\left({}^{14}\mathrm{N}\right)$ and cotrapping of ground-state imidogen (${}^{14}\mathrm{N}\mathrm{H}$, $X{}^3\Sigma ^{-}$). Both are loaded directly from a room-temperature beam via buffer gas cooling. We trap approximately $1\times {10}^{11}$ ${}^{14}\mathrm{N}$ atoms at a peak density of $5\times {10}^{11}{\mathrm{cm}}^{-3}$ at $550\mathrm{mK}$. The $12\pm 4\mathrm{s}$ $1∕e$ lifetime of atomic nitrogen in the trap is consistent with a model for loss of atoms over the edge of the trap in the presence of helium buffer gas. Cotrapping of ${}^{14}\mathrm{N}$ and ${}^{14}\mathrm{N}\mathrm{H}$ is accomplished, with ${10}^8$ NH trapped molecules at a peak density of ${10}^8{\mathrm{cm}}^{-3}$.

We show how it is possible to more than double the on-site interaction energy of neutral atoms in optical potentials by the technique of radio-frequency (rf) dressing, while maintaining interwell dynamics. We calculate Bose-Hubbard parameters for rf-dressed optical lattices and arrays of rf-dressed dipole traps. We show that decreasing the distance between wells, by the interpolation of wells confining different $m_F$ states, increases the interaction energy more than decreasing the height of the classically forbidden region between existing wells. The schemes we propose have negligible Landau-Zener losses caused by atomic motion; this was a dominant effect in the first experimental demonstration of the modification of an optical potential by radio-frequency dressing.

By defining “a virtual gap” for the continuous spectrum through the notion of eigendifferential (Weyl’s packet) and using the differential projector operator, we present a rigorous demonstration and discussion of the quantum adiabatic theorem and the validity condition of the adiabatic approximation for systems having a nondegenerate continuous spectrum. We show that a quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported around a closed curve $C$ by varying parameters in its Hamiltonian, will acquire a generalized geometrical phase factor where an explicit formula is derived in terms of the eigenstates of the Hamiltonian. Examples are given for illustration.

The human eye can detect optical signals containing only a few photons. We investigate the possibility to demonstrate entanglement with such biological detectors. While one person could not detect entanglement by simply observing photons, we discuss the possibility for several observers to demonstrate entanglement in a Bell-type experiment, in which standard detectors are replaced by human eyes. Using a toy model for biological detectors that captures their main characteristic, namely, a detection threshold, we show that Bell inequalities can be violated, thus demonstrating entanglement. Remarkably, when the response function of the detector is close to a step function, quantum nonlocality can be demonstrated without any further assumptions. For smoother response functions, as for the human eye, postselection is required.

We investigate the evolution of entanglement between local qubits in the presence of electron current which is flowing through and interacting with them. We find that if the electrons in the current are passing through one by one (sequentially), it is possible to generate or increase the entanglement of the local system by interacting with this current. To elucidate this we consider two local spins representing the qubit system and the electrons of the applied current tunneling through from one bath to another and interacting with the local spins. It is surprising that the entanglement between the local spins can increase and saturate to 1 even though the electrons injected into the system have random spins. We analyze the conditions of increasing or decreasing the entanglement by the current. This suggests an approach of controlling the entanglement of a local system which cannot only decrease but also increase the entanglement.

We present a framework for deciding whether a quantum state is separable or entangled using covariance matrices of locally measurable observables. This leads to the covariance matrix criterion as a general separability criterion. We demonstrate that this criterion allows us to detect many states where the familiar criterion of the positivity of the partial transpose fails. It turns out that a large number of criteria that have been proposed to complement the positive partial transpose criterion—the computable cross norm or realignment criterion, the criterion based on local uncertainty relations, criteria derived from extensions of the realignment map, and others—are in fact a corollary of the covariance matrix criterion.

Cubelike graphs are the Cayley graphs of the elementary Abelian group ${\mathbb{Z}}_2^n$ (e.g., the hypercube is a cubelike graph). We study perfect state transfer between two particles in quantum networks modeled by a large class of cubelike graphs. This generalizes the results of Christandl et al. [Phys. Rev. Lett. 92, 187902 (2004)] and Facer et al. [Phys. Rev. A 92, 187902 (2008)].

We describe a method for generating entanglement between two spatially separated dipoles coupled to optical microcavities. The protocol works even when the dipoles have different resonant frequencies and radiative lifetimes. This method is particularly important for solid-state emitters, such as quantum dots, which suffer from large inhomogeneous broadening. We show that high fidelities can be obtained over a large dipole detuning range without significant loss of efficiency. We analyze the impact of higher-order photon number states and cavity resonance mismatch on the performance of the protocol.

The four-wave mixing (4WM) signal is calculated for a three-level quantum system in a $\Lambda$ configuration (upper level 2, lower levels 1 and 3) that is driven by three fields. Pump fields $E$ and $E^{\prime }$ drive the 1-2 and 3-2 transitions, respectively. The probe field is detuned from field $E$ by an amount $\Delta$. If the detuning of field $E$ from the 1-2 transition frequency is equal to that of field $E^{\prime }$ from the 3-2 transition frequency (dark state pumping), there is a dark state in the absence of the probe field. Rather surprisingly, even though the probe field destroys the dark state for $\Delta \ne 0$, the 4WM mixing vanishes for all $\Delta$ in the limit of dark-state pumping. The 4WM spectra are explained within the context of a semiclassical, dressed-state picture that involves the sequential emission of a probe and signal photon.

With ultracold atoms in an optical lattice, we propose an experimental scheme to simulate and detect the integer quantum Hall effect and a peculiar phase transition in a uniform magnetic field and an additional staggered magnetic field. The phase transition is characterized by the direct change from Hall plateau state $N-1$ to $-1$ due to Chern number redistribution when the staggered magnetic field is varied. We propose the possibility to observe the Hall conductivity and the phase transition by varying experimental parameters and measuring the number density of the ultracold atoms.

Magnetization dynamics of a half-quantum vortex in a spin-1 Bose-Einstein condensate with a ferromagnetic interaction are investigated by mean-field and Bogoliubov analyses. The transverse magnetization is shown to break the axisymmetry and form threefold domains. This phenomenon originates from the topological structure of the half-quantum vortex and spin conservation.

We experimentally investigate interference pattern formation in second-order intensity correlation considering the polarization state of pseudothermal light beams. By placing a double slit in one of the beams it is shown that the interference pattern depends on the polarization state of the light after the slits. When different parts of the double slit are aligned in different beams, we found that the interference is always observed, even for the case where the beams are orthogonally polarized. Our results are analyzed using a filtering process and indistinguishability of paths interpretation. Extensions of our findings to massive particles are also discussed.

We present a theoretical framework to describe the collective emission of light by entangled atomic states. Our theory applies to the low-excitation regime, where most of the atoms are initially in the ground state, and relies on a bosonic description of the atomic excitations. In this way, the problem of light emission by an ensemble of atoms can be solved exactly, including dipole-dipole interactions and multiple light scattering. Explicit expressions for the emitted photonic states are obtained in several situations, such as those of atoms in regular lattices and atomic vapors. We determine the directionality of the photonic beam, the purity of the photonic state, and the renormalization of the emission rates. We also show how to observe collective phenomena with ultracold atoms in optical lattices and how to use these ideas to generate photonic states that are useful in the context of quantum information.

The differential cross sections for muonic atom scattering from hydrogenic molecules have been calculated using the Morse potential of the internuclear interaction in these molecules. Numerical calculations have been performed for the scattering $d\mu +{\mathrm{H}}_2$ and $t\mu +{\mathrm{H}}_2$ at collision energies of $\epsilon ⩽30\mathrm{eV}$. Our calculations are fully quantum mechanical. The obtained differential cross sections are necessary for a proper description of muonic atom scattering and diffusion over a wide energy range.

We have studied the quantum spin dynamics of small condensates of cold sodium atoms. For a condensate initially prepared in a mean-field ground state, we show that coherent spin dynamics is purely driven by quantum fluctuations of collective spin coordinates and can be tuned by quadratic Zeeman coupling and magnetization. This dynamics in small condensates can be probed in a high-finesse optical cavity where the temporal behaviors of the excitation spectra of a coupled condensate-photon system reveal the time evolution of populations of atoms at different hyperfine spin states.

We introduce a phase-space representation for qubits and spin models. The technique uses an $\mathrm{SU}\left(n\right)$ coherent-state basis and can equally be used for either static or dynamical simulations. We review previously known definitions and operator identities, and show how these can be used to define an off-diagonal, positive phase-space representation analogous to the positive-$P$ function. As an illustration of the phase-space method, we use the example of the Ising model, which has exact solutions for the finite-temperature canonical ensemble in two dimensions. We show how a canonical ensemble for an Ising model of arbitrary structure can be efficiently simulated using SU(2) or atomic coherent states. The technique utilizes a transformation from a canonical (imaginary-time) weighted simulation to an equivalent unweighted real-time simulation. The results are compared to the exactly soluble two-dimensional case. We note that Ising models in one, two, or three dimensions are potentially achievable experimentally as a lattice gas of ultracold atoms in optical lattices. The technique is not restricted to canonical ensembles or to Ising-like couplings. It is also able to be used for real-time evolution and for systems whose time evolution follows a master equation describing decoherence and coupling to external reservoirs. The case of $\mathrm{SU}\left(n\right)$ phase space is used to describe $n$-level systems. In general, the requirement that time evolution be stochastic corresponds to a restriction to Hamiltonians and master equations that are quadratic in the group generators or generalized spin operators.

We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schrödinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be detected by experimentally measuring mean values and variances of specific observables. Those observables must satisfy a specific condition in order to be used, and we show their general form in the $2\times 2$ (two qubits) dimension case. The criterion is applied on a variety of physical systems including bipartite and multipartite mixed states and reveals itself to be stronger than the Bell inequalities and other criteria. The criterion also work on continuous variable cat states and angular momentum states of the radiation field.

We study the rotational and vibrational heating of diatomic molecules placed near a surface at finite temperature on the basis of macroscopic quantum electrodynamics. The internal molecular evolution is governed by transition rates that depend on both temperature and position. Analytical and numerical methods are used to investigate the heating of several relevant molecules near various surfaces. We determine the critical distances at which the surface itself becomes the dominant source of heating and we investigate the transition between the long-range and short-range behavior of the heating rates. A simple formula is presented that can be used to estimate the surface-induced heating rates of other molecules of interest. We also consider how the heating depends on the thickness and composition of the surface.

This paper presents model numerical simulations of photoassociation and ionization of cold $\mathrm{Rb}+\mathrm{Cs}$ atoms steered by broadband optical pulses operating within the weak-field limit over a picosecond time scale. The primary focus of the work is on generation of RbCs molecules in bound levels of the $\left(1\right)0^{+}$ $\left(X{}^1\Sigma ^{+}\right)$ electronic ground state through a sequence of pump-dump transitions between $\left(1\right)0^{+}$ and $\left(4\right)0^{+}$ states driven by a field centered at $811\mathrm{nm}$ with different phase modulations. It is found that chirped fields generate substantially bound oscillator levels of the $X{}^1\Sigma ^{+}$ state by avoiding promotion of amplitude to vibrational levels in the upper state whose Franck-Condon factors for stimulated emission to levels in the $X{}^1\Sigma ^{+}$ state are detrimentally low, but which otherwise come into play when the driving field is transform limited. Optimal generation of molecules in the electronic ground state irrespective of vibrational level selectivity is calculated to occur when the temporal phase of the driving field is modulated by the classical energy difference for promotion of $\left(4\right)0^{+}\leftarrow \left(1\right)0^{+}$ photon absorption. Conversely, generation of deeply bound vibrational eigenlevels of the $X{}^1\Sigma ^{+}$ state is optimally promoted by a field whose temporal phase enhances $\left(4\right)0^{+}\to \left(1\right)0^{+}$ stimulated emission. Driving fields phase modulated by the classical difference potential or linearly down-chirped enhance molecule formation vis-à-vis the thermal collision; fields whose temporal phase is modulated according to the shape of the $\left(1\right)0^{+}$ potential energy curve or which are linearly up-chirped suppress molecule formation relative to the thermal probability, but generate deeply bound $X{}^1\Sigma ^{+}$ vibrational levels. Application of a bichromatic field comprising temporally overlapped components centered 811 and $622\mathrm{nm}$ also improves the probability of generating deeply bound vibrational levels, but at the expense of increased ionization. Model calculations of transition probabilities between neutral and ionic states of the collision lead to the conclusions that: transitions to individual vibrational levels of the $X{}^1\Sigma ^{+}$ state occur with a higher probability than resonant three-photon ionization prompted by a single-color field at $811\mathrm{nm}$; and application of bichromatic light at 811 and $622\mathrm{nm}$ preferentially ionizes the incipient molecule via a two-color two-photon absorption, the likelihood of which masks the occupation of deeply bound $X{}^1\Sigma ^{+}$ oscillator levels.

Photoionization cross-section calculations are performed for the ground $\left(\left[\mathrm{Ne}\right]3s^{2}3p^{6}3d{}^{2}D_{3∕2}^e\right)$ and the first two excited states $\left(\left[\mathrm{Ne}\right]3s^{2}3p^{6}3d{}^{2}D_{5∕2}^e\right)$, $\left(\left[\mathrm{Ne}\right]3s^{2}3p^{6}4s{}^{2}S_{1∕2}^e\right)$ of doubly-charged scandium $\left({\mathrm{Sc}}^{2+}\right)$ for photon energies from threshold to $68.0\mathrm{eV}$. The discrete ${\mathrm{Sc}}^{3+}$ orbitals are generated using the computer program AUTOSTRUCTURE; 24 configurations are included in the configuration-interaction calculation for ${\mathrm{Sc}}^{3+}$. In addition to the nonrelativistic (LS-coupling) $R$-matrix, we have used the relativistic (Breit-Pauli) $R$-matrix method to carry out the calculations to focus on relativistic effects. Relativistic and nonrelativistic results are compared to demonstrate the influence of relativistic effects. The prominent $3p\to 3d$ giant resonances are analyzed and identified, and our calculated positions and widths are compared with experimental results. Total oscillator strength calculations suggest that the experimental cross section is too small and should be multiplied by a factor of 1.63; with this factor, rather good agreement between theoretical and experimental cross section is found.