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arXiv:1007.4422 · Journal of Physics B Atomic Molecular and Optical Physics

Structure and stability of quasi-two-dimensional boson–fermion mixtures with vortex–antivortex superposed states

Linghua Wen, Yongping Zhang, Jian Feng

Published Oct 29, 2010• 7 citations
arXivHTMLPDF

Abstract

We investigate the equilibrium properties of a quasi-two-dimensional degenerate boson-fermion mixture (DBFM) with a bosonic vortex-antivortex superposed state (VAVSS) using a quantum-hydrodynamic model. We show that, depending on the choice of parameters, the DBFM with a VAVSS can exhibit rich phase structures. For repulsive boson-fermion (BF) interaction, the Bose-Einstein condensate (BEC) may constitute a petal-shaped "core" inside the honeycomb-like fermionic component, or a ring-shaped joint "shell" around the onion-like fermionic cloud, or multiple segregated "islands" embedded in the disc-shaped Fermi gas. For attractive BF interaction just below the threshold for collapse, an almost complete mixing between the bosonic and fermionic components is formed, where the fermionic component tends to mimic a bosonic VAVSS. The influence of an anharmonic trap on the density distributions of the DBFM with a bosonic VAVSS is discussed. In addition, a stability region for different cases of DBFM (without vortex, with a bosonic vortex, and with a bosonic VAVSS) with specific parameters is given.

DOI
10.1088/0953-4075/43/22/225302

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We investigate the equilibrium properties of a quasi-two-dimensional degenerate boson-fermion mixture (DBFM) with a bosonic vortex-antivortex superposed state (VAVSS) using a quantum-hydrodynamic model. We show that, depending on the choice of parameters, the DBFM with a VAVSS can exhibit rich phase structures. For repulsive boson-fermion (BF) interaction, the Bose-Einstein condensate (BEC) may constitute a petal-shaped "core" inside the honeycomb-like fermionic component, or a ring-shaped joint "shell" around the onion-like fermionic cloud, or multiple segregated "islands" embedded in the disc-shaped Fermi gas. For attractive BF interaction just below the threshold for collapse, an almost complete mixing between the bosonic and fermionic components is formed, where the fermionic component tends to mimic a bosonic VAVSS. The influence of an anharmonic trap on the density distributions of the DBFM with a bosonic VAVSS is discussed. In addition, a stability region for different cases of DBFM (without vortex, with a bosonic vortex, and with a bosonic VAVSS) with specific parameters is given.
We investigate the mixing-demixing transition and the collapse in a quasi-two-dimensional degenerate boson-fermion mixture (DBFM) with a bosonic vortex. We solve numerically a quantum-hydrodynamic model based on a new density functional which accurately takes into account the dimensional crossover. It is demonstrated that with the increase of interspecies repulsion, a mixed state of DBFM could turn into a demixed state. The system collapses for interspecies attraction above a critical value which depends on the vortex quantum number. For interspecies attraction just below this critical limit there is almost complete mixing of boson and fermion components. Such mixed and demixed states of a DBFM could be experimentally realized by varying an external magnetic field near a boson-fermion Feshbach resonance, which will result in a continuous variation of interspecies interaction.
We investigate the phase structure of two-component Bose-Einstein condensates (BECs) with repulsive intra- and interspecies interactions in the presence of respective vortex-antivortex superposition states (VAVSSs). We show that different winding numbers of the vortex and antivortex and different intra- and interspecies interaction strengths may lead to different phase configurations, such as fully separated phases, inlaid separated phases, asymmetric separated phases, and partially mixed phases, where the density profile of each component displays a petal-like (or modulated petal-like) structure. A phase diagram is given for the case of equal unit winding numbers of the vortex and antivortex in the respective components, and it is shown that the conventional criterion for phase separation of two-component BECs is not applicable for the present system due to the VAVSSs. In addition, our nonlinear stability analysis indicates that the typical phase structures of two-component BECs with VAVSSs allow them to be detected in experiments. Moreover, for the case of unequal winding numbers of the vortex and antivortex in the respective components, we find that each component in any of the possible phase structures is in a cluster state of vortices and antivortices, where the topological defects appear in the form of a singly quantized visible vortex, or a hidden vortex, or a ghost vortex, depending on the specific parameters of the system. Finally, a general relationship between the vortex-antivortex cluster state and the winding numbers of vortex and antivortex is revealed.
The structure of trapped binary mixtures of bosonic and fermionic atoms at zero temperature is studied using a modified Gross-Pitaevskii equation for the bosons which self-consistently includes the mean-field interaction generated by the fermionic cloud. The density of the fermionic component is described within the Thomas-Fermi approximation. The influence of the boson-boson and the boson-fermion s-wave interaction on the density profiles and the stability of the mixture is investigated systematically. Critical particle numbers for the mean-field collapse caused either by attractive boson-boson or by attractive boson-fermion interactions and for the onset of spatial component separation are discussed. It is shown that the interplay between the boson-boson and the boson-fermion interaction generates a rich and complex phase diagram. Finally, the specific properties and prospects of the boson-fermion mixtures available in present experiments are addressed.
We investigate the dynamic properties of the vortex–antivortex superposed state (VAVSS) as well as the pure vortex state for a Bose–Einstein condensate released from a harmonic trap into a confining two-dimensional (2D) infinite-depth square well. It is shown that with the development of time the VAVSS as well as the pure vortex is destroyed gradually and fragmented into a series of interference patterns. After the VAVSS collides with the boundary walls of the 2D square trap, the density distribution of the system shows no diagonal axis symmetry concerning the leading diagonals of the 2D square trap, which is evidently different from the case of the pure vortex. The present work provides an additional criterion or alternative scheme for detecting the VAVSS. In addition, this scheme can also distinguish two degenerate VAVSS and discriminate the VAVSS with equal superposition ratio from those with unequal ratio.
We investigate the properties of the vortex-antivortex superposed state for a Bose-Einstein condensate confined in a harmonic potential. The density distribution of the vortex-antivortex superposed state has a petal structure which is determined by the quantum circulations and proportion of the vortex and antivortex. Based on the Gross-Pitaevskii equation, we show that this vortex-antivortex superposed state can be stable through both analytical derivation and numerical calculations. Furthermore, we propose a feasible scheme to generate a coherently superposed vortex-antivortex state with arbitrary proportion by compressing and rehabilitating the harmonic trap with specific time order, which is proven by numerical simulations.
We study a confined mixture of bosons and fermions in the quantal degeneracy regime with attractive boson-fermion interaction. We discuss the effect that the presence of vortical states and the displacement of the trapping potentials may have on mixtures near collapse, and investigate the phase stability diagram of the K-Rb mixture in the mean-field approximation supposing in one case that the trapping potentials felt by bosons and fermions are shifted from each other, as it happens in the presence of a gravitational sag, and in another case, assuming that the Bose condensate sustains a vortex state. In both cases, we have obtained an analytical expression for the fermion effective potential when the Bose condensate is in the Thomas-Fermi regime, that can be used to determine the maxima of the Fermionic density. We have numerically checked that the values one obtains for the location of these maxima using the analytical formulas remain valid up to the critical boson and fermion numbers, above which the mixture collapses.