3,004 research outputs found
Uncertainty product of an out-of-equilibrium Bose-Einstein condensate
The variance and uncertainty product of the position and momentum
many-particle operators of structureless bosons interacting by a long-range
inter-particle interaction and trapped in a single-well potential are
investigated. In the first example, of an out-of-equilibrium interaction-quench
scenario, it is found that, despite the system being fully condensed, already
when a fraction of a particle is depleted differences with respect to the
mean-field quantities emerge. In the second example, of the pathway from
condensation to fragmentation of the ground state, we find out that, although
the cloud's density broadens while the system's fragments, the position
variance actually decreases, the momentum variance increases, and the
uncertainty product is not a monotonous function but has a maximum. Implication
are briefly discussed.Comment: 14 pages, 3 figure
The uncertainty product of an out-of-equilibrium many-particle system
In the present work we show, analytically and numerically, that the variance
of many-particle operators and their uncertainty product for an
out-of-equilibrium Bose-Einstein condensate (BEC) can deviate from the outcome
of the time-dependent Gross-Pitaevskii dynamics, even in the limit of infinite
number of particles and at constant interaction parameter when the system
becomes 100% condensed. We demonstrate our finding on the dynamics of the
center-of-mass position--momentum uncertainty product of a freely expanding as
well as of a trapped BEC. This time-dependent many-body phenomenon is explained
by the existence of time-dependent correlations which manifest themselves in
the system's reduced two-body density matrix used to evaluate the uncertainty
product. Our work demonstrates that one has to use a many-body propagation
theory to describe an out-of-equilibrium BEC, even in the infinite particle
limit.Comment: 26 pages, 5 figure
Zoo of quantum phases and excitations of cold bosonic atoms in optical lattices
Quantum phases and phase transitions of weakly- to strongly-interacting
bosonic atoms in deep to shallow optical lattices are described by a {\it
single multi-orbital mean-field approach in real space}. For weakly-interacting
bosons in 1D, the critical value of the superfluid to Mott insulator (MI)
transition found is in excellent agreement with {\it many-body} treatments of
the Bose-Hubbard model. For strongly-interacting bosons, (i) additional MI
phases appear, for which two (or more) atoms residing in {\it each site}
undergo a Tonks-Girardeau-like transition and localize and (ii) on-site
excitation becomes the excitation lowest in energy. Experimental implications
are discussed.Comment: 12 pages, 3 figure
Time-dependent multi-orbital mean-field for fragmented Bose-Einstein condensates
The evolution of Bose-Einstein condensates is usually described by the famous
time-dependent Gross-Pitaevskii equation, which assumes all bosons to reside in
a single time-dependent orbital. In the present work we address the evolution
of fragmented condensates, for which two (or more) orbitals are occupied, and
derive a corresponding time-dependent multi-orbital mean-field theory. We call
our theory TDMF(), where stands for the number of evolving fragments.
Working equations for a general two-body interaction between the bosons are
explicitly presented along with an illustrative numerical example.Comment: 16 pages, 1 figur
Build-up of coherence between initially-independent subsystems: The case of Bose-Einstein condensates
When initially-independent subsystems are made to contact, {\it coherence}
can develop due to interaction between them. We exemplify and demonstrate this
paradigm through several scenarios of two initially-independent Bose-Einstein
condensates which are allowed to collide. The build-up of coherence depends
strongly on time, interaction strength and other parameters of each condensate.
Implications are discussed.Comment: 11 pages, 3 figure
Quantum dynamics of attractive versus repulsive bosonic Josephson junctions: Bose-Hubbard and full-Hamiltonian results
The quantum dynamics of one-dimensional bosonic Josephson junctions with
attractive and repulsive interparticle interactions is studied using the
Bose-Hubbard model and by numerically-exact computations of the full many-body
Hamiltonian. A symmetry present in the Bose-Hubbard Hamiltonian dictates an
equivalence between the evolution in time of attractive and repulsive Josephson
junctions with attractive and repulsive interactions of equal magnitude. The
full many-body Hamiltonian does not possess this symmetry and consequently the
dynamics of the attractive and repulsive junctions are different.Comment: 9 pages, 2 figure
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