232 research outputs found
Ground state properties of a one-dimensional strongly-interacting Bose-Fermi mixture in a double-well potential
We calculate the reduced single-particle density matrix (RSPDM), momentum
distributions, natural orbitals and their occupancies, for a strongly
interacting one-dimensional Bose-Fermi mixture in a double-well potential with
a large central barrier. For mesoscopic systems, we find that the ground state
properties qualitatively differ for mixtures with even number of particles
(both odd-odd and even-even mixtures) in comparison to mixtures with odd
particle numbers (odd-even and even-odd mixtures). For even mixtures the
momentum distribution is smooth, whereas the momentum distribution of odd
mixtures possesses distinct modulations; the differences are observed also in
the off-diagonal correlations of the RSPDM, and in the occupancies of natural
orbitals. The calculation is based on a derived formula which enables efficient
calculation of the RSPDM for mesoscopic mixtures in various potentials.Comment: 10 figure
The pinning quantum phase transition in a Tonks Girardeau gas: diagnostics by ground state fidelity and the Loschmidt echo
We study the pinning quantum phase transition in a Tonks-Girardeau gas, both
in equilibrium and out-of-equilibrium, using the ground state fidelity and the
Loschmidt echo as diagnostic tools. The ground state fidelity (GSF) will have a
dramatic decrease when the atomic density approaches the commensurate density
of one particle per lattice well. This decrease is a signature of the pinning
transition from the Tonks to the Mott insulating phase. We study the
applicability of the fidelity for diagnosing the pinning transition in
experimentally realistic scenarios. Our results are in excellent agreement with
recent experimental work. In addition, we explore the out of equilibrium
dynamics of the gas following a sudden quench with a lattice potential. We find
all properties of the ground state fidelity are reflected in the Loschmidt echo
dynamics i.e., in the non equilibrium dynamics of the Tonks-Girardeau gas
initiated by a sudden quench of the lattice potential
Loschmidt echo in one-dimensional interacting Bose gases
We explore Loschmidt echo in two regimes of one-dimensional (1D) interacting
Bose gases: the strongly interacting Tonks-Girardeau (TG) regime, and the
weakly-interacting mean-field regime. We find that the Loschmidt echo of a TG
gas decays as a Gaussian when small perturbations are added to the Hamiltonian
(the exponent is proportional to the number of particles and the magnitude of a
small perturbation squared). In the mean-field regime the Loschmidt echo decays
faster for larger interparticle interactions (nonlinearity), and it shows
richer behavior than the TG Loschmidt echo dynamics, with oscillations
superimposed on the overall decay.Comment: Comparison between Tonks-Girardeau and mean-field fidelities
corrected; see new Figure 4 and the "Note added". New references are include
Laser assisted tunneling in a Tonks-Girardeau gas
We investigate the applicability of laser assisted tunneling in a strongly
interacting one-dimensional Bose gas (the Tonks-Girardeau gas) in optical
lattices. We find that the stroboscopic dynamics of the Tonks-Girardeau gas in
a continuous Wannier-Stark-ladder potential, supplemented with laser assisted
tunneling, effectively realizes the ground state of one-dimensional hard-core
bosons in a discrete lattice with nontrivial hopping phases. We compare
observables that are affected by the interactions, such as the momentum
distribution, natural orbitals and their occupancies, in the time-dependent
continuous system, to those of the ground state of the discrete system.
Stroboscopically, we find an excellent agreement, indicating that laser
assisted tunneling is a viable technique for realizing novel ground states and
phases with hard-core one-dimensional Bose gases.Comment: 17 pages, 5 figure
The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas
We study the reduced single-particle density matrix (RSPDM), the momentum
distribution, natural orbitals and their occupancies, of dark "soliton" (DS)
states in a Tonks-Girardeau gas. DS states are specially tailored excited
many-body eigenstates, which have a dark solitonic notch in their
single-particle density. The momentum distribution of DS states has a
characteristic shape with two sharp spikes. We find that the two spikes arise
due to the high degree of correlation observed within the RSPDM between the
mirror points ( and ) with respect to the dark notch at ; the
correlations oscillate rather than decay as the points and are being
separated.Comment: 9 pages, 8 figure
Random-Phase Solitons in Nonlinear Periodic Lattices
We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons exist when the nonlinear response time is much longer than the characteristic time of random phase fluctuations. The intensity profiles, power spectra, and statistical (coherence) properties of these stationary waves conform to the periodicity of the lattice. The general phenomenon of such solitons is analyzed in the context of nonlinear photonic lattices
Bursts in the Chaotic Trajectory Lifetimes Preceding the Controlled Periodic Motion
The average lifetime () it takes for a randomly started trajectory
to land in a small region () on a chaotic attractor is studied. is
an important issue for controlling chaos. We point out that if the region
is visited by a short periodic orbit, the lifetime strongly deviates
from the inverse of the naturally invariant measure contained within that
region (). We introduce the formula that relates
to the expanding eigenvalue of the short periodic orbit
visiting .Comment: Accepted for publication in Phys. Rev. E, 3 PS figure
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