38 research outputs found
Mechanism of Anomalous Tunneling in Condensed Bose System
We clarify the origin of anomalous tunneling [Yu. Kagan et al. Phys. Rev.
Lett. 90 (2003) 130402] i.e. the perfect transmission at low energy limit of
tunneling of phonon excitations across the potential barrier separating two
Bose condensates. The perfect transmission is a consequence of the coincidence
of the wave function of the excited state at low energy limit and the
macroscopic wave function of the condensate. We show that the perfect
transmission at low energy occurs even at finite temperatures within the scheme
of Popov approximation.Comment: 4 pages 1 figur
Absence of Anomalous Tunneling of Bogoliubov Excitations for Arbitrary Potential Barrier under the Critical Condensate Current
We derive the exact solution of low energy limit of Bogoliubov equations for
excitations of Bose-Einstein condensate in the presence of arbitrary potential
barrier and maximum current of condensate. Using this solution, we give the
explicit expression for the transmission coefficient against the potential
barrier, which shows partial transmission in the low energy limit. The
wavefunctions of excitations in the low energy limit do not coincide with that
of the condensate. The absence of the perfect transmission in the critical
current state originates from local enhancement of density fluctuations around
the potential barrier.Comment: 4 pages, 1 figur
Landau and dynamical instabilities of Bose-Einstein condensates with superfluid flow in a Kronig-Penney potential
We study the elementary excitations of Bose-Einstein condensates in a
one-dimensional periodic potential and discuss the stability of superfluid flow
based on the Kronig-Penney model. We analytically solve the Bogoliubov
equations and calculate the excitation spectrum. The Landau and dynamical
instabilities occur in the first condensate band when the superfluid velocity
exceeds certain critical values, which agrees with the result of condensates in
a sinusoidal potential. It is found that the onset of the Landau instability
coincides with the point where the perfect transmission of low-energy
excitations is forbidden, while the dynamical instability occurs when the
effective mass is negative. It is well known that the condensate band has a
peculiar structure called swallowtail when the periodic potential is shallow
compared to the mean field energy. We find that the upper side of the
swallowtail is dynamically unstable although the excitations have the linear
dispersion reflecting the positive effective mass.Comment: 6 pages, 2 figures, Proceedings of the International Symposium on
Quantum Fluids and Solids (QFS2006
Stability of superfluid Fermi gases in optical lattices
Critical velocities of superfluid Fermi gases in optical lattices are
theoretically investigated across the BCS-BEC crossover. We calculate the
excitation spectra in the presence of a superfluid flow in one- and
two-dimensional optical lattices. It is found that the spectrum of low-lying
Anderson-Bogoliubov (AB) mode exhibits a roton-like structure in the
short-wavelength region due to the strong charge density wave fluctuations, and
with increasing the superfluid velocity one of the roton-like minima reaches
zero before the single-particle spectrum does. This means that superfluid Fermi
gases in optical lattices are destabilized due to spontaneous emission of the
roton-like AB mode instead of due to Cooper pair breaking.Comment: 4 pages, 4 figures, conference proceeding for ISQM-TOKYO'0
Time-dependent currents of 1D bosons in an optical lattice
We analyse the time-dependence of currents in a 1D Bose gas in an optical
lattice. For a 1D system, the stability of currents induced by accelerating the
lattice exhibits a broad crossover as a function of the magnitude of the
acceleration, and the strength of the inter-particle interactions. This differs
markedly from mean-field results in higher dimensions. Using the infinite Time
Evolving Block Decimation algorithm, we characterise this crossover by making
quantitative predictions for the time-dependent behaviour of the currents and
their decay rate. We also compute the time-dependence of quasi-condensate
fractions which can be measured directly in experiments. We compare our results
to calculations based on phase-slip methods, finding agreement with the scaling
as the particle density increases, but with significant deviations near unit
filling.Comment: 19 pages, 10 figure
Quantum Many-Body Dynamics of Dark Solitons in Optical Lattices
We present a fully quantum many-body treatment of dark solitons formed by
ultracold bosonic atoms in one-dimensional optical lattices. Using
time-evolving block decimation to simulate the single-band Bose-Hubbard
Hamiltonian, we consider the quantum dynamics of density and phase engineered
dark solitons as well as the quantum evolution of mean-field dark solitons
injected into the quantum model. The former approach directly models how one
may create quantum entangled dark solitons in experiment. While we have already
presented results regarding the latter approach elsewhere [Phys. Rev. Lett.
{\bf 103}, 140403 (2009)], we expand upon those results in this work. In both
cases, quantum fluctuations cause the dark soliton to fill in and may induce an
inelasticity in soliton-soliton collisions. Comparisons are made to the
Bogoliubov theory which predicts depletion into an anomalous mode that fills in
the soliton. Our many-body treatment allows us to go beyond the Bogoliubov
approximation and calculate explicitly the dynamics of the system's natural
orbitals.Comment: 14 pages, 11 figures -- v3 has only minor changes from v2 -- this is
the print versio
Accurate numerical verification of the instanton method for macroscopic quantum tunneling: dynamics of phase slips
Instanton methods, in which imaginary-time evolution gives the tunneling
rate, have been widely used for studying quantum tunneling in various contexts.
Nevertheless, how accurate instanton methods are for the problems of
macroscopic quantum tunneling (MQT) still remains unclear because of lack of
their direct comparison with exact time evolution of the many-body Schroedinger
equation. Here, we verify instanton methods applied to coherent MQT.
Specifically applying the quasi-exact numerical method of time-evolving block
decimation to the system of bosons in a ring lattice, we directly simulate the
real-time quantum dynamics of supercurrents, where a coherent oscillation
between two macroscopically distinct current states occurs due to MQT. The
tunneling rate extracted from the coherent oscillation is compared with that
given by the instanton method. We show that the error is within 10% when the
effective Planck's constant is sufficiently small. We also discuss phase slip
dynamics associated with the coherent oscillations.Comment: 19 pages, 14 figures, 1 tabl
Exact Results for Tunneling Problems of Bogoliubov Excitations in the Critical Supercurrent State
We show the exact solution of Bogoliubov equations at zero-energy in the
critical supercurrent state for arbitrary shape of potential barrier. With use
of this solution, we prove the absence of perfect transmission of excitations
in the low-energy limit by giving the explicit expression of transmission
coefficient. The origin of disappearance of perfect transmission is the
emergence of zero-energy density fluctuation near the potential barrier.Comment: 6 pages, 3 figures; Proceedings of QFS200
Resonant Hawking radiation in Bose-Einstein condensates
We study double-barrier interfaces separating regions of asymptotically
subsonic and supersonic flow of Bose condensed atoms. These setups contain at
least one black hole sonic horizon from which the analog of Hawking radiation
should be generated and emitted against the flow in the subsonic region.
Multiple coherent scattering by the double-barrier structure strongly modulates
the transmission probability of phonons, rendering it very sensitive to their
frequency. As a result, resonant tunneling occurs with high probability within
a few narrow frequency intervals. This gives rise to highly non-thermal spectra
with sharp peaks. We find that these peaks are mostly associated to decaying
resonances and only occasionally to dynamical instabilities. Even at achievable
nonzero temperatures, the radiation peaks can be dominated by the spontaneous
emission, i.e. enhanced zero-point fluctuations, and not, as often in analog
models, by stimulated emission.Comment: 20 pages, 9 figures, revised versio
Transmission and Reflection of Collective Modes in Spin-1 Bose-Einstein Condensate
We study tunneling properties of collective excitations in spin-1
Bose-Einstein condensates. In the absence of magnetic fields, the total
transmission in the long wavelength limit occurs in all kinds of excitations
but the quadrupolar spin mode in the ferromagnetic state. The quadrupolar spin
mode alone shows the total reflection. A difference between those excitations
comes from whether the wavefunction of an excitation corresponds to that of the
condensate in the long wavelength limit. The correspondence results in the
total transmission as in the spinless BEC.Comment: 6 pages, 5 figure