138 research outputs found
Decay of superfluid currents in a moving system of strongly interacting bosons
We analyze the stability and decay of supercurrents of strongly interacting bosons on optical lattices. At the mean-field level, the system undergoes an irreversible dynamic phase transition, whereby the current decays beyond a critical phase gradient that depends on the interaction strength. At commensurate filling the transition line smoothly interpolates between the classical modulational instability of weakly interacting bosons and the equilibrium Mott transition at zero current. Below the mean-field instability, the current can decay due to quantum and thermal phase slips. We derive asymptotic expressions of the decay rate near the critical current. In a three-dimensional optical lattice this leads to very weak broadening of the transition. In one and two dimensions the broadening leads to significant current decay well below the mean-field critical current. We show that the temperature scale below which quantum phase slips dominate the decay of supercurrents is easily within experimental reach.Accepted manuscrip
Decay of super-currents in condensates in optical lattices
In this paper we discuss decay of superfluid currents in boson lattice
systems due to quantum tunneling and thermal activation mechanisms. We derive
asymptotic expressions for the decay rate near the critical current in two
regimes, deep in the superfluid phase and close to the superfluid-Mott
insulator transition. The broadening of the transition at the critical current
due to these decay mechanisms is more pronounced at lower dimensions. We also
find that the crossover temperature below which quantum decay dominates is
experimentally accessible in most cases. Finally, we discuss the dynamics of
the current decay and point out the difference between low and high currents.Comment: Contribution to the special issue of Journal of Superconductivity in
honor of Michael Tinkham's 75th birthda
Superfluid-insulator transition in a moving system of interacting bosons
We analyze stability of superfluid currents in a system of strongly
interacting ultra-cold atoms in an optical lattice. We show that such a system
undergoes a dynamic, irreversible phase transition at a critical phase gradient
that depends on the interaction strength between atoms. At commensurate
filling, the phase boundary continuously interpolates between the classical
modulation instability of a weakly interacting condensate and the equilibrium
quantum phase transition into a Mott insulator state at which the critical
current vanishes. We argue that quantum fluctuations smear the transition
boundary in low dimensional systems. Finally we discuss the implications to
realistic experiments.Comment: updated refernces and introduction, minor correction
Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation
The applicability of the so-called truncated Wigner approximation (-W) is
extended to multitime averages of Heisenberg field operators. This task splits
naturally in two. Firstly, what class of multitime averages the -W
approximates, and, secondly, how to proceed if the average in question does not
belong to this class. To answer the first question we develop an (in principle,
exact) path-integral approach in phase-space based on the symmetric (Weyl)
ordering of creation and annihilation operators. These techniques calculate a
new class of averages which we call time-symmetric. The -W equations emerge as
an approximation within this path-integral techniques. We then show that the
answer to the second question is associated with response properties of the
system. In fact, for two-time averages Kubo's renowned formula relating the
linear response function to two-time commutators suffices. The -W is trivially
generalised to the response properties of the system allowing one to calculate
approximate time-normally ordered two-time correlation functions with
surprising ease. The techniques we develop are demonstrated for the
Bose-Hubbard model.Comment: 20 pages, 6 figure
Adiabatic perturbation theory: from Landau-Zener problem to quenching through a quantum critical point
We discuss the application of the adiabatic perturbation theory to analyze
the dynamics in various systems in the limit of slow parametric changes of the
Hamiltonian. We first consider a two-level system and give an elementary
derivation of the asymptotics of the transition probability when the tuning
parameter slowly changes in the finite range. Then we apply this perturbation
theory to many-particle systems with low energy spectrum characterized by
quasiparticle excitations. Within this approach we derive the scaling of
various quantities such as the density of generated defects, entropy and
energy. We discuss the applications of this approach to a specific situation
where the system crosses a quantum critical point. We also show the connection
between adiabatic and sudden quenches near a quantum phase transitions and
discuss the effects of quasiparticle statistics on slow and sudden quenches at
finite temperatures.Comment: 20 pages, 3 figures, contribution to "Quantum Quenching, Annealing
and Computation", Eds. A. Das, A. Chandra and B. K. Chakrabarti, Lect. Notes
in Phys., Springer, Heidelberg (2009, to be published), reference correcte
Near-adiabatic parameter changes in correlated systems: Influence of the ramp protocol on the excitation energy
We study the excitation energy for slow changes of the hopping parameter in
the Falicov-Kimball model with nonequilibrium dynamical mean-field theory. The
excitation energy vanishes algebraically for long ramp times with an exponent
that depends on whether the ramp takes place within the metallic phase, within
the insulating phase, or across the Mott transition line. For ramps within
metallic or insulating phase the exponents are in agreement with a perturbative
analysis for small ramps. The perturbative expression quite generally shows
that the exponent depends explicitly on the spectrum of the system in the
initial state and on the smoothness of the ramp protocol. This explains the
qualitatively different behavior of gapless (e.g., metallic) and gapped (e.g.,
Mott insulating) systems. For gapped systems the asymptotic behavior of the
excitation energy depends only on the ramp protocol and its decay becomes
faster for smoother ramps. For gapless systems and sufficiently smooth ramps
the asymptotics are ramp-independent and depend only on the intrinsic spectrum
of the system. However, the intrinsic behavior is unobservable if the ramp is
not smooth enough. This is relevant for ramps to small interaction in the
fermionic Hubbard model, where the intrinsic cubic fall-off of the excitation
energy cannot be observed for a linear ramp due to its kinks at the beginning
and the end.Comment: 24 pages, 6 figure
Robustness of adiabatic passage trough a quantum phase transition
We analyze the crossing of a quantum critical point based on exact results
for the transverse XY model. In dependence of the change rate of the driving
field, the evolution of the ground state is studied while the transverse
magnetic field is tuned through the critical point with a linear ramping. The
excitation probability is obtained exactly and is compared to previous studies
and to the Landau-Zener formula, a long time solution for non-adiabatic
transitions in two-level systems. The exact time dependence of the excitations
density in the system allows to identify the adiabatic and diabatic regions
during the sweep and to study the mesoscopic fluctuations of the excitations.
The effect of white noise is investigated, where the critical point transmutes
into a non-hermitian ``degenerate region''. Besides an overall increase of the
excitations during and at the end of the sweep, the most destructive effect of
the noise is the decay of the state purity that is enhanced by the passage
through the degenerate region.Comment: 16 pages, 15 figure
Effects of random localizing events on matter waves: formalism and examples
A formalism is introduced to describe a number of physical processes that may
break down the coherence of a matter wave over a characteristic length scale l.
In a second-quantized description, an appropriate master equation for a set of
bosonic "modes" (such as atoms in a lattice, in a tight-binding approximation)
is derived. Two kinds of "localizing processes" are discussed in some detail
and shown to lead to master equations of this general form: spontaneous
emission (more precisely, light scattering), and modulation by external random
potentials. Some of the dynamical consequences of these processes are
considered: in particular, it is shown that they generically lead to a damping
of the motion of the matter-wave currents, and may also cause a "flattening" of
the density distribution of a trapped condensate at rest.Comment: v3; a few corrections, especially in Sections IV and
System size scaling of topological defect creation in a second-order dynamical quantum phase transition
We investigate the system size scaling of the net defect number created by a
rapid quench in a second-order quantum phase transition from an O(N) symmetric
state to a phase of broken symmetry. Using a controlled mean-field expansion
for large N, we find that the net defect number variance in convex volumina
scales like the surface area of the sample for short-range correlations. This
behaviour follows generally from spatial and internal symmetries. Conversely,
if spatial isotropy is broken, e.g., by a lattice, and in addition long-range
periodic correlations develop in the broken-symmetry phase, we get the rather
counterintuitive result that the scaling strongly depends on the dimension
being even or odd: For even dimensions, the net defect number variance scales
like the surface area squared, with a prefactor oscillating with the system
size, while for odd dimensions, it essentially vanishes.Comment: 20 pages of IOP style, 6 figures; as published in New Journal of
Physic
Many-body Landau-Zener dynamics in coupled 1D Bose liquids
The Landau-Zener model of a quantum mechanical two-level system driven with a
linearly time dependent detuning has served over decades as a textbook paradigm
of quantum dynamics. In their seminal work [L. D. Landau, Physik. Z. Sowjet. 2,
46 (1932); C. Zener, Proc. Royal Soc. London 137, 696 (1932)], Landau and Zener
derived a non-perturbative prediction for the transition probability between
two states, which often serves as a reference point for the analysis of more
complex systems. A particularly intriguing question is whether that framework
can be extended to describe many-body quantum dynamics. Here we report an
experimental and theoretical study of a system of ultracold atoms, offering a
direct many-body generalization of the Landau-Zener problem. In a system of
pairwise tunnel-coupled 1D Bose liquids we show how tuning the correlations of
the 1D gases, the tunnel coupling between the tubes and the inter-tube
interactions strongly modify the original Landau-Zener picture. The results are
explained using a mean-field description of the inter-tube condensate
wave-function, coupled to the low-energy phonons of the 1D Bose liquid.Comment: 13 pages, 10 figures
- …