Universal properties of Fermi gases in one dimension

Abstract

In this Rapid Communication, we investigate the universal properties of a spin-polarized twocomponent Fermi gas in one dimension (1D) using Bethe ansatz. We discuss the quantum phases and phase transitions by obtaining exact results for the equation of state, the contact, the magnetic susceptibility and the contact susceptibility, giving a precise understanding of the 1D analogue of the Bose-Einstein condensation and Bardeen-Cooper-Schrieffer crossover in three dimension (3D) and the associated universal magnetic properties. In particular, we obtain the exact form of the magnetic susceptibility χ ∼ 1/ √ T exp(−∆/T ) at low temperatures, where ∆ is the energy gap and T is the temperature. Moreover, we establish exact upper and lower bounds for the relation between polarization P and the contact C for both repulsive and attractive Fermi gases. Our findings emphasize the role of the pair fluctuations in strongly interacting 1D fermion systems that can shed light on higher dimensions. In the past decade, remarkable progresses have been made in the study of strongly interacting fermions in three-dimensional (3D) Bose-Einstein condensate(BEC)-Bardeen-Cooper-Schrieffer (BCS) crossover [1-4], including precise measurements of equations of states (EOS) [5][6][7][8], the investigations of magnetic and pairing/depairing phenomena [9][10][11] and polaron [12][13][14][15] in a spin polarized system. In addition, the 2D Fermi gas has also been realized and attracted a lot of attention both experimentally [16][17][18][19][20][21][22][23] and theoretically [24][25][26][27][28]. Despite these advances, fundamental questions still remain. In particular, what is the role of pair fluctuations on thermodynamics and transport phenomena, especially in the vicinity of transition temperature at unitarity.Similar questions can be answered in a more affirmative manner in the case of 1D Fermi gases due to the existence of exactly solvable models. Recently, dramatical progresses have been made in the experimental realizations of many exactly solvable models of 1D interacting bosons and fermions [29,30]. One naturally expects to gain deeper insight into the 1D analogue of the 3D BEC-BCS crossover as well as the associated universal thermodynamics from the Bethe ansatz perspective. In fact, the precise equation of state obtained from the thermodynamic Bethe ansatz (TBA) equations [31] not only gives rise to important characteristics of the Tomonaga-Luttinger liquids (TLL) but also * The authors WBH and YYC contributed equally to the calculations in this paper.provides universal laws, such as quantum scalings, dimensionless ratios, Tan's contact and universal relations between macroscopic properties [32][33][34], which could shed new light on many-body phenomena in higher dimensions. However, a complete derivation of the thermodynamics of an arbitrarily polarized gas and the role of pair fluctuation in 1D systems still remain a challenging problem in the field of cold atoms [25,30,35,36].In this Rapid Communication, we show that the TBA equati...

Low-dimensional fluctuations and pseudogap in Gaudin-Yang Fermi gases

“…In this way, we can check the validity of our approach in these parameter regimes. We note that these results are also consistent with the TBA [91].…”

Emergent s-wave interactions between identical fermions in quasi-one-dimensional geometries

“…We observe the q1D odd-wave contact parameter anticipated by Refs. [41][42][43][44][45][46] for the first time, and compare it to theoretical predictions. These correlations are found for a range of magnetic fields and confinement strengths that span −10 (k F o ) −1 0, as shown in Fig.…”

Probing open- and closed-channel p-wave resonances

“…Strong p-wave interactions are rare in nature, so their extreme tunability in ultracold systems [1,2] is an opportunity for discovery [3][4][5]. Despite recent advances in understanding, such as universal relations for p-wave systems [6][7][8][9][10], open questions remain, including the effect of confinement on Feshbach dimers [11][12][13][14][15][16][17][18][19][20][21][22][23] and correlation strength [24][25][26]. One-dimensional systems hold the prospect for duality between strongly interacting odd waves and weakly interacting even waves [27][28][29][30], for a topological phase transition in two-dimensional systems [31,32], and for engineered states [33][34][35].…”