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arXiv:1211.3866 · Physical Review Letters

Metastable Criticality and the Super Tonks-Girardeau Gas

Miłosz Panfil, Jacopo De Nardis, Jean-Sébastien Caux

Published Mar 20, 2013• 37 citations
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Abstract

We consider a 1D Bose gas with attractive interactions in a highly excited state containing no bound states. We show that in this so-called super Tonks-Girardeau gas, relaxation processes are suppressed, making the system metastable over long time scales. We compute dynamical correlation functions, revealing the structure of excitations, an enhancement of umklapp correlations and new branches due to intermediate bound states. These features give a clear signature of the super Tonks-Girardeau regime and can be used to experimentally identify it. We demonstrate that, despite its off-equilibrium nature, the system displays critical behavior: correlation functions are characterized by asymptotic power-law decay described by the Luttinger liquid framework.

DOI
10.1103/physrevlett.110.125302

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We consider a 1D Bose gas with attractive interactions in a highly excited state containing no bound states. We show that in this so-called super Tonks-Girardeau gas, relaxation processes are suppressed, making the system metastable over long time scales. We compute dynamical correlation functions, revealing the structure of excitations, an enhancement of umklapp correlations and new branches due to intermediate bound states. These features give a clear signature of the super Tonks-Girardeau regime and can be used to experimentally identify it. We demonstrate that, despite its off-equilibrium nature, the system displays critical behavior: correlation functions are characterized by asymptotic power-law decay described by the Luttinger liquid framework.
We investigate the dynamics of a one-dimensional Bose gas after a quench from the Tonks-Girardeau regime to the regime of strong attractive interactions applying analytical techniques and numerical simulations. After the quench the system is found to be predominantly in an excited gaslike state, the so-called super-Tonks gas, however with a small coherent admixture of two-particle bound states. Despite its small amplitude, the latter leads to a pronounced oscillation of the local density correlation with a frequency corresponding to the binding energy of the pair. Contributions from bound states with larger particle numbers are found to be negligible.
A significant feature of the one-dimensional super Tonks-Girardeau gas is its metastable gas-like state with a stronger Fermi-like pressure than for free fermions which prevents a collapse of atoms. This naturally suggests a way to search for such strongly correlated behavior in systems of interacting fermions in one dimension. We thus show that the strongly attractive Fermi gas without polarization can be effectively described by a super Tonks-Girardeau gas composed of bosonic Fermi pairs with attractive pair-pair interaction. A natural description of such super Tonks-Girardeau gases is provided by Haldane generalized exclusion statistics. In particular, they are equivalent to ideal particles obeying more exclusive statistics than Fermi-Dirac statistics.
We provide evidence in support of a recent proposal by Astrakharchik et al for the existence of a super Tonks–Girardeau gas-like state in the attractive interaction regime of quasi-one-dimensional Bose gases. We show that the super Tonks–Girardeau gas-like state corresponds to a highly excited Bethe state in the integrable interacting Bose gas for which the bosons acquire hard-core behaviour. The gas-like state properties vary smoothly throughout a wide range from strong repulsion to strong attraction. There is an additional stable gas-like phase in this regime in which the bosons form two-body bound states behaving like hard-core bosons.
We investigate transition of a one-dimensional interacting Bose gas from a strongly repulsive regime to a strongly attractive regime, where a stable highly excited state known as the super Tonks-Girardeau gas was experimentally realized very recently. By solving exact dynamics of the integrable Lieb-Liniger Bose gas, we demonstrate that such an excited gas state can be a very stable dynamic state. Furthermore we calculate the breathing mode of the super Tonks-Girardeau gas which is found to be in good agreement with experimental observation. Our results show that the highly excited super Tonks-Girardeau gas phase can be well understood from the fundamental theory of the solvable Bose gas.
Fermi gases confined in tight one-dimensional waveguides form two-particle bound states of atoms in the presence of a strongly attractive interaction. Based on the exact solution of the one-dimensional spin-1/2 interacting Fermi gas, we demonstrate that a stable excited state with no pairing between attractive fermionic atoms can be realized by a sudden switch of interaction from the strongly repulsive regime to strongly attractive regime. Such a state is an exact fermionic analog of the experimentally observed super-Tonks-Girardeau state of bosonic Cesium atoms [Science 325, 1224 (2009)] and should be possible to be observed by the experiment. The frequency of the lowest breathing mode of the fermionic super-Tonks-Girardeau gas is calculated as a function of the interaction strength, which could be used as a detectable signature for the experimental observation.
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.