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arXiv:1207.0459 · Physical Review Letters

Bound States in a Quasi-Two-Dimensional Fermi Gas

Jesper Levinsen, Meera M. Parish

Published Jan 29, 2013• 42 citations
arXivHTMLPDF

Abstract

We consider the problem of $N$ identical fermions of mass ${m}_{\ensuremath{\uparrow}}$ and one distinguishable particle of mass ${m}_{\ensuremath{\downarrow}}$ interacting via short-range interactions in a confined quasi-two-dimensional (quasi-2D) geometry. For $N=2$ and mass ratios ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}<13.6$, 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 $N+1$ system can be approximated by an effective two-channel model. We use this approximation to solve the $3+1$ problem and we find that a bound tetramer can exist for mass ratios ${m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}$ 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

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We consider the problem of NNN identical fermions of mass m\ensuremath↑{m}_{\ensuremath{\uparrow}}m\ensuremath↑​ and one distinguishable particle of mass m\ensuremath↓{m}_{\ensuremath{\downarrow}}m\ensuremath↓​ interacting via short-range interactions in a confined quasi-two-dimensional (quasi-2D) geometry. For N=2N=2N=2 and mass ratios m\ensuremath↑/m\ensuremath↓<13.6{m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}<13.6m\ensuremath↑​/m\ensuremath↓​<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+1N+1N+1 system can be approximated by an effective two-channel model. We use this approximation to solve the 3+13+13+1 problem and we find that a bound tetramer can exist for mass ratios m\ensuremath↑/m\ensuremath↓{m}_{\ensuremath{\uparrow}}/{m}_{\ensuremath{\downarrow}}m\ensuremath↑​/m\ensuremath↓​ as low as 5 for strong confinement, thus providing the first example of a universal, non-Efimov tetramer involving three identical fermions.
We consider the problem of three distinguishable fermions confined to a quasi-two-dimensional (quasi-2D) geometry, where there is a strong harmonic potential in one direction. We go beyond previous theoretical work and investigate the three-body bound states (trimers) for the case where the two-body short-range interactions between fermions are unequal. Using the scattering parameters from experiments on ultracold 6Li^{6}\mathrm{Li}6Li atoms, we calculate the trimer spectrum throughout the crossover from two to three dimensions. We find that the deepest Efimov trimer in the 6Li^{6}\mathrm{Li}6Li system is unaffected by realistic quasi-2D confinements, while the first excited trimer smoothly evolves from a three-dimensional-like Efimov trimer to an extended 2D-like trimer as the attractive interactions are decreased. We furthermore compute the excited trimer wave function and quantify the stability of the trimer against decay into a dimer and an atom by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry, thus opening the door to realizing long-lived trimers in three-component Fermi gases.
This thesis concerns quasi-two-dimensional (quasi-2D) ultracold Fermi systems with short range interactions. Here, quasi-2D geometries are those that lie between two- and three-dimensions. We study few- and many-body systems composed of two or three distinguishable species of fermions. Of principle interest are the bound states that form in these systems and how these bound states are affected by the quasi-2D geometries. In the first research chapter, we focus on the two-dimensional (2D) regime of quasi- 2D. We begin by developing an effective 2D model of this 2D-like geometry. We use this model to analyse a Fermi system consisting of three fermionic species with equal interactions between all distinguishable pairs. Starting with the few-body problem, we show that there is always a three-body bound state (trimer) in the effective 2D model and that these 2D trimers are stable. This is notably different from the extremely unstable ‘Efimov’ trimers found in three-dimensional (3D) systems. Using a low-density expansion and a variational approach, we investigate the fate of the 2D trimers as the system’s density is increased from the three-body limit to the many-body limit. We find that remnants of trimers can persist in the form of strong three-body correlations in the many-body system. In the second research chapter, we analyse a realistic experimental system of three distinguishable fermions confined to quasi-2D. We develop a model that goes beyond the previous chapter in two regards. Firstly, we allow for unequal interactions between the pairs of fermions. Secondly, we use a full quasi-2D model that is not specific to the 2D-like regime. With this general model, we use the scattering and confinement parameters from experiments on ultracold 6Li atoms to calculate the trimer spectrum across the dimensional crossover from 2D to 3D. We show that one state smoothly evolves from an unstable 3D-like trimer to a 2D-like trimer as the attractive interactions are decreased. We furthermore compute the trimer wave function and quantify the stability of the trimer with respect to three-body recombination by determining the probability that three fermions approach each other at short distances. Our results indicate that the lifetime of the trimer can be enhanced by at least an order of magnitude in the quasi-2D geometry. This opens the door to realising long-lifetime trimers in ultracold gas experiments and furthermore, the many-body state of trimers predicted in the preceding chapter. vii In the final research chapter, we examine an alternative approach to accessing quasi-2D geometries by using a system of coupled 2D planes. We study the two-component Fermi gas in this geometry, as a preliminary to studying the three-component gas. We find that the interplanar coupling can be tuned to drive a dimensional crossover from 2D to 3D. We study the effect of this dimensional crossover on the two- and many-body systems. In general, we find that two-body correlations are strengthened by weakening the coupling between 2D planes. In the many-body system, we use mean-field theory to find that the critical temperature of pairing is increased by weakening the coupling between 2D planes. This represents a first step towards a more general representation of quasi-2D geometries, namely: A system of coupled quasi-2D planes.
We study universal clusters in quasi-two-dimensions (q2D) that consist of a light (L) atom interacting with two or three heavy (H) identical fermions, forming the trimer or tetramer bound state. The axial confinement in q2D is shown to lift the threefold degeneracy of three-dimensional trimer (tetramer) in p -wave channel and uniquely select the ground state with magnetic angular momentum | m | = 1 ( m = 0 ). By varying the interaction or confinement strength, we explore the dimensional crossover of these clusters from 3D to 2D, characterized by a gradual change of critical H-L mass ratio for their emergence and momentum-space distribution. Importantly, we find that a finite effective range will not alter their critical mass ratios in the weak coupling regime. There, we establish an effective 2D model to quantitatively reproduce the properties of q2D clusters, and further identify the optimal interaction strengths for their detections in experiments. Our results suggest a promising prospect for observing universal clusters and associated high-order correlation effects in realistic q2D ultracold Fermi mixtures. Published by the American Physical Society 2024
The dimensionality of a system can fundamentally impact the behavior of interacting quantum particles. Classic examples range from the fractional quantum Hall effect to high-temperature superconductivity. As a general rule, one expects confinement to favor the binding of particles. However, attractively interacting bosons apparently defy this expectation: While three identical bosons in three dimensions can support an infinite tower of Efimov trimers, only two universal trimers exist in the two-dimensional case. Here, we reveal how these two limits are connected by investigating the problem of three identical bosons confined by a harmonic potential along one direction. We show that the confinement breaks the discrete Efimov scaling symmetry and successively destroys the weakest bound trimers. However, the deepest bound trimers persist even under strong confinement. In particular, the ground-state Efimov trimer hybridizes with the two-dimensional trimers, yielding a superposition of trimer configurations that effectively involves tunneling through a short-range repulsive barrier. Our results suggest a way to use strong confinement to engineer more stable Efimov-like trimers, which have so far proved elusive.
We investigate a two-species Fermi gas in which one species is confined in a two-dimensional plane (2D) or one-dimensional line (1D) while the other is free in the three-dimensional space (3D). We discuss the realization of such a system with the interspecies interaction tuned to resonance. When the mass ratio is in the range 0.0351<m_(2D)/m_(3D)<6.35 for the 2D-3D mixture or 0.006 46<m_(1D)/m_(3D)<2.06 for the 1D-3D mixture, the resulting system is stable against the Efimov effect and has universal properties. We calculate key quantities in the many-body phase diagram. Other possible scale-invariant systems with short-range few-body interactions are also elucidated.
We investigate the three-body properties of two identical "up" fermions and one distinguishable "down" atom interacting in a strongly confined two-dimensional geometry. We compute exactly the atom-dimer scattering properties and the three-body recombination rate as a function of collision energy and mass ratio m_up/m_down. We find that the recombination rate for fermions is strongly energy dependent, with significant contributions from higher partial waves at low energies. For m_up < m_down, the s-wave atom-dimer scattering below threshold is completely described by the scattering length. Furthermore, we examine the "up-up-down" bound states (trimers) appearing at large m_up/m_down and find that the energy spectrum for the deepest bound trimers resembles that of a hydrogen atom confined to two dimensions.