35 research outputs found
Momentum distribution and contacts of one-dimensional spinless Fermi gases with an attractive p-wave interaction
We present a rigorous study of momentum distribution and p-wave contacts of
one dimensional (1D) spinless Fermi gases with an attractive p-wave
interaction. Using the Bethe wave function, we analytically calculate the
large-momentum tail of momentum distribution of the model. We show that the
leading () and sub-leading terms () of the
large-momentum tail are determined by two contacts and , which we
show, by explicit calculation, are related to the short-distance behaviour of
the two-body correlation function and its derivatives. We show as one increases
the 1D scattering length, the contact increases monotonically from zero
while exhibits a peak for finite scattering length. In addition, we
obtain analytic expressions for p-wave contacts at finite temperature from the
thermodynamic Bethe ansatz equations in both weakly and strongly attractive
regimes.Comment: 19 pages,2 figure
Transition from Tonks-Girardeau gas to super-Tonks-Girardeau gas as an exact many-body dynamics problem
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.Comment: 4 pages, 4 figures, version to appear in Phys. Rev. A as a Rapid
Communicatio
Realization of effective super Tonks-Girardeau gases via strongly attractive one-dimensional Fermi gases
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 behaviour 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, we find that they are
equivalent to ideal particles obeying more exclusive statistics than
Fermi-Dirac statistics.Comment: 4 pages, 2 figure
Quantum criticality of a one-dimensional Bose-Fermi mixture
The one-dimensional interacting Bose-Fermi mixtures, exhibiting quantum phase
transitions at zero temperature, are particularly valuable for the study of
quantum critical phenomena. In the present paper, we analytically study quantum
phase diagram, equation of state and quantum criticality of the Bose-Fermi
mixture using the thermodynamic Bethe ansatz equations. We show that
thermodynamical properties display universal scaling behaviour at quantum
criticality. Furthermore, quantum criticality of the Bose-Fermi mixture in an
harmonic trap is also studied within the local density approximation. We thus
demonstrate that the phase diagram and critical properties of the bulk system
provide insights into understanding universal features of many-body critical
phenomena.Comment: 8 pages, 7 figure
Quantum criticality and universal scaling of strongly attractive spin-imbalanced Fermi gases in a 1D harmonic trap
We investigate thermodynamics and quantum criticality of strongly attractive
Fermi gases confined in a one-dimensional (1D) harmonic trap. Finite
temperature density profiles, entropy, compressibility and susceptibility of
the trapped gas are studied using analytic results for the thermodynamics
within the local density approximation. We demonstrate that current experiments
are capable of measuring universal Tomonaga-Luttinger liquid physics and
quantum criticality of 1D strongly interacting Fermi gases. The results provide
insights on recent measurements of key features of the phase diagram of a
spin-imbalanced atomic Fermi gas [Liao et al., Nature 467, 567 (2010)] and
point to further study of quantum critical phenomena in ultracold atomic Fermi
gases.Comment: 4 pages, 4 new figures, revised versio