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The time-dependent kinetics of formation and evolution of nano-size atomic clusters is investigated and illustrated with the nucleation dynamics of ion-seed Ar$_n$H$^+$ particles. The rates of growth and degradation of Ar-atomic shells around the seed ion are inferred from Molecular Dynamics (MD) simulations. Simulations of cluster formation have been performed with accurate quantum-mechanical binary interaction potentials. Both the nonequilibrium and equilibrium growth of Ar$_n$H$^+$ are investigated at different temperature and densities of the atomic gas and seed ions. Formation of Ar$_{n\leq 40}$ shells is the main mechanism which regulates the kinetics of nano-cluster growth and the diffusive fluctuations of the cluster size distribution. The time-evolution of the cluster intrinsic energy and cluster size distributions are analyzed at the non-thermal, quasi-equilibrium, and thermal equilibrium stages of Ar$_n$H$^+$ formation. We've determined the self-consistent model parameters for the temporal fluctuations of the cluster size and found coefficients of the diffusive growth mechanism describing the equilibrium distribution of nano-clusters. Nucleation of haze and nano-dust particles in astrophysical and atmospheric ionized gases are discussed., Comment: 12 pages, 10 figures

We apply Milne's phase-amplitude representation [W. E. Milne, Phys. Rev. 35, 863 (1930)] to a scattering problem involving disjoint classically allowed regions separated by a barrier. Specifically, we develop a formalism employing different sets of amplitude and phase functions --- each set of solutions optimized for a separate region --- and we use these locally adapted solutions to obtain the true value of the scattering phase shift and accurate tunneling rates for ultra-narrow shape resonances. We show results for an illustrative example of an attractive potential with a large centrifugal barrier., Comment: 6 figures

A novel integral representation for scattering phase shifts is obtained based on a modified version of Milne's phase-amplitude approach [W.E. Milne, Phys. Rev. $\mathbf{35}$, 863 (1930)]. We replace Milne's nonlinear differential equation for the amplitude function $y$ with an equivalent linear equation for the envelope $\rho=y^2$, which renders the integral representations highly amenable to numerical implementations. The phase shift is obtained directly from Milne's phase function, which in turn is expressed in terms of the envelope function. The integral representation presented in this work is fully general and it can be used for any type of scattering potential, including the Coulomb potential., Comment: 10 pages, 6 figures

This editorial introduces the J. Phys. B: Atomic, Molecular and Optical Physics Special Issue "Atomic and Molecular Processes in the Ultracold Regime, the Chemical Regime and Astrophysics" dedicated to Professor Alexander Dalgarno (1928-2015). After a brief biographical review, short summaries of the contributed papers and their relations to some of Prof. Dalgarno's work are given., Comment: 7 pp

Assuming that the nuclear magnetic resonance (NMR) signal from a $^{13}$C isotope enriched layer of graphene can be made sufficiently intense to be measured, we compute the NMR\ lineshape of the different crystals ground states that are expected to occur in graphene in a strong magnetic field. We first show that in nonuniform states, there is, in addition to the frequency shift due to the spin hyperfine interaction, a second contribution of equal importance from the coupling between the orbital motion of the electrons and the nuclei. We then show that, if the linewidth of the bare signal can be made sufficiently small, the Wigner and bubble crystals have line shapes that differ qualitatively from that of the uniform state at the same density while crystal states that have spin or valley pseudospin textures do not. Finally, we find that a relatively small value of the bare linewidth is sufficient to wash out the distinctive signature of the crystal states in the NMR line shape., Comment: 12 pages with 6 eps figures

Benchmark reactions involving molecular hydrogen, such as H$_2$+D or H$_2$+Cl, provide the ideal platforms to investigate the effect of Near Threshold Resonances (NTR) on scattering processes. Due to the small reduced mass of those systems, shape resonances due to particular partial waves can provide features at scattering energies up to a few Kelvins, reachable in recent experiments. We explore the effect of NTRs on elastic and inelastic scattering for higher partial waves $\ell$ in the case of H$_2$+Cl for $s$-wave and H$_2$+D for $p$-wave scattering, and find that NTRs lead to a different energy scaling of the cross sections as compared to the well known Wigner threshold regime. We give a theoretical analysis based on Jost functions for short range interaction potentials. To explore higher partial waves, we adopt a three channel model that incorporates all key ingredients, and explore how the NTR scaling is affected by $\ell$. A short discussion on the effect of the long-range form of the interaction potential is also provided.

We present numerical results for rate coefficients of reaction and vibrational quenching in the collision of H with D$_2(v,j)$ at cold and ultracold temperatures. We explore both ortho-D$_2(j\!=\!0)$ and para-D$_2(j\!=\!1)$ for several initial vibrational states $(v\leq 5)$, and find resonant structures in the energy range 0.01--10 kelvin, which are sensitive to the initial rovibrational state $(v,j)$. We compare the reaction rates for D$_2$+H with our previously obtained results for the isotopologue reaction H$_2$+D, and discuss the implications of our detailed study of this benchmark system for ultracold chemistry., Comment: 12 pages, 7 figures

We present novel approaches for solving Milne's equation, which was introduced in 1930 as an efficient numerical scheme for the Schr\"odinger equation. Milne's equation appears in a wide class of physical problems, ranging from astrophysics and cosmology, to quantum mechanics and quantum optics. We show how a third order linear differential equation is equivalent to Milne's non-linear equation, and can be used to accurately calculate Milne's amplitude and phase functions. We also introduce optimization schemes to achieve a convenient, fast, and accurate computation of wave functions using an economical parametrization. These new optimization procedures answer the long standing question of finding non-oscillatory solutions of Milne's equation. We apply them to long-range potentials and find numerically exact asymptotic solutions., Comment: 5 pages, 4 figures

We investigate the energy dependence of inelastic processes in systems which possess Efimov states. We consider the three-body recombination rate $K_3$ where three free atoms interact to produce an atom--dimer pair, and the relaxation rate $K_{\rm rel}$ where an atom quenches a weakly bound state of a dimer near an Efimov resonance to more deeply bound levels. Using a model capturing the key features of the Efimov problem, we identify new energy regimes for $K_3$, namely the NTR (Near Threshold Resonance) regime behavior $E^{-2}$ for negative scattering lengths and the NTS (Near Threshold Suppression) regime behavior $E^2$ for positive scattering lengths. We also confirm a previously found oscillatory behavior of $K_3$ at higher energy $E$. Finally, we find that $K_{\rm rel}$ behaves as $E^{-1}$ in the NTR regime.

The combined effect of a lateral square superlattice potential and the Coulomb interaction on the ground state of a two-dimensional electron gas in a perpendicular magnetic field is studied for different rational values of $\Gamma$, the inverse of the number of flux quanta per unit cell of the external potential, at filling factor $\nu =1$ in Landau level $N=0.$ When Landau level mixing and disorder effects are neglected, increasing the strength $W_{0}$ of the potential induces a transition, at a critical strength $W_{0}^{\left( c\right) },$ from a uniform and fully spin polarized state to a two-dimensional charge density wave (CDW) with a meronlike spin texture at each maximum and minimum of the CDW. The collective excitations of this vortex-CDW are similar to those of the Skyrme crystal that is expected to be the ground state near filling factor $\nu =1$. In particular, a broken U(1) symmetry in the vortex-CDW results in an extra gapless phase mode that could provide a fast channel for the relaxation of nuclear spins. The average spin polarization $% S_{z}$ changes in a continuous or discontinuous manner as $W_{0}$ is increased depending on whether $\Gamma \in \left[ 1/2,1\right] $ or $\Gamma \in \left[ 0,1/2\right] .$ The phase mode and the meronlike spin texture disappear at large value of $W_{0},$ leaving as the ground state a partially spin-polarized CDW if $\Gamma \neq 1/2$ or a spin-unpolarized CDW if $\Gamma =1/2.$, Comment: 11 pages with 9 eps figures

Transport experiments on the two-dimensional electron gas (2DEG) confined into a semiconductor quantum well and subjected to a quantizing magnetic field have uncovered a rich variety of uniform and nonuniform phases such as the Laughlin liquids, the Wigner, bubble and Skyrme crystals and the quantum Hall stripe state. Optically pumped nuclear magnetic resonance (OP-NMR) has also been extremely useful in studying the magnetization and dynamics of electron solids with exotic spin textures such as the Skyrme crystal. Recently, it has been demonstrated that a related technique, resistively-detected nuclear magnetic resonance (RD-NMR), could be a good tool to study the topography of the electron solids in the fractional and integer quantum Hall regimes. In this work, we compute theoretically the RD-NMR line shapes of various crystal phases of the 2DEG and study the relation between their spin density and texture and their NMR spectra. This allows us to evaluate the ability of the RD-NMR to discriminate between the various types of crystal states., Comment: 12 pages, 8 figures

In a quantizing magnetic field, the chiral two-dimensional electron gas in Landau level $N=0$ of bilayer graphene goes through a series of phase transitions at integer filling factors $\nu \in \left[ -3,3\right] $ when the strength of an electric field applied perpendicularly to the layers is increased. At filling factor $\nu =3,$ the electron gas can described by a simple two-level system where layer and spin degrees of freedom are frozen. The gas then behaves as an orbital quantum Hall ferromagnet. A Coulomb-induced Dzyaloshinskii-Moriya term in the orbital pseudospin Hamiltonian is responsible for a series of transitions first to a Wigner crystal state and then to a spiral state as the electric field is increased. Both states have a non trivial orbital pseudospin texture. In this work, we study how the phase diagram at $\nu =3$ is modified by an electric field applied in the plane of the layers and then derive several experimental signatures of the uniform and nonuniform states in the phase diagram. In addition to the transport gap, we study the electromagnetic absorption and the Kerr rotation due to the excitations of the orbital pseudospin-wave modes in the broken-symmetry states., Comment: 15 pages and 13 figures

We report results for reaction and vibrational quenching of the collision D with para-H$_2$($v,j=0$) and ortho-H$_2$($v,j=1$) at cold and ultracold temperatures. We investigate the effect of nuclear spin symmetry for barrier dominated processes ($0\le v\le 4$) and for one barrierless case ($v=5$). We find resonant structures for energies in the range corresponding to 0.01--10 K, which depend on the nuclear spin of H$_2$, arising from contributions of specific partial waves. We discuss the implications on the results in this benchmark system for ultracold chemistry., Comment: 17 figures, 30 pages

We study the effect of resonances near the threshold of low energy ($\varepsilon$) reactive scattering processes, and find an anomalous behavior of the $s$-wave cross sections. For reaction and inelastic processes, the cross section exhibits the energy dependence $\sigma\sim\varepsilon^{-3/2}$ instead of the standard Wigner's law threshold behavior $\sigma\sim\varepsilon^{-1/2}$. Wigner's law is still valid as $\varepsilon\rightarrow 0$, but in a narrow range of energies. We illustrate these effects with two reactive systems, a low-reactive system (H$_2$ + Cl) and a more reactive one (H$_2$ + F). We provide analytical expressions, and explain this anomalous behavior using the properties of the Jost functions. We also discuss the implication of the reaction rate coefficients behaving as $K\sim 1/T$ at low temperatures, instead of the expected constant rate of the Wigner regime in ultracold physics and chemistry., Comment: 15 pages, 12 figures

The chiral two-dimensional electron gas in Landau levels $\left\vert N\right\vert >0$ of a Bernal-stacked graphene bilayer has a valley-pseudospin Ising quantum Hall ferromagnetic behavior at odd filling factors $\nu _{N}=1,3$ of these fourfold degenerate states. At zero interlayer electrical bias, the ground state at these fillings is spin polarized and electrons occupy one valley or the other while a finite electrical bias produces a series of valley pseudospin-flip transitions. In this work, we extend the Ising behavior to chirally-stacked multilayer graphene and discuss the hysteretic behavior of the Ising quantum Hall ferromagnets. We compute the transport gap due to different excitations: bulk electron-hole pairs, electron-hole pairs confined to the coherent region of a valley-pseudospin domain wall, and spin or valley-pseudospin skyrmion-antiskyrmion pairs. We determine which of these excitations has the lowest energy at a given value of the Zeeman coupling, bias, and magnetic field., Comment: 18 pages with 9 eps figures

A magnetic field applied perpendicularly to the chiral two-dimensional electron gas (C2DEG)\ in a Bernal-stacked bilayer graphene quantizes the kinetic energy into a discrete set of Landau levels $N=0,\pm 1,\pm 2,...$ While Landau level $N=0$ is eighfold degenerate, higher Landau levels ($ \left\vert N\right\vert \geq 1$) are fourfold degenerate when counting spin and valley degrees of freedom. In this work, the Hartree-Fock approximation is used to study the phase diagram of the C2DEG at integer fillings $ \widetilde{\nu }=1,2,3$ of these higher Landau levels. At these filling factors, the C2DEG is a valley or spin Ising quantum Hall ferromagnet. At odd fillings, the C2DEG is spin polarized and has all its electrons in one valley or the other. There is no intervalley coherence in contrast with most of the the ground states in Landau level $N=0.$ At even filling, $\widetilde{\nu }=2,$ the C2DEG is either fully spin polarized with electrons occupying both valleys or spin unpolarized with electron occupying one of the two valleys. A finite electric field (or bias) applied perpendicularly to the plane of the C2DEG induces a series of first-order phase transitions between these different ground states. The transport gap or its slope is discontinuous at the bias where a transition occurs. Such discontinuity may result in a change in the transport properties of the C2DEG at that bias., Comment: 14 pages with 12 eps figures

We show that ultracold chemical reactions can be manipulated and controlled by using Rydberg-dressed interactions. Scattering in the ultracold regime is sensitive to long-range interactions, especially when weakly bound (or quasi-bound) states exist near the collision threshold. We investigate how, by Rydberg-dressing a reactant, one enhances its polarizability and modifies the long-range van der Waals collision complex, which can alter chemical reaction rates by shifting the position of near threshold bound states. We carry out a full quantum mechanical scattering calculation for the benchmark system H$_2$+D, and show that resonances can be moved substantially and that rate coefficients at cold and ultracold temperatures can be increased by several orders of magnitude.

The eigenstates of an electron in the chiral two-dimensional electron gas (C2DEG) formed in an AB-stacked bilayer or an ABC-stacked trilayer graphene is a spinor with $4$ or $6$ components respectively. These components give the amplitude of the wave function on the $4$ or $6$ carbon sites in the unit cell of the lattice. In the tight-binding approximation, the eigenenergies are thus found by diagonalizing a $4\times 4$ or a $6\times 6$ matrix. In the continuum approximation where the electron wave vector $% k<<1/a_{0},$ with $a_{0}$ the lattice constant of the graphene sheets, a common approximation is the two-band model\cite{McCann2006} (2BM)\ where the eigenstates for the bilayer and trilayer systems are described by a two-component spinor that gives the amplitude of the wave function on the two sites with low-energy $\left\vert E\right\vert <<\gamma_{1}$ where $% \gamma_{1}$ is the hopping energy between sites that are directly above one another in adjacent layers. The 2BM has been used extensively to study the phase diagram of the C2DEG in a magnetic field as well as its transport and optical properties. In this paper, we use a numerical approach to compute the eigenstates and Landau level energies of the full tight-binding model in the continuum approximation and compare them with the prediction of the 2BM when the magnetic field or an electrical bias between the outermost layers is varied. Our numerical analysis shows that the 2BM is a good approximation for bilayer graphene in a wide range of magnetic field and bias but mostly for Landau level $M=0.$ The applicability of the 2BM in trilayer graphene, even for level $M=0,$ is much more restricted. In this case, the 2BM\ fails to reproduce some of the level crossings that occur between the sub-levels of $M=0.$, Comment: 13 pages with 11 postscript figures

We investigate the effect of near threshold resonances in reactive scattering at low energy. We find a general type of anomalous behavior of the cross sections, and illustrate it with a real system (H$_2$ + Cl). For inelastic processes, the anomalous energy dependence of the total cross sections is given by $\sigma\sim\varepsilon^{-3/2}$. The standard threshold behavior given by Wigner's law ($\sigma\sim\varepsilon^{-1/2}$) is eventually recovered at vanishing energies, but its validity is now limited to a much narrower range of energies. The universal anomalous behavior leads to reaction rate coefficients behaving as $K\sim 1/T$ at low temperatures, instead of the expected constant rate of the Wigner regime. We also provide analytical expressions for s-wave cross sections, and discuss the implication in ultracold physics and chemistry., Comment: 5 figures

At half filling of the fourfold degenerate Landau levels |n| \geq 1 in graphene, the ground states are spin polarized quantum Hall states that support spin skyrmion excitations for |n| =1,2,3. Working in the Hartree-Fock approximation, we compute the excitation energy of an unbound spin skyrmion-antiskyrmion excitation as a function of the Zeeman coupling strength for these Landau levels. We find for both the bare and screened Coulomb interactions that the spin skyrmion-antiskyrmion excitation energy is lower than the excitation energy of an unbound spin 1/2 electron-hole pair in a finite range of Zeeman coupling in Landau levels |n| =1,2,3. This range decreases rapidly for increasing Landau level index and is extremely small for |n| =3. For valley skyrmions which should be present at 1/4 and 3/4 fillings of the Landau levels |n| =1,2,3, we show that screening corrections are more important in the latter case. It follows that an unbound valley skyrmion-antiskyrmion excitation has lower energy at 3/4 filling than at 1/4. We compare our results with recent experiments on spin and valley skyrmion excitations in graphene., Comment: 15 pages with 11 eps figures

In a Bernal-stacked graphene bilayer, an electronic state in Landau level $% N=0$ is described by its guiding-center index $X$ (in the Landau gauge) and by its valley, spin, and orbital indices $\xi =\pm K,\sigma =\pm 1,$ and $% n=0,1.$ When Coulomb interaction is taken into account, the chiral two-dimensional electron gas (C2DEG) in this system can support a variety of quantum Hall ferromagnetic (QHF)\ ground states where the spins and/or valley pseudospins and/or orbital pseudospins collectively align in space. In this work, we give a comprehensive account of the phase diagram of the C2DEG at integer filling factors $\nu \in [-3,3] $ in Landau level N=0 when an electrical potential difference $\Delta_{B}$ between the two layers is varied. We consider states with or without layer, spin, or orbital coherence. For each phase, we discuss the behavior of the transport gap as a function of $\Delta_{B},$ the spectrum of collective excitations and the optical absorption due to orbital pseudospin-wave modes. We also study the effect of an external in-plane electric field on a coherent state that has both valley and spin coherence and show that it is possible, in such a state, to control the spin polarization by varying the strength of the external in-plane electric field., Comment: 21 pages, 13 eps figures

In the presence of a perpendicular magnetic field, ABC-stacked trilayer graphene's chiral band structure supports a 12-fold degenerate N=0 Landau level (LL). Along with the valley and spin degrees of freedom, the zeroth LL contains additional quantum numbers associated with the LL orbital index $% n=0,1,2$. Remote inter-layer hopping terms and external potential difference $\Delta_{B}$ between the layers lead to LL splitting by introducing a gap $% \Delta_{LL}$ between the degenerate zero-energy triplet LL orbitals. Assuming that the spin and valley degrees of freedom are frozen, we study the phase diagram of this system resulting from competition of the single particle LL splitting and Coulomb interactions within the Hartree-Fock approximation at integer filling factors. Above a critical value $\Delta_{LL}^{c}$ of the external potential difference i,e, for $|\Delta_{LL}| >\Delta_{LL}^{c}$, the ground state is a uniform quantum Hall state where the electrons occupy the lowest unoccupied LL orbital index. For $|\Delta_{LL}| <\Delta_{LL}^{c}$ (which corresponds to large positive or negative values of $\Delta_{B}$) the uniform QH state is unstable to the formation of a crystal state at integer filling factors. This phase transition should be characterized by a Hall plateau transition as a function of $\Delta_{LL}$ at a fixed filling factor. We also study the properties of this crystal state and discuss its experimental detection., Comment: 16 pages with 13 figures

ABC-stacked trilayer graphene's chiral band structure results in three ($n=0,1,2$) Landau level orbitals with zero kinetic energy. This unique feature has important consequences on the interaction driven states of the 12-fold degenerate (including spin and valley) N=0 Landau level. In particular, at many filling factors $\nu_{T} =\pm5,\pm4,\pm2,\pm1$ a quantum phase transition from a quantum Hall liquid state to a triangular charge density wave occurs as a function of the single-particle induced LL orbital splitting $\Delta_{LL}$. This phase transition should be characterized by a re-entrant integer quantum Hall effect with the Hall conductivity corresponding to the {\it adjacent} interaction driven integer quantum Hall plateau., Comment: 4+ pages

The two-dimensional electron gas in a bilayer graphene in the Bernal stacking supports a variety of uniform broken-symmetry ground states in Landau level N=0 at integer filling factors $\nu \in [-3,4].$ When an electric potential difference (or bias) is applied between the layers at filling factors $\nu =-1,3$, the ground state evolves from an interlayer coherent state at small bias to a state with orbital coherence at higher bias where \textit{electric} dipoles associated with the orbital pseudospins order spontaneously in the plane of the layers. In this paper, we show that by further increasing the bias at these two filling factors, the two-dimensional electron gas goes first through a Skyrmion crystal state and then into an helical state where the pseudospins rotate in space. The pseudospin textures in both the Skyrmion and helical states are due to the presence of a Dzyaloshinskii-Moriya interaction in the effective pseudospin Hamiltonian when orbital coherence is present in the ground state. We study in detail the electronic structure of the helical and Skyrmion crystal states as well as their collective excitations and then compute their electromagnetic absorption., Comment: 17 pages, 17 postscript figures

A graphene bilayer in a transverse magnetic field has a set of Landau levels with energies $E=\pm \sqrt{N(N+1)}\hslash \omega_{c}^{\ast}$ where $\omega_{c}^{\ast}$ is the effective cyclotron frequency and $% N=0,1,2,...$ All Landau levels but N=0 are four times degenerate counting spin and valley degrees of freedom. The Landau level N=0 has an extra degeneracy due to the fact that orbitals $n=0$ and $n=1$ both have zero kinetic energies. At integer filling factors, Coulomb interactions produce a set of broken-symmetry states with partial or full alignement in space of the valley and orbital pseudospins. These quantum Hall pseudo-ferromagnetic states support topological charged excitations in the form of orbital and valley Skyrmions. Away from integer fillings, these topological excitations can condense to form a rich variety of Skyrme crystals with interesting properties. We study in this paper different crystal phases that occur when an electric field is applied between the layers. We show that orbital Skyrmions, in analogy with spin Skyrmions, have a texture of electrical dipoles that can be controlled by an in-plane electric field. Moreover, the modulation of electronic density in the crystalline phases are experimentally accessible through a measurement of their local density of states, Comment: 18 pages with 13 figures

We report calculations of Born-Oppenheimer potential energy curves of the chromium-rubidium heteronuclear molecule 52Cr-87Rb, and the long-range dispersion coefficient for the interaction between ground state Cr and Rb atoms. Our calculated van der Waals coefficient (C6=1770 a.u.) has an expected error of 3%. The ground state 6Sigma+ molecule at its equilibrium separation has a permanent electric dipole moment of de (Re=3.34 A) = 2.90 D. We investigate the hyperfine and dipolar collisions between trapped Cr and Rb atoms, finding elastic to inelastic cross section ratio of 100-1000.

In a graphene bilayer with Bernal stacking both $n=0$ and $n=1$ orbital Landau levels have zero kinetic energy. An electronic state in the N=0 Landau level consequently has three quantum numbers in addition to its guiding center label: its spin, its valley index $K$ or $K^{\prime}$, and an orbital quantum number $n=0,1.$ The two-dimensional electron gas (2DEG) in the bilayer supports a wide variety of broken-symmetry states in which the pseudospins associated these three quantum numbers order in a manner that is dependent on both filling factor $\nu $ and the electric potential difference between the layers. In this paper, we study the case of $\nu =-1$ in an external field strong enough to freeze electronic spins. We show that an electric potential difference between layers drives a series of transitions, starting from interlayer-coherent states (ICS) at small potentials and leading to orbitally coherent states (OCS) that are polarized in a single layer. Orbital pseudospins carry electric dipoles with orientations that are ordered in the OCS and have Dzyaloshinskii-Moriya interactions that can lead to spiral instabilities. We show that the microwave absorption spectra of ICSs, OCSs, and the mixed states that occur at intermediate potentials are sharply distinct., Comment: 21 pages, 14 figures

We analyse the formation of ultracold 7Li133Cs molecules in the rovibrational ground state through photoassociation into the B1Pi state, which has recently been reported [J. Deiglmayr et al., Phys. Rev. Lett. 101, 133004 (2008)]. Absolute rate constants for photoassociation at large detunings from the atomic asymptote are determined and are found to be surprisingly large. The photoassociation process is modeled using a full coupled-channel calculation for the continuum state, taking all relevant hyperfine states into account. The enhancement of the photoassociation rate is found to be caused by an `echo' of the triplet component in the singlet component of the scattering wave function at the inner turning point of the lowest triplet a3Sigma+ potential. This perturbation can be ascribed to the existence of a broad Feshbach resonance at low scattering energies. Our results elucidate the important role of couplings in the scattering wave function for the formation of deeply bound ground state molecules via photoassociation., Comment: Added Erratum, 20 pages, 9 figures

We report the observation of dipole-forbidden, but quadrupole-allowed, one-photon transitions to high Rydberg states in Rb. Using pulsed UV excitation of ultracold atoms in a magneto-optical trap, we excite $5s \to nd$ transitions over a range of principal quantum numbers $n=27-59$. Compared to dipole-allowed (E1) transitions from $5s \to np$, these E2 transitions are weaker by a factor of approximately 2000. We also report measurements of the anomalous $np_{3/2} : np_{1/2}$ fine-structure transition strength ratio for $n=28-75$. Both results are in agreement with theoretical predictions., Comment: 7 pages, 5 figures, 1 table

We present results from two-photon photoassociative spectroscopy of the least-bound vibrational level of the X$^1\Sigma_g^+$ state of the $^{88}$Sr$_2$ dimer. Measurement of the binding energy allows us to determine the s-wave scattering length, $a_{88}=-1.4(6) a_0$. For the intermediate state, we use a bound level on the metastable $^1S_0$-$^3P_1$ potential, which provides large Franck-Condon transition factors and narrow one-photon photoassociative lines that are advantageous for observing quantum-optical effects such as Autler-Townes resonance splittings., Comment: 9 pages, 9 figures

At low-energy, the band structure of graphene can be approximated by two degenerate valleys $(K,K^{\prime})$ about which the electronic spectra of the valence and conduction bands have linear dispersion relations. An electronic state in this band spectrum is a linear superposition of states from the $A$ and $B$ sublattices of the honeycomb lattice of graphene. In a quantizing magnetic field, the band spectrum is split into Landau levels with level N=0 having zero weight on the $B(A)$ sublattice for the $% K(K^{\prime})$ valley. Treating the valley index as a pseudospin and assuming the real spins to be fully polarized, we compute the energy of Wigner and Skyrme crystals in the Hartree-Fock approximation. We show that Skyrme crystals have lower energy than Wigner crystals \textit{i.e.} crystals with no pseudospin texture in some range of filling factor $\nu $ around integer fillings. The collective mode spectrum of the valley-skyrmion crystal has three linearly-dispersing Goldstone modes in addition to the usual phonon mode while a Wigner crystal has only one extra Goldstone mode with a quadratic dispersion. We comment on how these modes should be affected by disorder and how, in principle, a microwave absorption experiment could distinguish between Wigner and Skyrme crystals., Comment: 14 pages with 11 figures

Interaction driven integer quantum Hall effects are anticipated in graphene bilayers because of the near-degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate $k^{3/2}$ dispersion. We speculate on the possibility of unususal localization physics associated with these modes., Comment: 5 pages, 2 figures

We investigate the excitation dynamics of Rydberg atoms in ultracold atomic samples by expanding the excitation probability and the correlation function between excited atoms in powers of the isolated atom Rabi frequency $\Omega$. In the Heisenberg picture, we give recurrence relations to calculate any order of the expansions, which ere expected to be well-behaved for arbitrarily strong interactions. For homogeneous large samples, we give the explicit form of the expansions, up to $\Omega^4$, averaged over all possible random spatial distributions of atoms, for the most important cases of excitation pulses and interactions., Comment: 9 pages, 3 figures, 1 table

We have calculated long-range molecular potentials of the $0_g^{+}$, $0_u^{-}$ and $1_u$ symmetries between highly-excited rubidium atoms. Strong $np+np$ potentials characterized by these symmetries are important in describing interaction-induced phenomena in the excitation spectra of high $np$ Rydberg states. Long-range molecular resonances are such phenomena and they were first reported in S.M. Farooqi {\it et al.}, Phys. Rev. Lett. {\bf 91} 183002. One class of these resonances occurs at energies corresponding to excited atom pairs $(n-1)d+ns$. Such resonances are attributed to $\ell$-mixing due to Rydberg-Rydberg interactions so that otherwise forbidden molecular transitions become allowed. We calculate molecular potentials in Hund's case (c), use them to find the resonance lineshape and compare to experimental results., Comment: 11 pages, 7 figures

We investigate the collective aspects of Rydberg excitation in ultracold mesoscopic systems. Strong interactions between Rydberg atoms influence the excitation process and impose correlations between excited atoms. The manifestations of the collective behavior of Rydberg excitation are the many-body Rabi oscillations, spatial correlations between atoms as well as the fluctuations of the number of excited atoms. We study these phenomena in detail by numerically solving the many-body Schr\"edinger equation., Comment: 8 pages, 5 figures

The two-dimensional electron gas in a bilayer quantum Hall system can sustain an interlayer coherence at filling factor nu=1 even in the absence of tunneling between the layers. This system has low-energy charged excitations which may carry textures in real spin or pseudospin. Away from filling factor nu =1 a finite density of these is present in the ground state of the 2DEG and forms a crystal. Depending on the relative size of the various energy scales, such as tunneling (Delta_SAS), Zeeman coupling (Delta_Z) or electrical bias (Delta_b), these textured crystal states can involve spin, pseudospin, or both intertwined. In this article, we present a comprehensive numerical study of the collective excitations of these textured crystals using the GRPA. For the pure spin case, at finite Zeeman coupling the state is a Skyrmion crystal with a gapless phonon mode, and a separate Goldstone mode that arises from a broken U(1) symmetry. At zero Zeeman coupling, we demonstrate that the constituent Skyrmions break up, and the resulting state is a meron crystal with 4 gapless modes. In contrast, a pure pseudospin Skyrme crystal at finite tunneling has only the phonon mode. For Delta_SAS=0, the state evolves into a meron crystal and supports an extra gapless U(1) mode in addition to the phonon. For a CP(3) Skyrmion crystal, we find a U(1) gapless mode in the presence of the symmetry-breaking fields. In addition, a second mode with a very small gap is present in the spectrum., Comment: 16 pages and 12 eps figures

In a quantizing magnetic field, the two-dimensional electron (2DEG) gas has a rich phase diagram with broken translational symmetry phases such as Wigner, bubble, and stripe crystals. In this paper, we derive a method to get the dynamical matrix of these crystals from a calculation of the density response function performed in the Generalized Random Phase Approximation (GRPA). We discuss the validity of our method by comparing the dynamical matrix calculated from the GRPA with that obtained from standard elasticity theory with the elastic coefficients obtained from a calculation of the deformation energy of the crystal., Comment: Revised version published in Phys. Rev. B. 12 pages with 11 postscripts figures

We study fluctuations and topological melting transitions of quantum Hall stripes near half-filling of intermediate Landau levels. Taking the stripe state to be an anisotropic Wigner crystal (AWC) allows us to identify the quantum Hall nematic state conjectured in previous studies of the 2D electron gas as an {\em anisotropic hexatic}. The transition temperature from the AWC to the quantum Hall nematic state is explicitly calculated, and a tentative phase diagram for the 2D electron gas near half-filling is suggested., Comment: 5 pages, 4 figures; version published in the Rapid Communications section of Phys. Rev. B

Recent experiments on strongly correlated bilayer quantum Hall systems strongly suggest that, contrary to the usual assumption, the electron spin degree of freedom is not completely frozen either in the quantum Hall or in the compressibles states that occur at filling factor $\nu =1.$ These experiments imply that the quasiparticles at $\nu =1$ could have both spin and pseudospin textures i.e. they could be CP$^{3}$ skyrmions. Using a microscopic unrestricted Hartree-Fock approximation, we compute the energy of several crystal states with spin, pseudospin and mixed spin-pseudospin textures around $\nu =1$ as a function of interlayer separation $d$ for different values of tunneling ($\Delta_{SAS}$), Zeeman ($\Delta_{Z}$), and bias ($\Delta_{b}$) energies. We show that in some range of these parameters, crystal states involving a certain amount of spin depolarization have lower energy than the fully spin polarized crystals. We study this depolarization dependence on $d,\Delta_{SAS},\Delta_{Z}$ and $\Delta_{b}$ and discuss how it can lead to the fast NMR relaxation rate observed experimentally., Comment: 19 pages including 10 eps figures

We propose to use a new platform - ultracold polar molecules - for quantum computing with switchable interactions. The on/off switch is accomplished by selective excitation of one of the "0" or "1" qubits - long-lived molecular states - to an "excited" molecular state with a considerably different dipole moment. We describe various schemes based on this switching of dipolar interactions where the selective excitation between ground and excited states is accomplished via optical, micro-wave, or electric fields. We also generalize the schemes to take advantage of the dipole blockade mechanism when dipolar interactions are very strong. These schemes can be realized in several recently proposed architectures., Comment: 4 pages, 4 figures

Experiments in dense, ultracold gases of rubidium Rydberg atoms show a considerable decrease of the radiative excited state lifetimes compared to dilute gases. This accelerated decay is explained by collective and cooperative effects, leading to superradiance. A novel formalism to calculate effective decay times in a dense Rydberg gas shows that for these atoms the decay into nearby levels increases by up to three orders of magnitude. Excellent agreement between theory and experiment follows from this treatment of Rydberg decay behavior., Comment: 4 pages, 4 figures

We report the use of photoassociative spectroscopy to determine the ground state s-wave scattering lengths for the main bosonic isotopes of strontium, 86Sr and 88Sr. Photoassociative transitions are driven with a laser red-detuned by up to 1400 GHz from the 1S0-1P1 atomic resonance at 461 nm. A minimum in the transition amplitude for 86Sr at -494+/-5 GHz allows us to determine the scattering lengths 610a0 < a86 < 2300a0 for 86Sr and a much smaller value of -1a0 < a88 < 13a0 for 88Sr., Comment: 4 pages, 3 figures, submitted to Physical Review Letters

In some range of interlayer distances, the ground state of the two-dimensional electron gas at filling factor nu =4N+1 with N=0,1,2,... is a coherent stripe phase in the Hartree-Fock approximation. This phase has one-dimensional coherent channels that support charged excitations in the form of pseudospin solitons. In this work, we compute the transport gap of the coherent striped phase due to the creation of soliton-antisoliton pairs using a supercell microscopic unrestricted Hartree-Fock approach. We study this gap as a function of interlayer distance and tunneling amplitude. Our calculations confirm that the soliton-antisoliton excitation energy is lower than the corresponding Hartree-Fock electron-hole pair energy. We compare our results with estimates of the transport gap obtained from a field-theoretic model valid in the limit of slowly varying pseudospin textures., Comment: 15 pages, 8 figures

We study the collective states formed by two-dimensional electrons in Landau levels of index $n\ge 2$ near half-filling. By numerically solving the self-consistent Hartree-Fock (HF) equations for a set of oblique two-dimensional lattices, we find that the stripe state is an anisotropic Wigner crystal (AWC), and determine its precise structure for varying values of the filling factor. Calculating the elastic energy, we find that the shear modulus of the AWC is small but finite (nonzero) within the HF approximation. This implies, in particular, that the long-wavelength magnetophonon mode in the stripe state vanishes like $q^{3/2}$ as in an ordinary Wigner crystal, and not like $q^{5/2}$ as was found in previous studies where the energy of shear deformations was neglected., Comment: minor corrections; 5 pages, 4 figures; version to be published in Physical Review Letters

In higher Landau levels ($N>1$), the ground state of the two-dimensional electron gas in a strong perpendicular magnetic field evolves from a Wigner crystal for small filling $\nu $ of the partially filled Landau level, into a succession of bubble states with increasing number of guiding centers per bubble as $\nu $ increases, to a modulated stripe state near $\nu =0.5$. In this work, we compute the frequency-dependent longitudinal conductivity $% \sigma_{xx}(\omega) $ of the Wigner and bubble crystal states in the presence of disorder. We apply an elastic theory to the crystal states which is characterized by a shear and a bulk modulus. We obtain both moduli from the microscopic time-dependent Hartree-Fock approximation. We then use the replica and Gaussian variational methods to handle the effects of disorder. Within the semiclassical approximation we get the dynamical conductivity as well as the pinning frequency as functions of the Landau level filling factor and compare our results with recent microwave experiments., Comment: 19 pages and 6 eps figures