Metal-insulator transition revisited for cold atoms in non-Abelian gauge potentials

We discuss the possibility of realizing metal-insulator transitions with ultracold atoms in two-dimensional optical lattices in the presence of artificial gauge potentials. For Abelian gauges, such transitions occur when the magnetic flux penetrating the lattice plaquette is an irrational multiple of the magnetic flux quantum. Here we present the first study of these transitions for non-Abelian U(2) gauge fields. In contrast to the Abelian case, the spectrum and localization transition in the non-Abelian case is strongly influenced by atomic momenta. In addition to determining the localization boundary, the momentum fragments the spectrum. Other key characteristics of the non-Abelian case include the absence of localization for certain states and satellite fringes around the Bragg peaks in the momentum distribution and an interesting possibility that the transition can be tuned by the atomic momenta.     

Fragile black holes and an angular momentum cutoff in peripheral heavy ion collisions

In collisions of heavy ions at extremely high energies, it is possible for a significant quantity of angular momentum to be deposited into the Quark–Gluon Plasma which is thought to be produced. We develop a simple geometric model of such a system, and show that it is dual, in the AdS/CFT sense, to a rotating AdS black hole with a topologically planar event horizon. However, when this black hole is embedded in string theory, it proves to be unstable, for all non-zero angular momenta, to a certain non-perturbative effect: the familiar planar black hole, as used in most AdS/CFT analyses of QGP physics, is “fragile”. The upshot is that the AdS/CFT duality apparently predicts that the QGP should always become unstable when it is produced in peripheral collisions. However, we argue that holography indicates that relatively low angular momenta delay the development of the instability, so that in practice it may be observable only for peripheral collisions involving favorable impact parameters, generating extremely large angular momenta. In principle, the result may be holographic prediction of a cutoff for the observable angular momenta of the QGP, or perhaps of an analogous phenomenon in condensed matter physics.     

Angular momentum polarization in molecular collisions : Classical and quantum theory for measurements using resonance fluorescence

Inelastic or reactive collisions typically produce an anisotropic distribution of rotational angular momentum. An explicit and general treatment is given for the intensity and polarization of resonance fluorescence from molecules produced in such processes. Both classical and quantum results are expressed in terms of bipolar harmonics and state multipoles formed from linear combinations of density matrix elements. The treatment provides an inversion procedure for determining moments of the rotational angular momentum distribution ; twelve independent moments can be obtained. The combinations of angular momentum operators involved are even in eight of these moments and odd in four, with respect to reflection in a plane containing the initial and final relative velocity vectors. Measurements of the even moments require linearly polarized excitation and fluorescence, whereas measurements of the odd moments require circularly polarized excitation. The requisite experimental geometry and other practical aspects are discussed. In the three appendices are discussed the classical limits of transition intensities, a density matrix treatment of atom-rigid-rotor collisions, including analysis of state multipole symmetries ; and the coupling coefficients for parallel angular momenta.     

Elliptic dark states: Explicit invariant form

An analysis is made of coherent population trapping as a result of resonant interaction of elliptically polarized light with atoms whose energy levels are degenerate with respect to the projection of the angular momentum and are coupled by a dipole transition. Explicit invariant expressions for dark states are obtained in tensor form for all transitions where population trapping occurs. A correspondence is established between the vector of the elliptic polarization and the pair of associated spinors. It is shown that all dark states can be constructed from these spinors by means of a multiple tensor product. For integer values of the angular momenta of the transitions these constructions reduce to spherical functions of a complex variable. As applications analytic expressions are obtained for the dark magneto-optic and geometric potentials, and the change in their profile with increasing angular momenta is analyzed.     

Exponentially decaying correlations in a gas of strongly interacting spin-polarized 1D fermions with zero-range interactions

We consider the single-particle correlations and momentum distributions in a gas of strongly interacting, spinless 1D fermions with zero-range interactions. This system represents a fermionic version of the Tonks-Girardeau gas of impenetrable bosons as it can be mapped to a system of noninteracting 1D bosons. We use this duality to show that the T = 0, single-particle correlations exhibit an exponential decay with distance. This strongly interacting system is experimentally accessible using ultracold atoms and has a Lorentzian momentum distribution at large momenta whose width is given by the linear density.     

Reactive scattering of a supersonic oxygen atom beam O+ICl

Reactive scattering of O atoms with ICl molecules has been studied at an initial translational energy E = 40 kJ mol^-1 using a supersonic beam of O atoms seeded in He and at E = 15 kJ mol^-1 using O atoms seeded in Ne. Velocity distributions of OI product were measured by cross-correlation time-of-flight analysis. Full contour maps of the differential reaction cross-section have been obtained which show peaking almost equally in the forward and backward directions at both initial translational energies. The product translational energy distributions are consistent with a long-lived O-I-Cl collision complex dissociating via a loose transition state. The stability of the O-I-Cl complex is attributed to the low electronegativity of the central I atom compared with the peripheral atoms. This electronegativity ordering rule also determines the stability of the intermediates in the other reactions of oxygen atoms with halogen molecules. The mild peaking of the product angular distributions for O + ICl and IBr indicates that collision complexes have quite modest collision angular momenta L ～ 40 ? corresponding to impact parameters b ～ 1·4 Å and that the angular momentum of the OI molecule in the loose transition state may be approximately half the product orbital angular momentum.     

Two-electron excitation of an interacting cold Rydberg gas

We report the creation of an interacting cold Rydberg gas of strontium atoms. We show that the excitation spectrum of the inner valence electron is sensitive to the interactions in the Rydberg gas, even though they are mediated by the outer Rydberg electron. By studying the evolution of this spectrum we observe density-dependent population transfer to a state of higher angular momentum l. We determine the fraction of Rydberg atoms transferred, and identify the dominant transfer mechanism to be l-changing electron-Rydberg collisions associated with the formation of a cold plasma.     

Cold heteronuclear atom-ion collisions

We study cold heteronuclear atom-ion collisions by immersing a trapped single ion into an ultracold atomic cloud. Using ultracold atoms as reaction targets, our measurement is sensitive to elastic collisions with extremely small energy transfer. The observed energy-dependent elastic atom-ion scattering rate deviates significantly from the prediction of Langevin but is in full agreement with the quantum mechanical cross section. Additionally, we characterize inelastic collisions leading to chemical reactions at the single particle level and measure the energy-dependent reaction rate constants. The reaction products are identified by in-trap mass spectrometry, revealing the branching ratio between radiative and nonradiative charge exchange processes.     

Bragg spectroscopy and Ramsey interferometry with an ultracold Fermi gas

We report on the observation of Bragg scattering of an ultracold Fermi gas of ⁶Li atoms at a dynamic optical potential. The momentum states produced in this way oscillate in the trap for time scales on the order of seconds, nearly unperturbed by collisions, which are absent for ultracold fermions due to the Pauli principle. In contrast, interactions in a mixture with ⁸⁷Rb atoms lead to rapid damping. The coherence of these states is demonstrated by Ramsey-type matter wave interferometry. The signal is improved using an echo pulse sequence, allowing us to observe coherence times longer than 100 μs. Finally, we use Bragg spectroscopy to measure the in-situ momentum distribution of the ⁶Li cloud. Signatures for the degeneracy of the Fermi gas can be observed directly from the momentum distribution of the atoms inside the trap.     

Rabi oscillations and excitation trapping in the coherent excitation of a mesoscopic frozen Rydberg gas

We demonstrate the coherent excitation of a mesoscopic ensemble of about 100 ultracold atoms to Rydberg states by driving Rabi oscillations from the atomic ground state. We employ a dedicated beam shaping and optical pumping scheme to compensate for the small transition matrix element. We study the excitation in a weakly interacting regime and in the regime of strong interactions. When increasing the interaction strength by pair state resonances, we observe an increased excitation rate through coupling to high angular momentum states. This effect is in contrast to the proposed and previously observed interaction-induced suppression of excitation, the so-called dipole blockade.     

The time dependent solution of the masterequation for a laser system

Calculations of the cross sections for collision-induced transitions between Zeeman sublevels of excited alcali atoms are proposed, which are independent from dynamical models. 1. Supposing that the spin of the valence electron does not flip, the transition matrix, describing collision-induced deorientation of the orbital angular momentum, is analysed considering invariance principles only. Consequently the cross sections for depolarizing collisions are given by two dynamical parameters. 2. The full transition matrix, describing deorientation of the orbital angular momentum as well as of the spin of the valence electron, is analysed in the same way. In this general case the depolarizing cross sections are given by six dynamical parameters.     

Hybrid spin-exchange optical pumping of 3He

We demonstrate spin-exchange optical pumping of 3He using a "hybrid" K-Rb vapor mixture. The Rb atoms absorb light from a standard laser at 795 nm, then collisionally polarize the potassium atoms. Spin-exchange collisions of K and 3He atoms then transfer the angular momentum to the 3He with much greater efficiency than Rb-3He. For a K-rich vapor, the efficiency of the hybrid spin-exchange collisions approaches 1/4, an order of magnitude greater than achieved by pure Rb pumping. We present the first measurements of actual photon efficiencies (polarized nuclei produced per absorbed photon), and show that a new parasitic absorption process limits the total efficiencies for both hybrid and pure Rb pumping.     

Depolarization of luminescence of polyatomic molecules in the gas phase as a method of determining the efficiency of collisional transfer of angular momentum

The theory of collisional depolarization of luminescence of extended polyatomic molecules in rarefiedgases is considered. The interrelation between the frequency of collisions, the relaxation time of the angular momentum, and the cross section of the luminescence depolarization is established, and the dependence of these parameters on the efficiency of an abrupt change in the angular momentum is calculated. The use of the theory of collisions of solids in the Enskog approximation made it possible to take into account the effect of the shape and mass of colliding molecules on the degree of depolarization. It is established that, in terms of this theory, there exists a limiting efficiency of an abrupt change in the angular momentum, which, however, does not attain the value proposed in the model of strong collisions (Jdiffusion). The dependence of the depolarization of luminescence of 1,4-di-(2-5-p-tolyloxazolyl) benzene molecules on the concentration of a buffer gas (argon) is measured. It is found that about five collisions with Ar atoms are required for randomization of the angular momentum of these molecules.     

Suppression of angular momentum transfer in cold collisions of transition metal atoms in ground States with nonzero orbital angular momentum

The Zeeman relaxation rate in cold collisions of Ti(3d(2)4s(2) 3F2) with He is measured. We find that collisional transfer of angular momentum is dramatically suppressed due to the presence of the filled 4s(2) shell. The degree of electronic interaction anisotropy, which is responsible for Zeeman relaxation, is estimated to be about 200 times smaller in the Ti-He complex than in He complexes with typical non-S-state atoms.     

Scaling properties of resonant electron transfer in ion—metal-surface interactions

Scaling properties of resonant electron transfer in the interaction of atoms and positive ions with metal surfaces are revealed by examining the dependence of numerically calculated transition matrix elements and (first-order) transition rates upon the scaled ion-surface distance D = D/D_n, where D_n is the classical threshold distance for electron transfer involving ionic stat principal quantum number n. For zero orbital angular momentum and fixed energy of the ionic states, the n-dependence of the rates at D = 1 is found to approach, in the large-n limit, a simple power law. A scaling law is established that connects, in the range D 1, transition rates for arbitrary (large) principal quantum numbers.     

Internal state conversion in ultracold gases

We consider an ultracold gas of (noncondensed) bosons or fermions with two internal states, and we study the effect of a gradient of the transition frequency between these states. When a pi/2 rf pulse is applied to the sample, exchange effects during collisions transfer the atoms into internal states which depend on the direction of their velocity. This results, after a short time, in a spatial separation between the two states. A kinetic equation is solved analytically and numerically; the results agree well with the recent observations of Lewandowski et al.     

Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition

The evolution of on-site number fluctuations of ultracold atoms in optical lattices is experimentally investigated by monitoring the suppression of spin-changing collisions across the superfluid-Mott insulator transition. For low atom numbers, corresponding to an average filling factor close to unity, large on-site number fluctuations are necessary for spin-changing collisions to occur. The continuous suppression of spin-changing collisions is thus direct evidence for the emergence of number-squeezed states. In the Mott insulator regime, we find that spin-changing collisions are suppressed until a threshold atom number, consistent with the number where a Mott plateau with doubly occupied sites is expected to form.     

Properties of Universal Bosonic Tetramers

The system of four identical bosons is studied using momentum–space equations for the four-particle transition operators. Positions, widths and existence limits of universal unstable tetramers are determined with high accuracy. Their effect on the atom–trimer and dimer–dimer scattering observables is discussed. We show that a universal shallow tetramer intersects the atom–trimer threshold twice leading to resonant effects in ultracold atom–trimer collisions.     

Cold matter trapping via slowly rotating helical potential

We consider the cold bosonic ensemble trapped by a helical interference pattern in the optical loop scheme. This rotating helical potential is produced by the two slightly detuned counter-propagating Laguerre-Gaussian laser beams with counter-directed orbital angular momenta ±??. The detuning δω may occur due to rotational Doppler effect. The superfluid hydrodynamics is analyzed for the large number of trapped atoms in Thomas-Fermi approximation. For the highly elongated trap the Gross-Pitaevskii equation is solved in a slowly varying envelope approximation. The speed of axial translation and angular momenta of interacting atomic cloud are evaluated. In the T→0 limit the angular momentum of the helical cloud is expected to be zero while toroidal trapping geometry leads to 2?? angular momentum per trapped atom.     

Magnetic trapping of ultracold Rydberg atoms

We investigate the quantum dynamics of ultracold Rydberg atoms being exposed to a magnetic quadrupole field. A Hamiltonian describing the coupled dynamics of the electronic and center of mass motion is derived. Employing an adiabatic approach, the potential energy surfaces for intra-n-manifold mixing are computed. By determining the quantum states of the center of mass motion, we demonstrate that trapped states can be achieved if the total angular momentum of the atom is sufficiently large. This holds even if the extension of the electronic Rydberg state becomes equal to or even exceeds that of the ultracold center of mass motion.