James R. Anglin

Quantum liquid of repulsively bound pairs of particles in a lattice

Repulsively interacting particles in a periodic potential can form bound composite objects, whose dissociation is suppressed by a band gap. Nearly pure samples of such repulsively bound pairs of cold atoms--dimers--have recently been prepared by Winkler et al. [Nature (London) 441, 853 (2006)]. We here derive an effective Hamiltonian for a lattice loaded with dimers only and discuss its implications for the many-body dynamics of the system. We find that the dimer-dimer interaction includes strong on-site repulsion and nearest-neighbor attraction which always dominates over the dimer kinetic energy at low temperatures. The dimers then form incompressible, minimal-surface droplets of a quantum lattice liquid. For low lattice filling, the effective Hamiltonian can be mapped onto the spin-1/2 XXZ model with fixed total magnetization which exhibits a first-order phase transition from the droplet to a gas phase. This opens the door to studying first-order phase transitions using highly controllable ultracold atoms.

Minimal Fokker-Planck theory for the thermalization of mesoscopic subsystems.

We explore a minimal paradigm for thermalization, consisting of two weakly coupled, low dimensional, nonintegrable subsystems. As demonstrated for Bose-Hubbard trimers, chaotic ergodicity results in a diffusive response of each subsystem, insensitive to the details of the drive exerted on it by the other. This supports the hypothesis that thermalization can be described by a Fokker-Planck equation. We also observe, however, that Levy-flight type anomalies may arise in mesoscopic systems, due to the wide range of time scales that characterize sticky dynamics.

Vortex mass in a superfluid at low frequencies.

An inertial mass of a vortex can be calculated by driving it around in a circle with a steadily revolving pinning potential. We show that in the low-frequency limit this gives precisely the same formula that was used by Baym and Chandler, but find that the result is not unique and depends on the force field used to cause the acceleration. We apply this method to the Gross-Pitaevskii model, and derive a simple formula for the vortex mass. We study both the long-range and short-range properties of the solution. We agree with earlier results that the nonzero compressibility leads to a divergent mass. From the short-range behavior of the solution we find that the mass is sensitive to the form of the pinning potential, and diverges logarithmically when the radius of this potential tends to zero.

Finite-temperature coherence of the ideal Bose gas in an optical lattice

In current experiments with cold quantum gases in periodic potentials, interference fringe contrast is typically the easiest signal in which to look for effects of nontrivial many-body dynamics. In order better to calibrate such measurements, we analyze the background effect of thermal decoherence as it occurs in the absence of dynamical interparticle interactions. We study the effect of optical lattice potentials, as experimentally applied, on the condensed fraction of a noninteracting Bose gas in local thermal equilibrium at finite temperatures. We show that the experimentally observed decrease of the condensate fraction in the presence of the lattice can be attributed, up to a threshold lattice height, purely to ideal-gas thermodynamics; conversely, we confirm that sharper decreases in first-order coherence observed in stronger lattices are indeed attributable to many-body physics. Our results also suggest that the fringe visibility ``kinks observed in Gerbier et al., Phys. Rev. Lett. 95, 050404 (2005) may be explained in terms of the competition between increasing lattice strength and increasing mean gas density, as the Gaussian profile of the red-detuned lattice lasers also increases the effective strength of the harmonic trap.

Quantum optics: Particles of light

Bose–Einstein condensation, which demonstrates the wave nature of material particles, now offers further illumination of wave–particle duality: it has been observed in light itself. See Letter p.545n Bose–Einstein condensation has been observed in several physical systems, but is not predicted to occur for blackbody radiation such as photons. However, it becomes theoretically possible in the presence of thermalization processes that conserve photon number. Martin Weitz and colleagues have now realized such conditions experimentally, observing Bose–Einstein condensation of photons in a dye-filled optical microcavity. The effect is of interest for fundamental studies and may lead to new coherent ultraviolet sources.

Four-mode Bose-Hubbard model with two greatly differing tunneling rates as a model for the Josephson oscillation of heat

As a model for mesoscopic quantum systems in thermal contact, we consider a four-mode BoseHubbard model with two greatly differing tunneling rates. By a series of Holstein-Primakoff transformations we show that the low-frequency dynamics of this system consists in general of two slow Josephson oscillations, rather than the single slow mode predicted by linear Bogoliubov theory. We identify the second slow Josephson oscillation as a heat exchange mode analogous to second sound.

Quantum fluctuations in the time-dependent BCS-BEC crossover

We describe the time-dependent formation of a molecular Bose–Einstein condensate from a BCS state of fermionic atoms as a result of slow sweeping through a Feshbach resonance. We apply a path integral approach for the molecules, and use two-body adiabatic approximations to solve the atomic evolution in the presence of the classical molecular fields, obtaining an effective action for the molecules. In the narrow resonance limit, the problem becomes semiclassical, and we discuss the growth of the molecular condensate in the saddle point approximation. Considering this time-dependent process as an analogue of the cosmological Zurek scenario, we compare the way condensate growth is driven in this rigorous theory with its phenomenological description via time-dependent Ginzburg–Landau theory.

Theoretical physics: Why trapped atoms are attractive

Bose-Einstein condensates - ultracold atoms that share the same quantum state - were first created in 1995. Since then, techniques have improved to the extent that theorists now dream of using condensates to model physical systems such as black holes and galaxy clusters.

Length scales involved in decoherence of trapped bosons by buffer-gas scattering

We ask and answer a basic question about the length scales involved in quantum decoherence: how far apart in space do two parts of a quantum system have to be, before a common quantum environment decoheres them as if they were entirely separate? We frame this question specifically in a cold atom context. How far apart do two populations of bosons have to be, before an environment of thermal atoms of a different species (‘buffer gas’) responds to their two particle numbers separately? An initial guess for this length scale is the thermal coherence length of the buffer gas; we show that a standard Born-Markov treatment partially supports this guess, but predicts only inverse-square saturation of decoherence rates with distance, and not the much more abrupt Gaussian behavior of the buffer gas’s first-order coherence. We confirm this Born-Markov result with a more rigorous theory, based on an exact solution of a two-scatterer scattering problem, which also extends the result beyond weak scattering. Finally, however, we show that when interactions within the buffer gas reservoir are taken into account, an abrupt saturation of the decoherence rate does occur, exponentially on the length scale of the buffer gas’s mean free path.

Postadiabatic Hamiltonian for low-energy excitations in a slowly-time-dependent BCS-BEC crossover

We develop a Hamiltonian that describes the time-dependent formation of a molecular Bose-Einstein condensate (BEC) from a Bardeen-Cooper-Schrieffer (BCS) state of fermionic atoms as a result of slowly sweeping through a Feshbach resonance. In contrast to many other calculations in the field (see e.g. [1-4]), our Hamiltonian includes the leading post-adiabatic effects that arise because the crossover proceeds at a non-zero sweep rate. We apply a path integral approach and a stationary phase approximation for the molecular zero momentum background, which is a good approximation for narrow resonances (see e.g. [5, 6]). We use two-body adiabatic approximations to solve the atomic evolution within this background. The dynamics of the non-zero momentum molecular modes is solved within a dilute gas approximation and by mapping it onto a purely bosonic Hamiltonian. Our main result is a post-adiabatic effective Hamiltonian in terms of the instantaneous bosonic (Anderson-)Bogoliubov modes, which holds throughout the whole resonance, as long as the Feshbach sweep is slow enough to avoid breaking Cooper pairs.