We investigate single‐particle quantum states of degenerate fermions, which interact repulsively with a Bose‐Einstein condensate in a rotating harmonic trap. The boson‐fermion coupling partially lifts the degeneracies of the fermionic energy spectrum in a slow rotating regime, and causes level discontinuities of occupied states upon the formation of quantized vortices in the condensate. In a fast rotating regime, the Fermi energy is located in a highly quasidegenerate single band, and hence the lowest‐Landau‐level description is applicable. The probability of finding fermions on the vortex cores is significantly enhanced when the numbers of vortices and fermions are comparable. However, increasing the number of fermions expands the fermionic cloud outward, and phase separation occurs due to the Pauli pressure while the shape of the bosonic condensate remains unchanged.
We investigate single‐particle quantum states of degenerate fermions, which interact repulsively with a Bose‐Einstein condensate in a rotating harmonic trap. The boson‐fermion coupling partially lifts the degeneracies of the fermionic energy spectrum in a slow rotating regime, and causes level discontinuities of occupied states upon the formation of quantized vortices in the condensate. In a fast rotating regime, the Fermi energy is located in a highly quasidegenerate single band, and hence the lowest‐Landau‐level description is applicable. The probability of finding fermions on the vortex cores is significantly enhanced when the numbers of vortices and fermions are comparable. However, increasing the number of fermions expands the fermionic cloud outward, and phase separation occurs due to the Pauli pressure while the shape of the bosonic condensate remains unchanged.
By minimizing the coupled mean-field energy functionals, we investigate the ground-state properties of a rotating atomic boson-fermion mixture in a two-dimensional parabolic trap. At high angular frequencies in the mean-field lowest-Landau-level regime, quantized vortices enter the bosonic condensate, and a finite number of degenerate fermions form the maximum-density-droplet state. As the boson-fermion coupling constant increases, the maximum density droplet develops into a lower-density state associated with the phase separation, revealing characteristics of a Landau-level structure.
Vortices can form when finite quantal systems are set rotating. In the limit of small particle numbers, the vortex formation in a harmonically trapped fermion system, with repulsively interacting particles, shows similarities to the corresponding boson system, with vortices entering the rotating cloud for increasing rotation. For a larger number of fermions, N ≳ 15, the fermion vortices compete and co-exist with (Chamon–Wen) edge-reconstructed ground states, forcing some ground states, as for example the central single vortex, into the spectrum of excited states. Experimentally, the fermion system could, for instance, be electrons in a semiconductor heterostructure, a quantum dot, and the corresponding boson system, a Bose–Einstein condensate in a magneto optical trap.
We calculate the spectrum of low-lying collective excitations in a mesoscopic cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas as a function of the boson-fermion repulsions. The cloud is under isotropic harmonic confinement and its dynamics is treated in the collisional regime by using the equations of generalized hydrodynamics with inclusion of surface effects. For large numbers of bosons, we find that as the cloud moves towards spatial separation (demixing) with increasing boson-fermion coupling, the frequencies of a set of collective modes show a softening followed by a sharp upturn. This behavior permits a clear identification of the quantum phase transition. We propose a physical interpretation for the dynamical transition point in a confined mixture, leading to a simple analytical expression for its location.
Vortices can form when finite quantal systems are set to rotate. In the limit of small particle numbers the vortex formation in a harmonically trapped fermion system, with repulsively interacting particles, shows similarities to the corresponding boson system, with vortices entering the rotating cloud for increasing rotation. We show that for a larger number of fermions, N≳15, the fermion vortices compete and co-exist with (Chamon-Wen) edge-reconstructed ground states, forcing some ground states, for instance the central single vortex, into the spectrum of excited states. Experimentally, the fermion system could for instance be a semiconductor heterostructure, a quantum dot, and the corresponding boson system a magneto optical trap (MOT).
We study a single quantized vortex in the fermionic component of a mixture of Fermi superfluid and Bose-Einstein condensate. As the density ratio between the boson and the fermion components is tuned, we identify a transition in the vortex-core structure, across which fermions in the vortex core become completely depleted even in the weak-coupling Bardeen-Cooper-Schrieffer regime. This is accompanied by changes in key properties of the vortex state, as well as by the localization of the Bose-Einstein condensate in the vortex core. The transition in the vortex-core structure can be experimentally probed in Bose-Fermi superfluid mixtures by detecting the size and visibility of the vortices.
I review free and trapped Bose‐Einstein condensates (BECs) [1, 2, 3, 4, 5]. In an isotropic harmonic potential V(r) = 12Mω2r2, the single‐particle ground state introduces a new intrinsic scale of length [the ground‐state size d = ℏ/(Mω)] and energy [the ground‐state energy E0 = 32ℏω]. When the trap rotates [6, 7, 8], there is a critical angular velocity for the appearance of one or a few quantized vortices. For more rapid rotation [9, 10, 11, 12, 13] the condensate contains a vortex array. The resulting centrifugal forces expand the condensate radially and shrink it axially; thus the condensate becomes effectively two‐dimensional. If the external rotation speed approaches the frequency of the radial harmonic confining potential, the condensate enters the “lowest‐Landau‐level” regime, and a simple description again becomes possible [14, 15]. Eventually, the system is predicted to make a quantum phase transition to a highly correlated state analogous to the fractional quantum Hall states of electrons in a strong magnetic field [16, 17, 18, 19, 20].