Effective theory for ultracold strongly interacting fermionic atoms in two dimensions

Abstract

We propose a minimal theoretical model for the description of a two-dimensional (2D) strongly interacting Fermi gas confined transversely in a tight harmonic potential, and present accurate predictions for its equation of state and breathing mode frequency. We show that the minimal model Hamiltonian needs at least two independent interaction parameters, the 2D scattering length and effective range of interactions, in order to quantitatively explain recent experimental measurements at nonzero filling factor N/N2D, where N is the total number of atoms and N2D is the threshold number to reach the 2D limit. We therefore resolve in a satisfactory way the puzzling experimental observations of reduced equations of state and reduced quantum anomaly in breathing mode frequency, due to small yet non-negligible N/N2D. We argue that a conclusive demonstration of the much-anticipated quantum anomaly is possible at a filling factor of a few percent. Our establishment of the minimal model for 2D ultracold atoms could be crucial to understanding the fermionic Berezinskii-Kosterlitz-Thouless transition in the strongly correlated regime.Two-dimensional (2D) quantum many-body systems are of great interest, due to the interplay of reduced dimensionality and strong correlation, which leads to enhanced quantum and thermal fluctuations [1] and a number of ensuing quantum phenomena such as Berezinskii-Kosterlitz-Thouless (BKT) physics [2,3]. In this respect, the recently realized 2D Fermi gas of ultracold 6 Li and 40 K atoms under a tight axial confinement provides a unique platform [4,5], with unprecedented controllability particularly on interatomic interactions. To date, many interesting properties of ultracold 2D Fermi gases have been thoroughly experimentally explored [5], including the equation of state (EoS) at both zero temperature [6,7] and finite temperature [8,9], radio-frequency spectroscopy [10][11][12], pair momentum distribution [13], firstorder correlation function and BKT transition [14], and quantum anomaly in breathing mode frequency [15][16][17]. These results may shed light on understanding other important strongly correlated 2D systems, such as high-T c layered cuprate materials [18], 3 He submonolayers [19], exciton-polariton condensates [20] and neutron stars [21].The present theoretical model of ultracold 2D Fermi gases is simple [4,5]. Under a tight harmonic confinement with trapping frequency ω z along the axial z-axis and a weak confinement ω ⊥ in the transverse direction, the kinematic 2D regime is reached when the number of atoms N is smaller than a threshold N 2D ≃ (ω z /ω ⊥ ) 2 , so all the atoms are forced into the ground state of the motion along z [5]. The interatomic interactions are then described by a single s-wave scattering length a 2D [6], which is related to a 3D scattering length a 3D via the quasi-2D scattering amplitude [22]. Various experimental data have been compared and benchmarked with different theoretical predictions of the simple 2D model [23][24][25][26][27][28][29][30][31][32]. For ...

Quantum fluctuations in a strongly interacting Bardeen-Cooper-Schrieffer polariton condensate at thermal equilibrium

“…We note that the model Hamiltonian also describes a strongly interacting Fermi gas of ultracold atoms near a narrow Feshbach resonance [24], which unfortunately suffers from severe atom loss [35]. A nearequilibrium high-density exciton-polariton therefore realizes an interesting example to explore the many-body physics with large effective range of interactions [35][36][37].…”

Few-Body Perspective of a Quantum Anomaly in Two-Dimensional Fermi Gases

“…Surprisingly, the measured quantum anomaly, about 2 − 3%, is still at the same level as in the first observation [7]. This unexpected, much reduced quantum anomaly is now understood as a result of a significant effective range of interactions induced by the tight axial confinement [12][13][14] that is necessary to restrict the motion of atoms into two dimensions [12,15]. An approximate many-body theory that takes into account Gaussian pair fluctuations (GPF) has then been developed, giving rise to a qualitative explanation for the experimental observation [13].…”

Role of the confinement-induced effective range in the thermodynamics of a strongly correlated Fermi gas in two dimensions

“…Instead, it is caused by a confinement-induced effective range of interactions, which is negative and turns out be significant under the current experimental conditions [38]. By adopting a twochannel model to account for the effective range, both measurements on low-temperature EoS and breathing mode anomaly can now be satisfactorily explained by calculations at zero temperature [39].…”

“…The determination of the effective range R s is also straightforward. We require that the two-body T -matrix T 2B (E + ) and the quasi-2D scattering amplitude share the same pole or the same binding energy ε B [39]. For the former, it is readily seen from Eq.…”

“…(26) to calculate R s . In this way, we can determine the dimensionless ratio R s /a 2 s as a function of a z /a 3D [39].…”