Strongly interacting quantum gases in one-dimensional traps

Abstract

Under second-order degenerate perturbation theory, we show that the physics of N particles with arbitrary spin confined in a one-dimensional trap in the strongly interacting regime can be described by superexchange interaction. An effective spin-chain Hamiltonian (non-translationally-invariant Sutherland model) can be constructed from this procedure. For spin-1/2 particles, this model reduces to the non-translationally-invariant Heisenberg model, where a transition between Heisenberg antiferromagnetic (AFM) and ferromagnetic (FM) states is expected to occur when the interaction strength is tuned from the strongly repulsive to the strongly attractive limit. We show that the FM and the AFM states can be distinguished by two different methods: the first is based on their distinct responses to a spin-dependent magnetic gradient, and the second is based on their distinct momentum distributions. We confirm the validity of the spin-chain model by comparison with results obtained from several unbiased techniques.

Repulsive Fermi polarons with negative effective mass

“…This is particularly true for the system of repulsive polaron, since it lies in an excited upper branch of atomic system rather than the ground state. On the other hand, one might be able to gain important insights by studying the counterpart problem in 1D, where the exact solutions can be accessible [21] and effective spin-chain models can be established in strong coupling limit [22][23][24][25][26][27][28]. For 1D fermion system, the ferromagnetic transition has been exactly proved with arbitrary number and arbitrary potential [29], and the polaron problem in continuum has also been exactly solved by McGuire in 1960's [30,31] and recently by Guan [32].…”

Interaction-induced Bloch oscillation in a harmonically trapped and fermionized quantum gas in one dimension

“…In this way, various spin-chain Hamiltonians can be constructed in response to different external perturbations, including interactions, gauge fields and trapping potentials, which have been used to address and engineer novel spin spirals and magnetic orders in 1D systems [12][13][14][15][16][17][18][19][20][21][22][23][24]. Experimentally, an anti-ferromagnetic spin chain has been recently confirmed in a small cluster of 1D trapped fermions [25].…”

“…Following this idea one can construct various spin chain models as studied in the literature [12][13][14][15][16][17][18][19][20][21][22][23][24].…”

“…[8], by adopting the concept of effective spin chain in strongly interacting atomic gases in one dimensional (1D) traps [12][13][14][15][16]. The idea of spin chain is based on the fact that for fermionized (or impenetrable) particles in one dimension, their spatial order is fixed, and the probability peak of finding the i-th ordered particle (see ρ i (x) in Fig.…”

Effective spin-chain model for strongly interacting one-dimensional atomic gases with an arbitrary spin

“…Recently, taking advantage of the high controllability of a few particles in the trapped ultra-cold systems [20], a number of studies have revealed the energy spectra and correlation effects for a few spin-1/2 fermions by numerical simulations [21][22][23][24]. In the strong coupling regime, an effective Heisenberg spin-chain model has also been deduced [25][26][27][28]. The resulted anti-ferromagnetic correlation has recently been confirmed through the tunneling measurement of a few spin-1/2 fermions in 1D traps [29].…”