Shallow heteronuclear trimers are predicted for mixtures of two atomic species strongly trapped in a quasi-two-dimensional (2D) atomic waveguide. The binding energies are functions of the 2D scattering length and of the mass ratio and can be thus tuned by various ways. These universal trimers are composed of two identical noninteracting particles and of a third particle of the other species. Depending on the statistics of the two identical particles, the trimers have an odd (fermions) or even (bosons) internal angular momentum. These results permit one to draw conclusions on the stability issue for the quasi-2D gaseous phase of heteronuclear dimers.

A phase shifter in neutron interferometry creates not only a phase shift but also a spatial displacement of the neutron wave packet, leading to a reduced interference contrast. This wave-packet displacement constitutes a major hindrance in measuring large phase shifts. Here we present a nondispersive configuration with two identical phase shifters placed on one path in successive gaps of a symmetric triple Laue (LLL) interferometer. As compared to a single phase shifter, the dual phase shifter generates double the phase shift, yet a net null displacement of the wave packet. The interferometer thus remains fully focused however large the phase shift or the incident wavelength spread, permitting a white incident neutron beam as in the case of a purely topological phase measurement. Misalignment angles of a monolithic nondispersive dual phase shifter are equal and opposite in the two gaps. Its phase therefore remains nondispersive over a much wider angular range and attains a minimum magnitude at the correct orientation, obviating the need to alternate the phase shifter between the two interferometer paths during its alignment. The setup is hence ideally suited for measuring neutron coherent scattering lengths to ultrahigh precision.

We analyze quantitatively how imaging techniques with single-site resolution allow to measure thermodynamical properties that cannot be inferred from time-of-flight images for the trapped Bose-Hubbard model. If the normal state extends over a sufficiently large range, the chemical potential and the temperature can be extracted from a single shot, provided the sample is in thermodynamic equilibrium. When the normal state is too narrow, temperature is low but can still be extracted using the fluctuation-dissipation theorem over the entire trap range as long as the local-density approximation remains valid, as was recently suggested by Q. Zhou and T.-L. Ho [arXiv:0908.3015]. However, for typical present-day experiments, the number of samples needed is on the order of 1000 in order to get the temperature at least $10\%$ accurate, but it is possible to reduce the variance by $2$ orders of magnitude if the density-density correlation length is short, which is the case for the Bose-Hubbard model. Our results provide further evidence that cold gases in optical lattices can be viewed as quantum analog computers.

We found an analytical solution for the vortex structure in a rapidly rotating trapped Bose-Einstein condensate in the lowest Landau level approximation. This solution is exact in the limit of a large number of vortices and is obtained for the case of a condensate in a anisotropic harmonic potential. The solution describes as limiting cases both a triangle vortex lattice in the symmetric potential trap and a quasi-one-dimensional structure of vortex rows in an asymmetric case, when the rotation frequency is very close to the lower trapping potential frequency. The shape of the density profile is found to be close to the Thomas-Fermi inverted paraboloid form, except in the vicinity of edges of a condensate cloud.

We investigate the photoemission-type spectrum in a cold Fermi gas which was recently measured by the JILA group [Stewart et al., Nature (London) 454, 744 (2008)]. This quantity gives us very useful information about single-particle properties in the BCS-BEC crossover. In this paper, including pairing fluctuations within a $T$-matrix theory, as well as effects of a harmonic trap within the local density approximation, we show that spatially inhomogeneous pairing fluctuations due to the trap potential are an important key to understanding the observed spectrum. In the crossover region, while strong pairing fluctuations lead to the so-called pseudogap phenomenon in the trap center, such strong-coupling effects are found to be weak around the edge of the gas. Our results including this effect are shown to agree well with the recent photoemission data of the JILA group.

To analyze the ground-state phase diagram of Bose-Bose mixtures loaded into $d$-dimensional hypercubic optical lattices, we perform a strong-coupling power-series expansion in the kinetic energy term (plus a scaling analysis) for the two-species Bose-Hubbard model with onsite boson-boson interactions. We consider both repulsive and attractive interspecies interaction, and obtain an analytical expression for the phase boundary between the incompressible Mott insulator and the compressible superfluid phase up to third order in the hoppings. In particular, we find a re-entrant quantum phase transition from paired superfluid (superfluidity of composite bosons, i.e., Bose-Bose pairs) to Mott insulator and again to a paired superfluid in all one, two, and three dimensions, when the interspecies interaction is sufficiently large and attractive. We hope that some of our results could be tested with ultracold atomic systems.

We study the effect of atom-molecule internal tunneling on the ground state of atom-molecule Bose-Einstein condensates in a double-well potential. In the absence of internal tunneling between atomic and molecular states, the ground state is symmetric, which has equal-particle populations in two wells. From the linear stability analysis, we show that the symmetric stationary state becomes dynamically unstable at a certain value of the atom-molecule internal tunneling strength. Above the critical value of the internal tunneling strength, the ground state bifurcates to the particle-localized ground states. The origin of this transition can be attributed to the effective attractive interatomic interaction induced by the atom-molecule internal tunneling. This effective interaction is similar to that familiar in the context of BCS-BEC crossover in a Fermi gas with Feshbach resonance. Furthermore, we point out the possibility of reentrant transition in the case of the large detuning between the atomic and molecular states.

We obtain the thermodynamic properties for a noninteracting Bose gas constrained on multilayers modeled by a periodic Kronig-Penney delta potential in one direction and allowed to be free in the other two directions. We report Bose-Einstein condensation (BEC) critical temperatures, chemical potential, internal energy, specific heat, and entropy for different values of a dimensionless impenetrability $P⩾0$ between layers. The BEC critical temperature $T_c$ coincides with the ideal gas BEC critical temperature $T_0$ when $P=0$ and rapidly goes to zero as $P$ increases to infinity for any finite interlayer separation. The specific heat $C_V$ as a function of absolute temperature $T$ for finite $P$ and plane separation $a$ exhibits one minimum and one or two maxima in addition to the BEC, for temperatures larger than that of BEC $T_c$. This highlights the effects due to particle confinement. We then discuss a distinctive dimensional crossover of the system through the specific heat behavior driven by the magnitude of $P$. For $T<T_c$ the crossover is revealed by a change in slope of $\log C_V(T)$ and when $T>T_c$, it is exhibited by a broad minimum in $C_V(T)$.

Transformation-optics devices of arbitrary shapes usually result in material parameters inside the device that feature level sets of different shapes. Consequently, these devices cannot easily be implemented using a layered architecture and thus are, generally, more difficult to realize in practice. We present a method of designing two-dimensional transformation-optics devices of arbitrary shapes characterized by material parameters of same-level sets, thus suitable to be implemented through concentric layers, each layer being made of a single type of material or metamaterial. Remarkably, we show that transformations leading to such designs are obtained from solutions to the well-known eikonal equation. This approach allows fabrication techniques developed for cylindrical designs of circular cross section to be directly applied to devices of other shapes.

We consider a quantum memory scheme based on the conversion of a signal pulse into a long-lived spin coherence via stimulated off-resonant Raman process. For a storing medium consisting of alkali-metal atoms, we have calculated the Autler-Townes resonance structure created by a strong control field. By taking into account the upper hyperfine states of the $D_1$ optical transition, we show important deviations from the predictions of the usual three-level $\Lambda$-scheme approximation and we demonstrate an enhancement of the process for particular detunings of the control. We estimate the memory efficiency one can obtain using this configuration.

Magnetic resonance techniques provide a powerful tool for controlling spin systems, with applications ranging from quantum information processing to medical imaging. Nevertheless, the behavior of a spin system under strong excitation remains a rich dynamical problem. In this paper, we examine spin resonance of the nitrogen-vacancy center in diamond under conditions outside the regime where the usual rotating-wave approximation applies, focusing on effects of multifrequency excitation and excitation with orientation parallel to the spin quantization axis. Strong-field phenomena such as multiphoton transitions and coherent destruction of tunneling are observed in the spectra and analyzed via numerical and analytic theory. In addition to illustrating the response of a spin system to strong multifrequency excitation, these observations may inform techniques for manipulating electron-nuclear spin quantum registers.

We derive the expressions for the anisotropic heterogeneous tensors of permittivity and permeability associated with two-dimensional and three-dimensional carpets of an arbitrary shape. In the former case, we map a segment onto smooth curves whereas in the latter case we map an arbitrary region of the plane onto smooth surfaces. Importantly, these carpets display no singularity of the permeability and permeability tensor components. Moreover, a reduced set of parameters leads to nonmagnetic two-dimensional carpets in $p$ polarization (i.e., for a magnetic field orthogonal to the plane containing the carpet). Such an arbitrarily shaped carpet is shown to work over a finite bandwidth when it is approximated by a checkerboard with 190 homogeneous cells of piecewise constant anisotropic permittivity. We finally perform some finite element computations in the full vector three-dimensional case for a plane wave in normal incidence and a Gaussian beam in oblique incidence. The latter requires perfectly matched layers set in a rotated coordinate axis which exemplifies the role played by geometric transforms in computational electromagnetism.

We study evolution equations and stationary homogeneous solutions for electric and magnetic field amplitudes in a ring cavity with flat mirrors. The cavity is filled with a positive or negative refraction index material with third order Kerr-like electric nonlinearities and also magnetic nonlinearities, which can be relevant in metamaterials. We consider the degree of freedom of polarization in the incident beam. It is found that considering a magnetic nonlinearity increases the variety of possible qualitatively different solutions. A classification of solutions is proposed in terms of the number of bifurcations. The analysis can be useful for the implementation of optical switching or memory storage using ring cavities with non linear materials.

We propose a polarized intensity interferometry experiment, which measures the nonlocal Pancharatnam phase acquired by a pair of Hanbury-Brown–Twiss photons. The setup involves two polarized thermal sources illuminating two polarized detectors. Varying the relative polarization angle of the detectors introduces a two-photon geometric phase. Local measurements at either detector do not reveal the effects of the phase, which is an optical analog of the multiparticle Aharonov-Bohm effect. The geometric phase sheds light on the three-slit experiment and suggests ways of tuning entanglement.

We report a scheme for implementing a multiqubit quantum phase gate in a neutral atomic ensemble via an asymmetric Rydberg blockade. The multiqubit gate is successfully realized by following a three-step approach. The neutral-atom qubits are always illuminated by the common laser beams and therefore individual addressing of the atoms is not required. The gate errors induced by atomic spontaneous emission, imperfect excitation blockade, and atomic motion are discussed.

A scheme to drive and manipulate a finite-dimensional quantum system in decoherence-free subspaces (DFSs) by Lyapunov control is proposed. Control fields are established by the Lyapunov function. This proposal can drive the open quantum system into DFSs and manipulate it to any desired eigenstate of the free Hamiltonian. An example which consists of a four-level system with three long-lived states driven by two lasers is presented to demonstrate the scheme. We have performed numerical simulations of the dynamics of the four-level system, which show that the scheme works well.

The momentum-space coupled-channels optical method has been used to study negative-ion resonance phenomena in electron impact on atomic oxygen in the energy region of $9-11.4$ eV. Total scattering cross sections have been calculated, and negative-ion resonances have been located. Most of the known resonances of available experimental observations and theoretical results have been confirmed, and some new resonance features have been found in the present calculation.

We study the effect of one-electron model potentials on the tunneling ionization rates of molecules in strong fields. By including electron correlation using the modified Leeuwen-Baerends (LB $\alpha$) model, the binding energies of outer shells of molecules are significantly improved. However, we show that the tunneling ionization rates from the LB $\alpha$ do not differ much from the earlier calculations [Phys. Rev. A 81, 033423 (2010)], in which the local correlation potential was neglected.