Coherent states and quantum oscillations of BEC-BCS systems

Huang, Hongbin; Yang, Chunxiang; Liang, Sun; Guo, Jiyuan; Li, J.

doi:10.1016/j.physleta.2008.07.025

Cited by 4 publications

(12 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Later on, the BCS ground state was shown to be related to coherent states [2,3]. By analyzing the algebraic structure of the BCS ground state, we will show that it is actually a second order nilpotent SU(2) generalized coherent state.…”

Section: Introductionmentioning

confidence: 94%

Berry phase, entanglement entropy, and algebraic properties of ground states of BCS and BEC superfluids

Guo

Chien

2017

Physics Letters A

View full text Add to dashboard Cite

By using Bogoliubov transformations to construct the ground states of fermionic Bardeen-CooperSchrieffer (BCS) superfluids and weakly-interacting Bose gases supporting Bose Einstein Condensation (BEC), their algebraic structures and implications can be analyzed in detail. Both ground states are generalized squeezed coherent states saturating a generalized Heisenberg uncertainty relation, and they acquire quantized Berry phases when the corresponding systems are transported along a closed path in their parameter spaces. While the Berry phase of the BCS ground state depends on the total particle number, the Berry phase of the BEC ground state depends only on the particles outside the BEC. The Berry phases are associated with magnetic monopoles in the parameter spaces and we found that the Dirac quantization condition is satisfied. Moreover, both ground states are entangled states of the fermion or boson quanta and we found the entanglement entropy quantifying the internal correlations. A fixed particle-number approach of fermionic superfluids does not saturate the generalized uncertainty relation, exhibits internal entanglement, and gives corresponding Berry phase. In addition, the algebraic structures of the ground states can be classified by the q-deformed Hopf algebra, k hq k (1) for bosons and q-deformed Hopf superalgebra k hq k (1|1) for fermions, respectively.

show abstract

Section: Introductionmentioning

confidence: 94%

Berry phase, entanglement entropy, and algebraic properties of ground states of BCS and BEC superfluids

Guo

Chien

2017

Physics Letters A

View full text Add to dashboard Cite

show abstract

“…al. [11] have obtained the excitation spectra of this Hamiltonian in the mean field, and Roy [21] has demonstrated that the relaxation time of these excitations are faster than E −1 c , where E c = 2 µ 2 F + |∆ + g r b 0 | 2 , ∆ is the equilibrium BCS gap computed from the gap equation [28], and b 0 is the ground state population of the bosons. Therefore, impulse quenches that are slower than E −1 c allow an analysis of the dynamical system based only on a ground state BEC field and fermion pair field to completely capture the non-equilibrium state.…”

Section: Dynamics Of the Order Parametersmentioning

confidence: 99%

“…Here, h F (r)(h B (r)) = − ∇ 2 2(4)m + V (r) are the single particle Hamiltonians for the fermions (Bosons), and m is the fermion mass (the mass of the composite bosons is thus 2m). The second line represents the Hamiltonian of the composite bosons [11,26]. Here, the Feshbach threshold energy (also called the Feshbach 'detuning' from the molecular channel to the continuum [26]) is represented by 2ν, and u B represents the amplitude of the repulsion between the composite bosons.…”

Section: Dynamics Of the Order Parametersmentioning

confidence: 99%

“…The literature can be broadly divided into two kinds, one that looks at the macroscopic dynamics of the order parameters, covered in section II, and one that looks at the dynamics of the microscopic degrees of freedom, covered in section III. In the former case, the excited quasiparticles in the Bogoliubov de-Gennes spectrum of the superfluid relax very quickly compared to the relaxation of the time dependent superfluid gap ∆(t), and excitations of the quasimolecular states relax similarly [10,11]. Thus, the dynamics of the system can be described by a mean field treatment of the macroscopic order parameter ∆(t) in the single channel Feshbach resonance, and a two-parameter system spanned by ∆(t) and the BEC matter field b 0 (t) in the dual channel case.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Nonequilibrium dynamics of ultracold Fermi superfluids

Roy

2013

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

The aim of this mini review is to survey the literature on the study of nonequilibrium dynamics of Fermi superfluids in the BCS and BEC limits, both in the single channel and dual channel cases. The focus is on mean field approaches to the dynamics, with specific attention drawn to the dynamics of the Ginzburg-Landau order parameters of the Fermi and composite Bose fields, as well as on the microscopic dynamics of the quantum degrees of freedom. The two approaches are valid approximations in two different time scales of the ensuing dynamics. The system is presumed to evolve during and/or after a quantum quench in the parameter space. The quench can either be an impulse quench with virtually instantaneous variation, or a periodic variation between two values. The literature for the order parameter dynamics, described by the time-dependent Ginzburg-Landau equations, is reviewed, and the works of the author in this area highlighted. The mixed phase regime in the dual channel case is also considered, and the dual order parameter dynamics of Fermi-Bose mixtures reviewed. Finally, the nonequilibrium dynamics of the microscopic degrees of freedom for the superfluid is reviewed for the self-consistent and non self-consistent cases. The dynamics of the former can be described by the Bogoliubov de-Gennes equations with the equilibrium BCS gap equation continued in time and self -consistently coupled to the BdG dynamics. The latter is a reduced BCS problem and can be mapped onto the dynamics of Ising and Kitaev models. This article reviews the dynamics of both impulse quenches in the Feshbach detuning, as well as periodic quenches in the chemical potential, and highlights the author's contributions in this area of research. I. INTRODUCTIONStudies of the coherent quantum dynamics of closed many body systems have gained considerable interest in the last two decades. This interest has been brought about by such states becoming experimentally accessible using ultracold atoms, cooled to near absolute zero temperatures by the use of optical molasses [1] , evaporative cooling [2], laser culling [3] , cavity QED methods [4] , and other experimental techniques. The experimental realization of the Bose Einstein condensate by Cornell, Ketterle and Weiman in 1995 [2] , as well as the realization of the Bosonic Superfluid Mott-Insulator transition by Greiner et. al. in 2002 [5] (theoretically predicted by Jaksch et. al. in 1998 [6] ), motivated strong theoretical interest in the coherent dynamics of ultracold bosons. Previously, the regimes where fermionic coherent dynamics can be realized were unattainable in either solid state systems or with ultracold atoms. The difficulties for ultracold atoms were eventually circumvented by experiments performed over the first decade of the 21 st century. Studies of fermionic atoms gained momentum after these experiments realized pure fermionic BCS states [7] , as well as the BCS-BEC crossover that was predicted theoretically a decade earlier [8] . The formation of Fermi superfluids were realized ...

show abstract

“…In order to do so, the Timmermans' Hamiltonian in equation 2 is written in momentum space with the closed channel excitations included, yielding q through this coupling. The Hamiltonian above can be written in terms of the generators of the SU (2) ⊗ SU (1, 1) Lie algebra [32]. Assuming that most of the Bosons are in the ground state given by q = 0, treating b 0 as a c-number, retaining only terms up to second order in b † q (b q ) and neglecting fluctuations about the mean field for all generators, the Hamiltonian can be diagonalized in a manner similar to that done for a pure Boson system in Bogoliubov theory [32], with the eigenstates given by the generalized SU (2) ⊗ SU (1, 1) coherent state.…”

Section: Quenched Time Evolutionmentioning

confidence: 99%

Dynamics of quantum quenching for BCS-BEC systems in the shallow-BEC regime

Roy

2012

Eur. Phys. J. Plus

View full text Add to dashboard Cite

The problem of coupled Fermi-Bose mixtures of an ultracold gas near a narrow Feshbach resonance is approached through the time-dependent and complex Ginzburg-Landau (TDGL) theory. The dynamical system is constructed using Ginzburg-Landau-Abrikosov-Gor'kov (GLAG) path integral methods with the single mode approximation for the composite Bosons. The equilibrium states are obtained in the BEC regime for adiabatic variations of the Feshbach detuning along the stationary solutions of the dynamical system. Investigations into the rich superfluid dynamics of this system in the shallow BEC regime yield the onset of multiple interference patterns in the dynamics as the system is quenched from the deep-BEC regime. This results in a partial collapse and revival of the coherent matter wave field of the BEC, whose temporal profile is reported.

show abstract

Coherent states and quantum oscillations of BEC-BCS systems

Cited by 4 publications

References 27 publications

Berry phase, entanglement entropy, and algebraic properties of ground states of BCS and BEC superfluids

Berry phase, entanglement entropy, and algebraic properties of ground states of BCS and BEC superfluids

Nonequilibrium dynamics of ultracold Fermi superfluids

Dynamics of quantum quenching for BCS-BEC systems in the shallow-BEC regime

Contact Info

Product

Resources

About