Bound States in a Quasi-Two-Dimensional Fermi Gas

Abstract

We consider the problem of N identical fermions of mass m " and one distinguishable particle of mass m # interacting via short-range interactions in a confined quasi-two-dimensional (quasi-2D) geometry. For N ¼ 2 and mass ratios m " =m # < 13:6, we find non-Efimov trimers that smoothly evolve from 2D to 3D. In the limit of strong 2D confinement, we show that the energy of the N þ 1 system can be approximated by an effective two-channel model. We use this approximation to solve the 3 þ 1 problem and we find that a bound tetramer can exist for mass ratios m " =m # as low as 5 for strong confinement, thus providing the first example of a universal, non-Efimov tetramer involving three identical fermions. DOI: 10.1103/PhysRevLett.110.055304 PACS numbers: 67.85.Àd, 05.30.Fk, 34.50.Às An understanding of the few-body problem can be important for gaining insight into the many-body system. In dimensions higher than one, few-body bound states can, for instance, impact the statistics of the many-body quasiparticle excitations. Indeed, for fermionic systems, the two-body bound state is fundamental to the understanding of the BCS-BEC crossover [1][2][3][4], while the existence of three-body bound states of fermions [5,6] with unequal masses can lead to dressed trimer quasiparticles in the highly polarized Fermi gas [7]. Even in one dimension (1D), few-body bound states can impact the many-body phase: It has already been shown that one can have a Luttinger liquid of trimers [8].In general, attractively interacting bosons readily form bound clusters, with the celebrated example being the Efimov effect in 3D [9]. Here, there is a universal hierarchy of trimer states for resonant short-range interactions, while clusters of four or more bosons can also form [10][11][12][13]. Even in the limit of a 2D geometry, where the Efimov effect is absent, both trimers [14] and tetramers [15] have been predicted. On the other hand, bound states of identical fermions are constrained to have odd angular momentum owing to Pauli exclusion and thus, even for attractive interactions, identical fermions are subject to a centrifugal barrier. For short-range s-wave [16] interactions in 3D, non-Efimov trimers consisting of two identical fermions with mass m " and one distinguishable particle with mass m # can only exist above the critical mass ratio m " =m # ' 8:2 [5], while Efimov trimers only appear once m " =m # * 13:6 [17]. However, the existence of larger (N þ 1)-body bound states involving N > 2 identical fermions remains largely unknown-it has only recently been shown that Efimov tetramers exist in 3D [18].In this Letter, we investigate the problem of N identical fermions interacting with one distinguishable particle in a confined quasi-2D geometry, where the centrifugal barrier is reduced and the binding of fermions should be favored. Such 2D geometries have recently been realised in ultracold atomic Fermi gases [19][20][21][22][23], where the fermions are confined to 2D with an effective harmonic potential. In addition to allowing one to ...

Born-Oppenheimer study of two-component few-particle systems under one-dimensional confinement

“…Kartavtsev and Malykh [41] found that universal (nonEfimov) fermionic states in 3D exist for mass ratios β [43] established that these states are continuously connected as confinement is increased. It is interesting to speculate whether the fermionic state that appears in 1D at β −1 = 1 (β −1 ≈ 1.170 in our calculation) is continuously connected to these universal trimer states in higher dimensions.…”

“…In 2D, Levinsen and Parish [43] found a critical mass ratio of β −1 ≈ 5.0. It is interesting to speculate whether these states are continuously connected to each other, and to the universal state that appears in these calculations at β −1 ≈ 2.0 for negativeparity fermions.…”

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Pairing and radio-frequency spectroscopy in two-dimensional Fermi gases

“…[4], implications of the quasi-2D nature of the gas seem to be unavoidable since the Fermi energy was larger than the level splitting in the tightly confined direction. The formalism constructed for molecule formation in quasi-2D systems [60] has recently been extended to study the polaron problem [64] and could be used to investigate the rf spectroscopy of quasi-2D systems.…”