743 research outputs found
Loop structure of the lowest Bloch band for a Bose-Einstein condensate
We investigate analytically and numerically Bloch waves for a Bose--Einstein
condensate in a sinusoidal external potential. At low densities the dependence
of the energy on the quasimomentum is similar to that for a single particle,
but at densities greater than a critical one the lowest band becomes
triple-valued near the boundary of the first Brillouin zone and develops the
structure characteristic of the swallow-tail catastrophe. We comment on the
experimental consequences of this behavior.Comment: 4 pages, 7 figure
Scaling property of the critical hopping parameters for the Bose-Hubbard model
Recently precise results for the boundary between the Mott insulator phase
and the superfluid phase of the homogeneous Bose-Hubbard model have become
available for arbitrary integer filling factor g and any lattice dimension d >
1. We use these data for demonstrating that the critical hopping parameters
obey a scaling relationship which allows one to map results for different g
onto each other. Unexpectedly, the mean-field result captures the dependence of
the exact critical parameters on the filling factor almost fully. We also
present an approximation formula which describes the critical parameters for d
> 1 and any g with high accuracy.Comment: 5 pages, 5 figures. to appear in EPJ
Quantum phase transition of condensed bosons in optical lattices
In this paper we study the superfluid-Mott-insulator phase transition of
ultracold dilute gas of bosonic atoms in an optical lattice by means of Green
function method and Bogliubov transformation as well. The superfluid-
Mott-insulator phase transition condition is determined by the energy-band
structure with an obvious interpretation of the transition mechanism. Moreover
the superfluid phase is explained explicitly from the energy spectrum derived
in terms of Bogliubov approach.Comment: 13 pages, 1 figure
Theoretical analysis of quantum dynamics in 1D lattices: Wannier-Stark description
This papers presents a formalism describing the dynamics of a quantum
particle in a one-dimensional tilted time-dependent lattice. The description
uses the Wannier-Stark states, which are localized in each site of the lattice
and provides a simple framework leading to fully-analytical developments.
Particular attention is devoted to the case of a time-dependent potential,
which results in a rich variety of quantum coherent dynamics is found.Comment: 8 pages, 6 figures, submitted to PR
Nuclear target search at the single molecule level: protein interactions define the exploration landscape
Gene regulation relies on highly mobile transcription factors (TFs) exploring the nucleoplasm in search of their targets. Our view of the nucleus has evolved from that of an isotropic and homogenous reactor to that of a highly organized yet very dynamic organelle. However important questions remain on how these regulatory factors explore the nuclear environment in search of their DNA or protein targets, and how their exploration strategy affects the kinetics of transcriptional regulation.
We implemented a single-molecule tracking assay to determine the TFs dynamics using photoactivatable tags in human cells. We investigated the mobility of several nuclear proteins, including the transcription factor c-Myc and the elongation factor P-TEFb. We found that, while their diffusion speed was comparable, these proteins largely differed in terms of their exploration geometry. We discovered that c-Myc is a global explorer diffusing in the nucleus without spatial constraints. In contrast, the positive transcription elongation factor P-TEFb is a local explorer that oversamples its environment, constrained by a fractal nuclear architecture. Consequently, each c-Myc molecule is equally available for all nuclear sites while P-TEFb reaches its targets in a position-dependent manner. We also measured the mobility of a P-TEFb mutant in which the interaction with the CTD of the RNA Pol II was truncated. In this case, the single-molecule experiments suggested a global exploration of the P-TEFb mutant, consistent with free diffusion.
Our observations are in line with a model in which the exploration geometry of TFs is constrained by their interactions and not by exclusion properties. Our findings have strong implications on how proteins react in the nucleus and how their function can be regulated in space and time
Bloch oscillations and mean-field effects of Bose-Einstein condensates in 1-D optical lattices
We have loaded Bose-Einstein condensates into one-dimensional, off-resonant
optical lattices and accelerated them by chirping the frequency difference
between the two lattice beams. For small values of the lattice well-depth,
Bloch oscillations were observed. Reducing the potential depth further,
Landau-Zener tunneling out of the lowest lattice band, leading to a breakdown
of the oscillations, was also studied and used as a probe for the effective
potential resulting from mean-field interactions as predicted by Choi and Niu
[Phys. Rev. Lett. {\bf 82}, 2022 (1999)]. The effective potential was measured
for various condensate densities and trap geometries, yielding good qualitative
agreement with theoretical calculations.Comment: 5 pages, 3 figures; accepted for publication in Physical Review
Letter
Wavepacket reconstruction via local dynamics in a parabolic lattice
We study the dynamics of a wavepacket in a potential formed by the sum of a
periodic lattice and of a parabolic potential. The dynamics of the wavepacket
is essentially a superposition of ``local Bloch oscillations'', whose frequency
is proportional to the local slope of the parabolic potential. We show that the
amplitude and the phase of the Fourier transform of a signal characterizing
this dynamics contains information about the amplitude and the phase of the
wavepacket at a given lattice site. Hence, {\em complete} reconstruction of the
the wavepacket in the real space can be performed from the study of the
dynamics of the system.Comment: 4 pages, 3 figures, RevTex
Superfluid and Dissipative Dynamics of a Bose-Einstein Condensate in a Periodic Optical Potential
We create Bose-Einstein condensates of 87-rubidium in a static magnetic trap
with a superimposed blue-detuned 1D optical lattice. By displacing the magnetic
trap center we are able to control the condensate evolution. We observe a
change in the frequency of the center-of-mass oscillation in the harmonic
trapping potential, in analogy with an increase in effective mass. For fluid
velocities greater than a local speed of sound, we observe the onset of
dissipative processes up to full removal of the superfluid component. A
parallel simulation study visualizes the dynamics of the BEC and accounts for
the main features of the observed behavior.Comment: 4 pages, including figure
Bloch-Like Quantum Multiple Reflections of Atoms
We show that under certain circumstances an atom can follow an oscillatory
motion in a periodic laser profile with a Gaussian envelope. These oscillations
can be well explained by using a model of energetically forbidden spatial
regions. The similarities and differences with Bloch oscillations are
discussed. We demonstrate that the effect exists not only for repulsive but
also for attractive potentials, i.e. quantum multiple reflections are also
possible.Comment: LaTeX, 7 pages, 7 figure
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