Measuring the dispersive frequency shift of a rectangular microwave cavity induced by an ensemble of Rydberg atoms

In recent years the interest in studying interactions of Rydberg atoms or ensembles thereof with optical and microwave frequency fields has steadily increased, both in the context of basic research and for potential applications in quantum information processing. We present measurements of the dispersive interaction between an ensemble of helium atoms in the 37s Rydberg state and a single resonator mode by extracting the amplitude and phase change of a weak microwave probe tone transmitted through the cavity. The results are in quantitative agreement with predictions made on the basis of the dispersive Tavis-Cummings Hamiltonian. We study this system with the goal of realizing a hybrid between superconducting circuits and Rydberg atoms. We measure maximal collective coupling strengths of 1 MHz, corresponding to 3*10^3 Rydberg atoms coupled to the cavity. As expected, the dispersive shift is found to be inversely proportional to the atom-cavity detuning and proportional to the number of Rydberg atoms. This possibility of measuring the number of Rydberg atoms in a nondestructive manner is relevant for quantitatively evaluating scattering cross sections in experiments with Rydberg atoms

Collective shuttling of attracting particles in asymmetric narrow channels

The rectification of a single file of attracting particles subjected to a low frequency ac drive is proposed as a working mechanism for particle shuttling in an asymmetric narrow channel. Increasing the particle attraction results in the file condensing, as signalled by the dramatic enhancement of the net particle current. Magnitude and direction of the current become extremely sensitive to the actual size of the condensate, which can then be made to shuttle between two docking stations, transporting particles in one direction, with an efficiency much larger than conventional diffusive models predict

Localization in non-chiral network models for two-dimensional disordered wave mechanical systems

Scattering theoretical network models for general coherent wave mechanical systems with quenched disorder are investigated. We focus on universality classes for two dimensional systems with no preferred orientation: Systems of spinless waves undergoing scattering events with broken or unbroken time reversal symmetry and systems of spin 1/2 waves with time reversal symmetric scattering. The phase diagram in the parameter space of scattering strengths is determined. The model breaking time reversal symmetry contains the critical point of quantum Hall systems but, like the model with unbroken time reversal symmetry, only one attractive fixed point, namely that of strong localization. Multifractal exponents and quasi-one-dimensional localization lengths are calculated numerically and found to be related by conformal invariance. Furthermore, they agree quantitatively with theoretical predictions. For non-vanishing spin scattering strength the spin 1/2 systems show localization-delocalization transitions.Comment: 4 pages, REVTeX, 4 figures (postscript

Dissociation energy of the hydrogen molecule at 10−9^{-9} accuracy

The ionization energy of ortho-H$_2$ has been determined to be $E^\mathrm{o}_\mathrm{I}(\mathrm{H}_2)/(hc)=124\,357.238\,062(25)$ cm$^{-1}$ from measurements of the GK(1,1)--X(0,1) interval by Doppler-free two-photon spectroscopy using a narrow band 179-nm laser source and the ionization energy of the GK(1,1) state by continuous-wave near-infrared laser spectroscopy. $E^\mathrm{o}_\mathrm{I}$(H$_2$) was used to derive the dissociation energy of H$_2$, $D^{N=1}_{0}$(H$_2$), at $35\,999.582\,894(25)$ cm$^{-1}$ with a precision that is more than one order of magnitude better than all previous results. The new result challenges calculations of this quantity and represents a benchmark value for future relativistic and QED calculations of molecular energies.Comment: 6 pages, 5 figure

The two electron artificial molecule

Exact results for the classical and quantum system of two vertically coupled two-dimensional single electron quantum dots are obtained as a function of the interatomic distance (d) and with perpendicular magnetic field. The classical system exhibits a second order structural transition as a function of d which is smeared out and shifted to lower d values in the quantum case. The spin-singlet - spin-triplet oscillations are shifted to larger magnetic fields with increasing d and are quenched for a sufficiently large interatomic distance.Comment: 4 pages, 4 ps figure

Screening and inplane magnetoresistance of anisotropic two-dimensional gas

In order to split the influence of the orbital and spin effects on the inplane magnetoresistance of a quasi two-dimensional gas we derive its linear response function and dielectric function for the case of anisotropic effective mass. This result is used for the calculation of elastic transport relaxation time of a quasi two dimensional system in a parallel magnetic field. The relaxation time is proved to be isotropic in the low density limit for the case of charged impurity scattering, allowing to separate the two contributions.Comment: as published. 4 pages, 1 figur

Coherent current transport in wide ballistic Josephson junctions

We present an experimental and theoretical investigation of coherent current transport in wide ballistic superconductor-two dimensional electron gas-superconductor junctions. It is found experimentally that upon increasing the junction length, the subharmonic gap structure in the current-voltage characteristics is shifted to lower voltages, and the excess current at voltages much larger than the superconducting gap decreases. Applying a theory of coherent multiple Andreev reflection, we show that these observations can be explained in terms of transport through Andreev resonances.Comment: 4 pages, 4 figure

Two Electrons in a Quantum Dot: A Unified Approach

Low-lying energy levels of two interacting electrons confined in a two-dimensional parabolic quantum dot in the presence of an external magnetic field have been revised within the frame of a novel model. The present formalism, which gives closed algebraic solutions for the specific values of magnetic field and spatial confinement length, enables us to see explicitly individual effects of the electron correlation.Comment: 14 page

Coulomb correlation effects in semiconductor quantum dots: The role of dimensionality

We study the energy spectra of small three-dimensional (3D) and two-dimensional (2D) semiconductor quantum dots through different theoretical approaches (single-site Hubbard and Hartree-Fock hamiltonians); in the smallest dots we also compare with exact results. We find that purely 2D models often lead to an inadequate description of the Coulomb interaction existing in realistic structures, as a consequence of the overestimated carrier localization. We show that the dimensionality of the dots has a crucial impact on (i) the accuracy of the predicted addition spectra; (ii) the range of validity of approximate theoretical schemes. When applied to realistic 3D geometries, the latter are found to be much more accurate than in the corresponding 2D cases for a large class of quantum dots; the single-site Hubbard hamiltonian is shown to provide a very effective and accurate scheme to describe quantum dot spectra, leading to good agreement with experiments.Comment: LaTeX 2.09, RevTeX, 25 pages, 9 Encapsulated Postscript figures. To be published in Physical Review

Addition Spectra of Quantum Dots in Strong Magnetic Fields

We consider the magnetic field dependence of the chemical potential for parabolically confined quantum dots in a strong magnetic field. Approximate expressions based on the notion that the size of a dot is determined by a competition between confinement and interaction energies are shown to be consistent with exact diagonalization studies for small quantum dots. Fine structure is present in the magnetic field dependence which cannot be explained without a full many-body description and is associated with ground-state level crossings as a function of confinement strength or Zeeman interaction strength. Some of this fine structure is associated with precursors of the bulk incompressible states responsible for the fractional quantum Hall effect.Comment: 11 pages, 3 figures (available from [email protected]). Revtex 3.0. (IUCM93-010