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arXiv:1607.05908 · Physical Review A

Probing an effective-range-induced super fermionic Tonks-Girardeau gas with ultracold atoms in one-dimensional harmonic traps

Xiao-Long Chen, Xia-Ji Liu, Hui Hu

Published Sep 26, 2016• 4 citations
arXivHTMLPDF

Abstract

We theoretically investigate an ultracold spin-polarized atomic Fermi gas with resonant odd-channel $(p$-wave) interactions trapped in one-dimensional harmonic traps. We solve the Yang-Yang thermodynamic equations based on the exact Bethe ansatz solution, and predict the finite-temperature density profile and breathing mode frequency by using a local density approximation to take into account the harmonic trapping potential. The system features an exotic super fermionic Tonks-Girardeau (super-fTG) phase, due to the large effective range of the interatomic interactions. We explore the parameter space for such a fascinating super-fTG phase at finite temperature and provide smoking-gun signatures of its existence in both breathing mode frequencies and density profiles. Our results suggest that the super-fTG phase can be readily probed at temperatures of about $0.1{T}_{F}$, where ${T}_{F}$ is the Fermi temperature. These results are to be confronted with future cold-atom experiments with $^{6}\mathrm{Li}$ and $^{40}\mathrm{K}$ atoms.

DOI
10.1103/physreva.94.033630

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We theoretically investigate an ultracold spin-polarized atomic Fermi gas with resonant odd-channel (p(p(p-wave) interactions trapped in one-dimensional harmonic traps. We solve the Yang-Yang thermodynamic equations based on the exact Bethe ansatz solution, and predict the finite-temperature density profile and breathing mode frequency by using a local density approximation to take into account the harmonic trapping potential. The system features an exotic super fermionic Tonks-Girardeau (super-fTG) phase, due to the large effective range of the interatomic interactions. We explore the parameter space for such a fascinating super-fTG phase at finite temperature and provide smoking-gun signatures of its existence in both breathing mode frequencies and density profiles. Our results suggest that the super-fTG phase can be readily probed at temperatures of about 0.1TF0.1{T}_{F}0.1TF​, where TF{T}_{F}TF​ is the Fermi temperature. These results are to be confronted with future cold-atom experiments with 6Li^{6}\mathrm{Li}6Li and 40K^{40}\mathrm{K}40K atoms.
The fermionic Tonks-Girardeau (FTG) gas is a one-dimensional spin-polarized Fermi gas with infinitely strong attractive zero-range odd-wave interactions, arising from a confinement-induced resonance reachable via a three-dimensional ppp-wave Feshbach resonance. We investigate the off-diagonal long-range order (ODLRO) of the FTG gas subjected to a longitudinal harmonic confinement by analyzing the two-particle reduced density matrix for which we derive a closed-form expression. Using a variational approach and numerical diagonalization we find that the largest eigenvalue of the two-body density matrix is of order N∕2N∕2N∕2, where NNN is the total particle number, and hence a partial ODLRO is present for a FTG gas in the trap.
Possible signatures are discussed of a super-Tonks-Girardeau gas in bosonic systems of trapped quasi-one-dimensional dipoles at zero temperature. We provide an estimation of the frequency of the lowest compressional mode and compare it to analytical results derived using the harmonic approach in the high-density regime. We construct an exact mapping of the ground-state wave function of a one-dimensional dipolar system of bosons, fermions, and a Bose-Fermi mixture and conclude that the local properties and energy are the same at zero temperature. The question as to what extent the dipolar potential can be treated as long or short range is discussed.
A harmonically trapped, ultracold, one-dimensional (1D) spin-1 Bose gas with strongly repulsive or attractive 1D even-wave interactions induced by a three-dimensional (3D) Feshbach resonance is studied. The exact ground state, a hybrid of Tonks-Girardeau (TG) and ideal Fermi gases, is constructed in the TG limit of infinite even-wave repulsion by a spinor Fermi-Bose mapping to a spinless ideal Fermi gas. It is then shown that in the limit of infinite even-wave attraction this same state remains an exact many-body eigenstate, now highly excited relative to the collapsed generalized McGuire-cluster ground state, showing that the hybrid TG state is completely stable against collapse to this cluster ground state under a sudden switch from infinite repulsion to infinite attraction. It is shown to be the TG limit of a hybrid super-Tonks-Girardeau (STG) state, which is metastable under a sudden switch from finite but very strong repulsion to finite but very strong attraction. It should be possible to create it experimentally by a sudden switch from strongly repulsive to strongly attractive interaction, as in the recent Innsbruck experiment on a spin-polarized bosonic STG gas. In the case of strong attraction, there should also exist another STG state of much lower energy, consisting of strongly bound dimers, a bosonic analog of a recently predicted STG state which is an ultracold gas of strongly bound bosonic dimers of fermionic atoms, but it is shown that this STG state cannot be created by such a switch from strong repulsion to strong attraction.
A growing expertise to engineer, manipulate, and probe different cold-atom analogs of electronic condensed-matter systems allows to probe properties of exotic pairing. We study paired states of spin-imbalanced ultracold atomic system of fermions with attractive short-range interactions in one-dimensional traps. Calculations are done using the Bethe ansatz technique, and the trap is incorporated into the solution via a local-density approximation. The thermodynamic Bethe ansatz equations are solved numerically and different local-density profiles are calculated for zero and finite temperatures. A procedure to identify the homogeneous-system phase diagram using local-density profiles in the trap is also proposed. Such scheme would be immediately useful for the experiments.
We determine some exact static and time-dependent properties of the fermionic Tonks-Girardeau (FTG) gas, a spin-aligned one-dimensional Fermi gas with infinitely strongly attractive zero-range odd-wave interactions. We show that its two-particle reduced density matrix exhibits superconductive off-diagonal long-range order, and on a ring an FTG gas with an even number of atoms has a highly degenerate ground state with quantization of Coriolis rotational flux and high sensitivity to rotation and to external fields and accelerations. For a gas initially under harmonic confinement, we show that during an expansion the momentum distribution undergoes a "dynamical bosonization," approaching that of an ideal Bose gas without violating the Pauli exclusion principle.
A harmonically trapped ultracold 1D spinor Fermi gas with a strongly attractive 1D even-wave interaction induced by a 3D Feshbach resonance is studied. It is shown that it has two different super Tonks-Girardeau (sTG) energy eigenstates which are metastable against collapse in spite of the strong attraction, due to their close connection with 1D hard sphere Bose gases which are highly excited gaslike states. One of these sTG states is a hybrid between an sTG gas with strong $(\ensuremath{\uparrow}\ensuremath{\downarrow})$ attractions and an ideal Fermi gas with no $(\ensuremath{\uparrow}\ensuremath{\uparrow})$ or $(\ensuremath{\downarrow}\ensuremath{\downarrow})$ interactions, the sTG component being an exact analog of the recently observed sTG state of a 1D ultracold Bose gas. It should be possible to create it experimentally by a sudden switch of the $(\ensuremath{\uparrow}\ensuremath{\downarrow})$ interaction from strongly repulsive to strongly attractive, as in the recent Innsbruck experiment on the bosonic sTG gas. The other is a trapped analog of a recently predicted sTG state which is an ultracold gas of strongly bound $(\ensuremath{\uparrow}\ensuremath{\downarrow})$ fermion dimers which behave as bosons with a strongly attractive boson-boson interaction leading to sTG behavior. It is proved that the probability of a transition from the ground state for strongly repulsive interaction to this dimer state under a sudden switch from strongly repulsive to strongly attractive interaction is $\ensuremath{\ll}$111, contrary to a previous suggestion.