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Time-Dependent Dynamics of the Bose-Fermi Mixed Condensed System ∗

Tomoyuki Maruyama, Hiroyuki Yabu, Takahiro Suzuki

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

We study the monopole oscillation in the bose-fermi mixed condensed system by performing the time-dependent Gross-Pitaevsky (GP) and Vlasov equations. We find that the big damping exists for the fermion oscillation in the mized system even at zero temperature It is one of the most excited theme in recent physics to study the time-dependent dynamical motions of traped atoms under the existence of the Bose-Einstein condensates (BEC) [1, 2], such as the collective motions[3], quantum votices [4] and atomic novae [5]. In the view of the theoretical research, these phenomena are very important also to construct and to examine the transport theory in finite many body system. In fact many atomic system must give good probes for such study because the fundamental interaction is clear and weak. In this work we construct the transport model including the condensed bosons and fermions, and as a first step study the collective monopole motion. Here we briefly explain our formalism. First we define the Hamiltonian for boson-fermion coexistent system as follows. with HB =

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We study the monopole oscillation in the bose-fermi mixed condensed system by performing the time-dependent Gross-Pitaevsky (GP) and Vlasov equations. We find that the big damping exists for the fermion oscillation in the mized system even at zero temperature It is one of the most excited theme in recent physics to study the time-dependent dynamical motions of traped atoms under the existence of the Bose-Einstein condensates (BEC) [1, 2], such as the collective motions[3], quantum votices [4] and atomic novae [5]. In the view of the theoretical research, these phenomena are very important also to construct and to examine the transport theory in finite many body system. In fact many atomic system must give good probes for such study because the fundamental interaction is clear and weak. In this work we construct the transport model including the condensed bosons and fermions, and as a first step study the collective monopole motion. Here we briefly explain our formalism. First we define the Hamiltonian for boson-fermion coexistent system as follows. with HB =
We study the dipole collective oscillations in Bose-Fermi mixtures in a dynamical time-dependent approach, which is formulated with the time-dependent Gross-Pitaevskii equation and the Vlasov equation. While the Bose gas oscillates monotonously, the fermion oscillation shows a beat and damping. We find big differences in behaviors of fermion oscillation between the time-dependent approach and usual approaches such as the sum-rule approach. When the amplitude is not minimal, the dipole oscillation of the Fermi gas cannot be described with a simple center-of-mass motion.
We study quadrupole collective oscillations in the bose-fermi mixtures of ultracold atomic gases of Yb isotopes, which are realized by Kyoto group. Three kinds of combinations are chosen, 170Yb-171Yb^{170}\text{Y}\text{b-}^{171}\text{Y}\text{b}170Yb-171Yb, 170Yb-173Yb^{170}\text{Y}\text{b-}^{173}\text{Y}\text{b}170Yb-173Yb and 174Yb-173Yb^{174}\text{Y}\text{b-}^{173}\text{Y}\text{b}174Yb-173Yb, where boson-fermion interactions are weakly repulsive, strongly attractive and strongly repulsive respectively. Collective oscillations in these mixtures are calculated in a dynamical time-evolution approach with the time-dependent Gross-Pitaevskii and the Vlasov equations. The boson oscillations are shown to have one collective mode, and the fermions are shown to have the boson-forced and two intrinsic modes, which correspond to the inside- and outside-fermion oscillations for the boson-distributed regions. The oscillations obtained in the dynamical approach show discrepancies from the results obtained in the small-amplitude approximations, e.g., the random phase approximation, except in the case of weak boson-fermion interactions. We also analyze these discrepancies, and show that they originated in the change of the fermion distributions through oscillation.
Trapped Bose-condensed atomic gases are remarkable because, in spite of the fact that these are very dilute systems, they exhibit robust coherent dynamic behaviour when perturbed. These quantum “wisps of matter” are a new phase of highly coherent matter. While binary collisions are very infrequent, the large coherent mean field associated with the Bose condensate ensures that interactions play a crucial role in determining the collective response of these trapped superfluid gases. In our discussion of the theory of collective oscillations of atomic condensates, the macroscopic Bose wavefunction Φ( r , t ) plays a central role. This wavefunction is the BEC order parameter. As discussed in Chapter 1, the initial attempts at defining this order parameter began with the pioneering work of London (1938a), were further developed by Bogoliubov (1947) and finally extended to deal with any Bose superfluid using the general quantum field theoretic formalism developed by Beliaev (1958a). Almost all this early theoretical work was limited to T = 0 where, in a dilute weakly interacting Bose gas, all the atoms are in the condensate. The first extension of these ideas to nonuniform Bose condensates was by Pitaevskii (1961) and, independently, by Gross (1961), which led to the now famous Gross–Pitaevskii (GP) equation of motion for Φ( r , t ). Before the discovery of BEC in trapped gases, the time-dependent GP equation was mainly used to study vortices in Bose superfluids, which involve a spatially nonuniform ground state. Apart from this application, the GP equation was largely unknown. The situation changed overnight in 1995 with the creation of trapped nonuniform Bose condensates in atomic gases.