Quantum dynamics of solitons in strongly interacting systems on optical lattices (original) (raw)
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Critical fluctuations in a soliton formation of attractive Bose-Einstein condensates
Physical Review A, 2006
We employ mean-field, Bogoliubov and many-body theories to study critical fluctuations in the position and momentum of a Bose-Einstein condensate whose translation symmetry is spontaneously broken due to attractive interactions. In a homogeneous system, the many-body ground state of the symmetry-preserving Hamiltonian is very fragile against superposition of low-lying states, while the mean-field theory predicts a stable bright soliton which spontaneously breaks translation symmetry. We show that weak symmetry-breaking perturbations cause the translation-symmetric many-body ground state to cross over to a many-body bright soliton. We argue that the centerof-mass fluctuations in the soliton state arise primarily from the depletion of the condensate to translation modes. We develop an extended mean-field theory to analytically reproduce these results obtained by the exact diagonalization method.
Quantum many-body dynamics of dark solitons in optical lattices
Physical Review A, 2009
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 [R. V. Mishmash and L. D. Carr, Phys. Rev. Lett. 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.
Fluctuation- and interaction-induced instability of dark solitons in single and binary condensates
Physical Review A, 2014
We examine the stability of dark soliton in single and two-species Bose-Einstein condensates. We show that the presence of soliton in a single-species condensate enhances the quantum depletion of the ground state which is sufficient enough to induce dynamical instability of the solitons in the condensate. We also predict that for two-species condensates, in addition to the third Goldstone mode that emerges at higher interspecies interaction, due to the presence of the soliton in one of the components, a fourth Goldstone mode arises. We use Hartree-Fock-Bogoliubov theory with Popov approximation to examine the mode evolution and demonstrate for specific values of interspecies interaction, when the anomalous mode collides with a higher energy mode it renders the solitonic state oscillatory unstable. We also observe soliton induced change in the topology of the density profiles of the two-species condensates.
Dynamics and stability of Bose-Einstein solitons in tilted optical lattices
Physical Review A, 2010
Bloch oscillations of Bose-Einstein condensates realize sensitive matter-wave interferometers. We investigate the dynamics and stability of bright-soliton wave packets in one-dimensional tilted optical lattices with a modulated mean-field interaction g(t). By means of a time-reversal argument, we prove the stability of Bloch oscillations of breathing solitons that would be quasistatically unstable. Floquet theory shows that these breathing solitons can be more stable against certain experimental perturbations than rigid solitons or even noninteracting wave packets.
Quantum Fluctuations of Low Dimensional Bose-Einstein Condensates in Optical Systems
Momona Ethiopian Journal of Science, 2011
A system of low dimensional condensed ultracold atomic gases inside a field of a laser-driven optical cavity exhibits dispersive optical bistability. During such a process the system also shows quantum fluctuations. Condensate fluctuations are highly manifested particularly in low dimensional systems. In this paper we have investigated the theory and manifestation of fluctuations in quantum optical systems in low dimensional Bose-Einstein condensates. We have described the system using the mean-field approximation. In this study we have verified that low dimensional quantum gases exhibit not only highly fascinating properties but also we have indicated that the use of mean field theory to describe quantum gases in low dimensions is highly restricted since the possibility of generating low dimensional bosonic condensates is dominated by the existence of highly sensitive and intrinsic quantum fluctuations.
Quantum Switching at a Mean-Field Instability of a Bose-Einstein Condensate in an Optical Lattice
Physical Review Letters, 2009
It is shown that bifurcations of the mean-field dynamics of a Bose-Einstein condensate can be related with the quantum phase transitions of the original many-body system. As an example we explore the intra-band tunneling in the two-dimensional optical lattice. Such a system allows for easy control by the lattice depth as well as for macroscopic visualization of the phase transition. The system manifests switching between two selftrapping states or from a selftrapping state to a superposition of the macroscopically populated selftrapping states with the step-like variation of the control parameter about the bifurcation point. We have also observed the magnification of the microscopic difference between the even and odd number of atoms to a macroscopically distinguishable dynamics of the system. PACS numbers: 03.75.Lm; 03.75.Nt
Dynamics of two coupled Bose-Einstein Condensate solitons in an optical lattice
Optics Express, 2006
The characteristics of two coupled Bose-Einstein Condensate (BEC) bright solitons trapped in an optical lattice are investigated with the variational approach and direct numerical simulations of the Gross-Pitaevskii equation. It is found that the optical lattice can be controllably used to capture and drag the coupled BEC solitons. Its effect depends on the initial location of the BEC solitons, the lattice amplitude and wave-number, and the amplitude of the coupled BEC solitons. The effective interaction between the two coupled solitons is the attractive effect.
Pramana-journal of Physics, 2009
We make use of a coordinate-free approach to implement Vakhitov-Kolokolov criterion for stability analysis in order to study the effects of three-body atomic recombination and lattice potential on the matter-wave bright solitons formed in Bose-Einstein condensates. We analytically demonstrate that (i) the critical number of atoms in a stable BEC soliton is just half the number of atoms in a marginally stable Townes-like soliton and (ii) an additive optical lattice potential further reduces this number by a factor of √1 − bg 3 with g 3 the coupling constant of the lattice potential and b = 0.7301.
Metastable Bose-Einstein condensation in a strongly correlated optical lattice
Physical Review A, 2015
We experimentally and theoretically study the peak fraction of a Bose-Einstein condensate loaded into a cubic optical lattice as the lattice potential depth and entropy per particle are varied. This system is well-described by the superfluid regime of the Bose-Hubbard model, which allows for comparison with mean-field theories and exact quantum Monte Carlo (QMC) simulations. Despite correcting for systematic discrepancies between condensate fraction and peak fraction, we discover that the experiment consistently shows the presence of a condensate at temperatures higher than the critical temperature predicted by QMC simulations. This metastability suggests that turning on the lattice potential is non-adiabatic. To confirm this behavior, we compute the timescales for relaxation in this system, and find that equilibration times are comparable with the known heating rates. The similarity of these timescales implies that turning on the lattice potential adiabatically may be impossible. Our results point to the urgent need for a better theoretical and experimental understanding of the timescales for relaxation and adiabaticity in strongly interacting quantum gases, and the importance of model-independent probes of thermometry in optical lattices. arXiv:1411.5593v2 [cond-mat.quant-gas]
Physical Review Letters, 2005
The dynamics of matter-wave solitons in Bose-Einstein condensates (BEC) is considerably affected by the presence of a thermal cloud and the dynamical depletion of the condensate. Our numerical results, based on the time-dependent Hartree-Fock-Bogoliubov theory, demonstrate the collapse of the attractively interacting BEC via collisional emission of atom pairs into the thermal cloud, which splits the (quasi-onedimensional) BEC soliton into two partially coherent solitonic structures of opposite momenta. These incoherent matter waves are analogous to optical random-phase solitons.