The light-matter-wave Sagnac interferometer based on ultraslow light proposed recently in Zimmer and Fleischhauer, Phys. Rev. Lett. 92, 253201 (2004), is analyzed in detail. In particular the effect of confining potentials is examined and it is shown that the ultraslow light attains a rotational phase shift equivalent to that of a matter wave, if and only if the coherence transfer from light to atoms associated with slow light is associated with a momentum transfer and if an ultracold gas in a ring trap is used. The quantum sensitivity limit of the Sagnac interferometer is determined and the minimum detectable rotation rate calculated. It is shown that the slow-light interferometer allows for a significantly higher signal-to-noise ratio as possible in current matter-wave gyroscopes.

We propose a coupled modes analysis of second-harmonic generation in microdisk resonators. We demonstrate that whispering gallery modes can be used to obtain a combination of modal and geometrical quasi-phase-matching (without domain inversion) to obtain efficient conversion in isotropic and nonferroelectric materials such as III-V semiconductor compounds. Finally we use an analytical model to describe the coupling between a bus waveguide and the nonlinear microdisk to achieve an optimization scheme for practical configuration.

We investigate signals of trapping states in the micromaser system in terms of the average number $⟨n⟩$ of cavity photons as well as a suitably defined correlation length of atoms leaving the cavity. In the description of collective two-atom effects we allow the mean number, $ϵ$, of pump atoms inside the cavity during the characteristic atomic cavity transit time to be as large as of order one. The master equation we consider, which describes the micromaser including collective two-atom effects, still exhibits trapping states for $ϵ\ne 0$, even for a mean number of atoms inside the cavity close to one. We, however, argue more importantly that the trapping states are more pronounced in terms of the correlation length as compared to $⟨n⟩$, i.e., we suggest that trapping states can be more clearly revealed experimentally in terms of the atom correlation length. For axion detection in the micromaser this observable may, therefore, be an essential ingredient.

Let us consider two quantum systems: system $A$ and system $B$. Suppose that some classical information is encoded to quantum states of the system $A$ and we distribute this information to both systems by making them interact with each other. We show that it is impossible to achieve this goal perfectly if the strength of interaction between the quantum systems is smaller than a quantity that is determined by noncommutativity between a Hamiltonian of the system $A$ and the states (density operators) used for the information encoding. This is a consequence of a generalized Winger-Araki-Yanase theorem which enables us to treat conserved quantities other than additive ones.

We show that if an electromagnetic energy pulse in a multimode coherent state with average photon number $\overline{n}$ is used to carry out the same quantum logical operation on a set of $N$ atoms, either simultaneously or sequentially, the overall error probability in the worst-case scenario (i.e., maximized over all the possible initial atomic states) scales as $N^2∕\overline{n}$. This means that in order to keep the error probability bounded by $Nϵ$, with $ϵ\sim 1∕\overline{n}$, one needs to use $N\overline{n}$ photons or, equivalently, $N$ separate “minimum-energy” pulses: in this sense the pulses cannot, in general, be shared. The origin of this phenomenon is found in atom-field entanglement. These results may have important consequences for quantum logic and, in particular, for large-scale quantum computation.

We give formulas for transduction in magnetic resonance—i.e., the appearance of an emf due to Larmor precession of spins—based upon the modified Lorentz reciprocity principle for gyrotropic (also called “nonreciprocal”) media, i.e., in which a susceptibility tensor is carried to its transpose by reversal of an external static field [cf., R. F. Harrington and A. T. Villeneuve IRE Trans. Microwave Theory and Technique MTT6, 308 (1958)]. Prior applications of reciprocity to magnetic resonance, despite much success, have ignored the gyrotropism which necessarily arises due to nuclear and/or unpaired electronic spins. For detection with linearly polarized fields, oscillating at the Larmor frequency, the emf is written in terms of a volume integral containing a product of two factors which we define as the antenna patterns, i.e., $(H_{1x}\pm i{H}_{1y})$, where, e.g., for a single transceive antenna, the $H$’s are just the spatially dependent oscillatory magnetic field strengths, per the application of some reference current at the antenna terminals, with the negative sign obtaining for transmission, and the positive for reception. Similar expressions hold for separate transmit and receive antennas; expressions are also given for circular polarization of the fields. We then exhibit a receive-only array antenna of two elements for magnetic resonance imaging of protons, which, due an intensity artifact arising from stray reactive coupling of the elements, produces, despite its own bilateral symmetry, asymmetric proton NMR images of a symmetric cylindrical phantom containing aqueous saline solution [J. Tropp and T. Schirmer, J. Magn. Reson. 151, 146 (2001)]. Modification of this two-port antenna, to function in transmit-receive mode, allows us to demonstrate highly nonreciprocal behavior: that is, to record images (of cylindrical test phantoms containing aqueous saline solution) whose appearance dramatically changes, when the roles of transmission and reception are swapped between the two antenna ports—giving in one instance a signal intensity pattern whose form resembles an umbrella (i.e., with a central column of moderate intensity surmounted by a bright canopy), and in the other, a distorted oval with slight concavities at its horizontal extremes, whose outline suggests that of a cat’s eye. The relation between image patterns and drive scheme can be shown to reverse if the static polarizing field is reversed. Electromagnetic and circuit calculations, together with the modified reciprocity principle, allow us to reproduce these pattern changes in numerical simulations, closely and convincingly. Although the imaging experiments are performed at a static field of $3.0\mathrm{T}$, and consequently a Larmor frequency of $128\mathrm{MHz}$, the nonreciprocal effects are not related to the shortness of the wavelength in aqueous medium, but appear equally in simulations based in either the quasistatic or full electromagnetic regimes. Finally, we show that although antenna patterns for transmission and reception are swapped with reversal of the polarizing field, meaning that the receive pattern equals the transmit pattern with the field reversed, this in no way invalidates the familiar rotating wave model of spin dynamics in magnetic resonance.

We have investigated the Coster-Kronig transition probability $f_{23}$ in gold atoms (nuclear charge $Z=79$) using the $L$ x-ray versus $K$ x-ray coincidence method. K vacancies were created using synchrotron radiation and the cascade decays were measured using germanium x-ray detectors. We find $f_{23}=0.112\pm 0.004$ which is somewhat lower than the recent coincidence measurement of Santra et al. which yielded $f_{23}=0.119\pm 0.003$. Our result is smaller than the values calculated by McGuire $(f_{23}=0.132)$ and Puri et al. $(f_{23}=0.129)$ but agrees with our own single-configuration Pauli-Fock calculation, which gives $f_{23}=0.114$, as well as the global set of prior experimental data.

The electron propagator is calculated for a set of closed-shell atoms using $GW$-like self-energies that contain the coupling of single-particle degrees of freedom with excited states in the framework of the random phase approximation. The effect of including exchange diagrams is investigated. Calculations are performed in the Hartree-Fock (HF) basis of the neutral atom. The HF continuum is taken into account using a discretization procedure, and the basis set limit is estimated using a systematic increase of basis set size. We check the approximation of taking the self-energy diagonal in the HF basis, and to what extent the extended Koopman’s theorem is fulfilled using an approximate self-energy. Finally we try to model the information contained in the propagator in terms of a functional containing Hartree-Fock quantities and demonstrate the feasibility of simultaneously reproducing the correlation and ionization energy of an underlying ab initio model.

Atomic properties involving the low-lying excited ${}^{2}D_{3∕2,5∕2}$ states in alkaline-earth-metal ions are of current interest in many different applications ranging from tests of physics beyond the standard model to astrophysics. We have used the relativistic coupled-cluster theory to perform accurate calculations of the lifetimes of the lowest excited ${}^{2}D_{3∕2}$ and ${}^{2}D_{5∕2}$ states in singly ionized calcium, strontium, and barium. The importance of electron correlation in these calculations is emphasized. Our results are compared with the available experimental and theoretical data.

This paper is aimed at the theoretical investigation of the inelastic processes taking place in resonant collisions of low-energy electrons with the chlorine molecule. Dissociative electron attachment and vibrational excitation of ${\mathrm{Cl}}_2$ by electron impact is investigated in the energy range $0–1.5\mathrm{eV}$, where the ${}^2\Sigma _u^{+}$ resonance plays the central role. The calculations were carried out within the framework of the nonlocal resonance model. This approach makes it possible to calculate the integrated cross sections of the above-mentioned processes for a variety of initial and final rovibrational states of the target molecule. The present model is constructed on the basis of ab initio fixed-nuclei $R$-matrix calculations using the so-called Feshbach-Fano $R$-matrix method. The Schwinger-Lanczos algorithm was utilized to solve the Lippmann-Schwinger equation describing the motion of the nuclei.

The electrostrictive response of small carbon clusters, hydrocarbon molecules, and carbon nanotubes is investigated using the density functional theory. For ringlike carbon clusters, one can get insight on the deformations induced by an electric field from a simple two-dimensional model in which the positive charge of the carbon ions is smeared out in a circular homogeneous line of charge and the electronic density is calculated for a constant applied electric field within a two-dimensional Thomas-Fermi method. According to the Hellmann-Feynman theorem, this model predicts, for fields of about $1\mathrm{V}∕\mathrm{\AA }$, only a small elongation of the ring clusters in the direction of the electric field. Full three-dimensional density functional calculations with an external electric field show similar small deformations in the ring carbon clusters compared to the simple model. The saturated benzene and phenanthrene hydrocarbon molecules do not experience any deformation, even under the action of relatively intense $(1\mathrm{V}∕\mathrm{\AA })$ electric fields. In contrast, finite carbon nanotubes experience larger elongations $(\sim 2.9\%)$ induced by relatively weak ($0.1\mathrm{V}∕\mathrm{\AA })$ applied electric fields. Both C-C bond length elongation and the deformation of the honeycomb structure contribute equally to the nanotube elongation. The effect of the electric field in hydrogen terminated nanotubes is reduced with respect to the nanotubes with dangling bonds in the edges.

Bose gases in rotating optical lattices combine two important topics in quantum physics: superfluid rotation and strong correlations. In this paper, we examine square two-dimensional systems at zero temperature comprised of strongly repulsive bosons with filling factors of up to one atom per lattice site. The entry of vortices into the system is characterized by jumps of $2\pi$ in the phase winding of the condensate wave function. A lattice of size $L\times L$ can have at most $L-1$ quantized vortices in the lowest Bloch band. In contrast to homogeneous systems, angular momentum is not a good quantum number since the continuous rotational symmetry is broken by the lattice. Instead, a quasiangular momentum captures the discrete rotational symmetry of the system. Energy level crossings indicative of quantum phase transitions are observed when the quasiangular momentum of the ground state changes.

We investigate the quantum superchemistry or Bose-enhanced atom-molecule conversions in a coherent output coupler of matter waves, as a simple generalization of the two-color photoassociation. The stimulated effects of molecular output step and atomic revivals are exhibited by steering the rf output couplings. The quantum noise-induced molecular damping occurs near a total conversion in a levitation trap. This suggests a feasible two-trap scheme to make a stable coherent molecular beam.

The photoionization of the $4s$ Rydberg state in hydrogen by an intense femtosecond $400\text{−}\mathrm{nm}$ light pulse is studied beyond the dipole approximation. We show that a recently predicted nondipole, high-frequency ionization mechanism [M. Førre et al., Phys. Rev. Lett. 97, 043601 (2006)] has a low-frequency counterpart in excited atomic systems. This opens the possibility that the effect could be measured in the near future.

We theoretically investigate the dynamic properties of a Bose-Einstein condensate in a toroidal trap. A periodic modulation of the transverse confinement is shown to produce a density pattern due to parametric amplification of phonon pairs. By imaging the density distribution after free expansion one obtains (i) a precise determination of the Bogoliubov spectrum and (ii) a sensitive detection of quantized circulation in the torus. The parametric amplification is also sensitive to thermal and quantum fluctuations.

We describe the influence of continuous measurement in a decaying system and the role of the distance from the detector to the initial location of the system. The detector is modeled first by a step absorbing potential. For a close and strong detector, the decay rate of the system is reduced; weaker detectors do not modify the exponential decay rate but suppress the long-time deviations above a coupling threshold. Nevertheless, these perturbing effects of measurement disappear by increasing the distance between the initial state and the detector, as well as by improving the efficiency of the detector.

Polar molecules in high-field seeking states cannot be trapped in static traps as Maxwell’s equations do not allow a maximum of the electric field in free space. It is possible to generate an electric field that has a saddle point by superposing an inhomogeneous electric field to an homogeneous electric field. In such a field, molecules are focused along one direction, while being defocused along the other. By reversing the direction of the inhomogeneous electric field the focusing and defocusing directions are reversed. When the fields are being switched back and forth at the appropriate rate, this leads to a net focusing force in all directions. We describe possible electrode geometries for creating the desired fields and discuss their merits. Trapping of ${}^{15}\mathrm{ND}_3$ ammonia molecules in a cylindrically symmetric ac trap is demonstrated. We present measurements of the spatial distribution of the trapped cloud as a function of the settings of the trap and compare these to both a simple model assuming a linear force and to full three-dimensional simulations of the experiment. With the optimal settings, molecules within a phase-space volume of $270{\mathrm{mm}}^3(\mathrm{m}∕\mathrm{s}{)}^3$ remain trapped. This corresponds to a trap depth of about $5\mathrm{mK}$ and a trap volume of about $20{\mathrm{mm}}^3$.

We treat three-dimensional bosonic clusters with up to $N=40$ atoms, interacting additively through two-body van der Waals potentials, in the near-threshold regime. Our study includes super-borromean systems with $N$ atoms for which all subsystems are unbound. We determine the energetics and structural properties such as the expectation value of the interparticle distance as a function of the coupling strength. It has been shown that the coupling strength $g_{*}^{\left(N\right)}$, for which the $N$-body system becomes unbound, is bounded by the coupling constant $g_{*}^{(N-1)}$, for which the next smaller system with $N-1$ atoms becomes unbound, i.e., $g_{*}^{\left(N\right)}⩾(N-1)g_{*}^{(N-1)}∕N$. By fitting our numerically determined ground-state energies to a simple functional form with three fitting parameters, we determine the relationship between $g_{*}^{\left(N\right)}$ and $g_{*}^{(N-1)}$. Our trimer and tetramer energies fall on the so-called Tjon line, which has been studied in nuclear physics. We confirm the existence of generalized Tjon lines for larger clusters. Signatures of the universal behavior of weakly bound three-dimensional clusters can possibly be observed in ultracold Bose gases.

Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed-matter, atomic, and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.