154 research outputs found
Polarization in a three-dimensional Fermi gas with Rabi coupling
We investigate the polarization of a two-component three-dimensional
fermionic gas made of repulsive alkali-metal atoms. The two pseudo-spin
components correspond to two hyperfine states which are Rabi coupled. The
presence of Rabi coupling implies that only the total number of atoms is
conserved and a quantum phase transition between states dominated by
spin-polarization along different axses is possible. By using a variational
Hartree-Fock scheme we calculate analytically the ground-state energy of the
system and determine analytically and numerically the conditions under which
there is this quantum phase transition. This scheme includes the well-known
criterion for the Stoner instability. The obtained phase diagram clearly shows
that the polarized phase crucially depends on the interplay among the Rabi
coupling energy, the interaction energy per particle, and the kinetic energy
per particle.Comment: 12 pages, 2 figure
Pathway toward the formation of supermixed states in ultracold boson mixtures loaded in ring lattices
We investigate the mechanism of formation of supermixed soliton-like states
in bosonic binary mixtures loaded in ring lattices. We evidence the presence of
a common pathway which, irrespective of the number of lattice sites and upon
variation of the interspecies attraction, leads the system from a mixed and
delocalized phase to a supermixed and localized one, passing through an
intermediate phase where the supermixed soliton progressively emerges. The
degrees of mixing, localization and quantum correlation of the two condensed
species, quantified by means of suitable indicators commonly used in
Statistical Thermodynamics and Quantum Information Theory, allow one to
reconstruct a bi-dimensional mixing-supermixing phase diagram featuring two
characteristic critical lines. Our analysis is developed both within a
semiclassical approach capable of capturing the essential features of the
two-step mixing-demixing transition and with a fully-quantum approach.Comment: 12 pages, 8 figure
Phase separation can be stronger than chaos
We investigate several dynamical regimes characterizing a bosonic binary
mixture loaded in a ring trimer, with particular reference to the persistence
of demixing. The degree of phase separation is evaluated by means of the
"Entropy of mixing", an indicator borrowed from Statistical Thermodynamics.
Three classes of demixed stationary configurations are identified and their
energetic and linear stability carefully analyzed. An extended set of
trajectories originating in the vicinity of fixed points are explicitly
simulated and chaos is shown to arise according to three different mechanisms.
In many dynamical regimes, we show that chaos is not able to disrupt the order
imposed by phase separation, i.e. boson populations, despite evolving in a
chaotic fashion, do not mix. This circumstance can be explained either with
energetic considerations or in terms of dynamical restrictions.Comment: 21 pages, 9 figure
The phase-separation mechanism of a binary mixture in a ring trimer
We show that, depending on the ratio between the inter- and the intra-species
interactions, a binary mixture trapped in a three-well potential with periodic
boundary conditions exhibits three macroscopic ground-state configurations
which differ in the degree of mixing. Accordingly, the corresponding quantum
states feature either delocalization or a Schr\"odinger cat-like structure. The
two-step phase separation occurring in the system, which is smoothed by the
activation of tunnelling processes, is confirmed by the analysis of the energy
spectrum that collapses and rearranges at the two critical points. In such
points, we show that also Entanglement Entropy, a quantity borrowed from
quantum-information theory, features singularities, thus demonstrating its
ability to witness the double mixining-demixing phase transition. The developed
analysis, which is of interest to both the experimental and theoretical
communities, opens the door to the study of the demixing mechanism in complex
lattice geometries.Comment: 14 pages, 9 figure
Two-species boson mixture on a ring: A group theoretic approach to the quantum dynamics of low-energy excitations
We investigate the weak excitations of a system made up of two condensates
trapped in a Bose-Hubbard ring and coupled by an interspecies repulsive
interaction. Our approach, based on the Bogoliubov approximation scheme, shows
that one can reduce the problem Hamiltonian to the sum of sub-Hamiltonians
, each one associated to momentum modes . Each is
then recognized to be an element of a dynamical algebra. This uncommon and
remarkable property allows us to present a straightforward diagonalization
scheme, to find constants of motion, to highlight the significant microscopic
processes, and to compute their time evolution. The proposed solution scheme is
applied to a simple but still very interesting closed circuit, the trimer. The
dynamics of low-energy excitations, corresponding to weakly-populated vortices,
is investigated considering different choices of the initial conditions, and
the angular-momentum transfer between the two condensates is evidenced.
Finally, the condition for which the spectral collapse and dynamical
instability are observed is derived analytically.Comment: 11 pages, 7 figure
Fractional-filling Mott domains in two dimensional optical superlattices
Ultracold bosons in optical superlattices are expected to exhibit
fractional-filling insulating phases for sufficiently large repulsive
interactions. On strictly 1D systems, the exact mapping between hard-core
bosons and free spinless fermions shows that any periodic modulation in the
lattice parameters causes the presence of fractional-filling insulator domains.
Here, we focus on two recently proposed realistic 2D structures where such
mapping does not hold, i.e. the two-leg ladder and the trimerized kagome'
lattice. Based on a cell strong-coupling perturbation technique, we provide
quantitatively satisfactory phase diagrams for these structures, and give
estimates for the occurrence of the fractional-filling insulator domains in
terms of the inter-cell/intra-cell hopping amplitude ratio.Comment: 4 pages, 3 figure
Residual entropy and critical behavior of two interacting boson species in a double well
Motivated by the importance of entanglement and correlation indicators in the
analysis of quantum systems, we study the equilibrium and the bipartite
residual entropy in a two-species Bose Hubbard dimer when the spatial phase
separation of the two species takes place. We consider both the zero and
non-zero-temperature regime. We present different kinds of residual entropies
(each one associated to a different way of partitioning the system), and we
show that they strictly depend on the specific quantum phase characterizing the
two species (supermixed, mixed or demixed) even at finite temperature. To
provide a deeper physical insight into the zero-temperature scenario, we apply
the fully-analytical variational approach based on su(2) coherent states and
provide a considerably good approximation of the entanglement entropy. Finally,
we show that the effectiveness of bipartite residual entropy as a critical
indicator at non-zero temperature is unchanged when considering a restricted
combination of energy eigenstates.Comment: 18 pages, 9 figure
Inter-species entanglement of Bose-Bose mixtures trapped in optical lattices
In the present work we discuss inter-species entanglement in Bose-Bose
mixtures trapped in optical lattices. This work is motivated by the observation
that, in the presence of a second component, the Mott-insulator lobe shifts
{\em{differently}} on the hole- and particle-side with respect to the Mott lobe
of the single species system (Phys. Rev. A 82, 021601, Laser Phys. 21, 1443).
We use perturbation theory, formulated in a Hilbert space decomposed by means
of lattice symmetries, in order to show that the nonuniform shift of the Mott
lobe is a consequence of an inter-species entanglement which differs in the
lowest excited states to remove and add a particle. Our results indicate that
inter-species entanglement in mixtures can provide a new perspective in
understanding quantum phase transitions. To validate our approach, we compare
our results from perturbation theory with quantum Monte Carlo simulations
Analysis and resolution of the ground-state degeneracy of the two-component Bose-Hubbard model
We study the degeneracy of the ground-state energy of the two-component
Bose-Hubbard model and of the perturbative correction . We show that the
degeneracy properties of and are closely related to the connectivity
properties of the lattice. We determine general conditions under which is
nondegenerate. This analysis is then extended to investigate the degeneracy of
. In this case, in addition to the lattice structure, the degeneracy also
depends on the number of particles present in the system. After identifying the
cases in which is degenerate and observing that the standard (degenerate)
perturbation theory is not applicable, we develop a method to determine the
zeroth-order correction to the ground state by exploiting the symmetry
properties of the lattice. This method is used to implement the perturbative
approach to the two-component Bose-Hubbard model in the case of degenerate
and is expected to be a valid tool to perturbatively study the asymmetric
character of the Mott-insulator to superfluid transition between the particle
and hole side
Quantum Dynamics of Coupled Bosonic Wells within the Bose-Hubbard Picture
We relate the quantum dynamics of the Bose-Hubbard model (BHM) to the
semiclassical nonlinear equations that describe an array of interacting Bose
condensates by implementing a standard variational procedure based on the
coherent state method. We investigate the dynamics of the two-site BHM from the
purely quantum viewpoint by recasting first the model within a spin picture and
using then the related dynamical algebra. The latter allows us to study
thoroughly the energy spectrum structure and to interpret quantally the
classical symmetries of the two-site dynamics. The energy spectrum is also
evaluated through various approximations relying on the coherent state
approach.Comment: 22 pages, 7 figure
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