Why are vortex lattices so regular even though the condensate density varies greatly across the gaseous BEC? How does the density envelope effect the collective excitations of the vortex lattice? We compare the perspectives of experiment,... more
Why are vortex lattices so regular even though the condensate density varies greatly across the gaseous BEC? How does the density envelope effect the collective excitations of the vortex lattice? We compare the perspectives of experiment, multi-scale hydrodynamics and the local density approximation on these questions.
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Adiabatic approximations break down classically when a constant-energy contour splits into separate contours, forcing the system to choose which daughter contour to follow; the choices often represent qualitatively different behavior, so... more
Adiabatic approximations break down classically when a constant-energy contour splits into separate contours, forcing the system to choose which daughter contour to follow; the choices often represent qualitatively different behavior, so that slowly changing conditions induce a sudden and drastic change in dynamics. The Kruskal–Neishtadt–Henrard (KNH) theorem relates the probability of each choice to the rates at which the phase space areas enclosed by the different contours are changing. This represents a connection within closed-system mechanics, and without dynamical chaos, between spontaneous change and increase in phase space measure, as required by the Second Law of Thermodynamics. Quantum mechanically, in contrast, dynamical tunneling allows adiabaticity to persist, for very slow parameter change, through a classical splitting of energy contours; the classical and adiabatic limits fail to commute. Here we show that a quantum form of the KNH theorem holds nonetheless, due to u...
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We present a master equation governing the reduced density operator for a single trapped mode of a cold, dilute, weakly interacting Bose gas; and we obtain an operator fluctuationdissipation relation in which the Ginzburg-Landau effective... more
We present a master equation governing the reduced density operator for a single trapped mode of a cold, dilute, weakly interacting Bose gas; and we obtain an operator fluctuationdissipation relation in which the Ginzburg-Landau effective potential plays a physically transparent role. We also identify a decoherence effect that tends to preserve symmetry, even when the effective potential has a “Mexican hat” form.
1 Experiments on periodically driven quantum systems have effectively realized 2 quasi-Hamiltonians, in the sense of Floquet theory, that are otherwise inaccessi3 ble in static condensed matter systems. Although the Floquet... more
1 Experiments on periodically driven quantum systems have effectively realized 2 quasi-Hamiltonians, in the sense of Floquet theory, that are otherwise inaccessi3 ble in static condensed matter systems. Although the Floquet quasi-Hamiltonians 4 are time-independent, however, these continuously driven systems can still suf5 fer from heating due to a secular growth in the expectation value of the time6 dependent physical Hamiltonian. Here we use an exact space-time mapping to 7 construct a class of many-body systems with rapid periodic driving which we 8 nonetheless prove to be completely free of heating, by mapping them exactly onto 9 time-independent systems. The absence of heating despite the periodic driving 10 occurs in these cases of harmonically trapped dilute Bose gas because the driving 11 is a certain periodic but anharmonic modulation of the gas’s two-body contact 12 interaction, at a particular frequency. Although we prove that the absence of 13 heating is exact within ful...
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We study the dynamics of a two-mode Bose-Einstein condensate in the vicinity of a mean-field dynamical instability. Convergence to mean-field theory (MFT) on increasing the total number of particles N, is shown to be logarithmically slow.... more
We study the dynamics of a two-mode Bose-Einstein condensate in the vicinity of a mean-field dynamical instability. Convergence to mean-field theory (MFT) on increasing the total number of particles N, is shown to be logarithmically slow. Using a density matrix formalism rather than the conventional wavefunction methods, we derive an improved set of equations of motion for the mean-field and the fluctuations, which goes beyond MFT and provides accurate predictions for the leading quantum corrections and the quantum break time. Considering the decoherence due to the coupling to a thermal bath, we show that the leading quantum corrections appear as decoherence of the reduced single-particle quantum state. References: (1) A. Vardi and J. R. Anglin, "Bose-Einstein condensates beyond mean-field theory: Quantum backreaction as decoherence", Phys. Rev. Lett. 86, 568 (2001). (2) J. R. Anglin and A. Vardi, "Dynamics of a two-mode Bose-Einstein condensate beyond mean-field theo...
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Workhorse theories throughout all of physics derive effective Hamiltonians to describe slow time evolution, even though low-frequency modes are actually coupled to high-frequency modes. Such effective Hamiltonians are accurate because of... more
Workhorse theories throughout all of physics derive effective Hamiltonians to describe slow time evolution, even though low-frequency modes are actually coupled to high-frequency modes. Such effective Hamiltonians are accurate because of adiabatic decoupling: the high-frequency modes "dress" the low-frequency modes, and renormalize their Hamiltonian, but they do not steadily inject energy into the low-frequency sector. Here, however, we identify a broad class of dynamical systems in which adiabatic decoupling fails to hold, and steady energy transfer across a large gap in natural frequency ("steady downconversion") instead becomes possible, through nonlinear resonances of a certain form. Instead of adiabatic decoupling, the special features of multiple time scale dynamics lead in these cases to efficiency constraints that somewhat resemble thermodynamics.
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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... more
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 441, 853 (2006)]. We here derive an effective Hamiltonian for a lattice loaded with dimers only and discuss its implications to 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.
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We derive and discuss the complete set of exact solutions to the one-dimensional Bogoliubov-de Gennes equations for small amplitude excitations around general grey soliton solutions to the cubic nonlinear Schr\"odinger equation. Our... more
We derive and discuss the complete set of exact solutions to the one-dimensional Bogoliubov-de Gennes equations for small amplitude excitations around general grey soliton solutions to the cubic nonlinear Schr\"odinger equation. Our results extend the previously known case of the motionless dark soliton background. We derive our non-zero frequency solutions using a variant of the factorization method for Schr\"odinger equations with reflectionless potentials. We also discuss the zero mode solutions at length.
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Stars form when cold cosmic nebulae spontaneously develop hot spots that steadily intensify until they reach fusion temperatures. Without this process, the universe would be dark and dead. Yet the spontaneous concentration of heat is... more
Stars form when cold cosmic nebulae spontaneously develop hot spots that steadily intensify until they reach fusion temperatures. Without this process, the universe would be dark and dead. Yet the spontaneous concentration of heat is exactly what the Second Law of Thermodynamics is in most cases supposed to forbid. The formation of protostars has been much discussed, for its consistency with the Second Law depends on a thermodynamical property that is common in systems whose strongest force is their own gravity, but otherwise very rare: negative specific heat. Negative specific heat turns the world upside down, thermodynamically; it implies that entropy increases when energy flows from lower to higher energy subsystems, opposite to the usual direction. Recent experiments have reported negative specific heat in melting atomic clusters and fragmenting nuclei, but these arguably represent transient phenomena outside the proper scope of thermodynamics. Here we show that the counter-intu...
Recently, Winkler et al. [Nature 441, 853 (2006)] have observed repulsively bound atom pairs in an optical lattice. In a tight-binding periodic potential described by the Bose-Hubbard model, when the on-site repulsion between the... more
Recently, Winkler et al. [Nature 441, 853 (2006)] have observed repulsively bound atom pairs in an optical lattice. In a tight-binding periodic potential described by the Bose-Hubbard model, when the on-site repulsion between the particles exceeds their inter-site tunneling rate, such ``dimers'' are well localized at single sites and are stable over the time scale on which the energy dissipation is negligible. We derive an effective many-body Hamiltonian for a lattice loaded with dimers only, and discuss its implications for the dynamics of the system. We show that strong on-site repulsion and nearest-neighbor attraction favor clusters of dimers with minimum surface area and uniform, commensurate filling, representing thus incompressible ``droplets'' of a lattice liquid.
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ABSTRACT Bose-Einstein condensates held in effectively one-dimensional traps can support localized ‘bubbles’ known as grey solitons. We show that, in an inhomoge-neous trapping potential, grey solitons move through the background... more
ABSTRACT Bose-Einstein condensates held in effectively one-dimensional traps can support localized ‘bubbles’ known as grey solitons. We show that, in an inhomoge-neous trapping potential, grey solitons move through the background condensate cloud as particles, interacting only weakly with other condensate excitations. As realistic proposals already exist for one-dimensional traps and for creating solitons in them, these objects offer an unprecedentedly controllable laboratory for studying the mesoscopic regime between closed-system quantum mechanics and classical dynamics.
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ABSTRACT We maintain that the reservations against the use of stimulated Raman adiabatic photoassociation in a nondegenerate gas, expressed by Mackie and Javanainen in a recent manuscript [Phys. Rev. A 60, 3174 (1999)], do not account for... more
ABSTRACT We maintain that the reservations against the use of stimulated Raman adiabatic photoassociation in a nondegenerate gas, expressed by Mackie and Javanainen in a recent manuscript [Phys. Rev. A 60, 3174 (1999)], do not account for the coherence induced by the photoassociating laser. The authors treat the problem of two-color stimulated photoassociation using a set of decoupled three-mode problems, each containing a box eigenstate and the two bound states. We argue that such decomposition is not justified, since in the limit of a very large box all three-mode problems are, in fact, coherently coupled. The three-mode condition can only be met with a set of wave packets whose bandwidth matches the spectral width of the photoassociating pulse. Using this basis set, we show that by the authors' own formalism; stimulated Raman photoassociation is a viable process in the thermal ensemble.