We examine the breathing mode of a strongly interacting two-dimensional Fermi gas and the role of temperature on the anomalous breaking of scale invariance. By calculating the equation of state with different many-body $T$ -matrix theories and the virial expansion, we obtain a hydrodynamic equation of the harmonically trapped Fermi gas (with trapping frequency ${\ensuremath{\omega}}_{0}$) through the local density approximation. By solving the hydrodynamic equations, we determine the breathing mode frequencies as a function of interaction strength and temperature. We find that the breathing mode anomaly depends sensitively on both interaction strength and temperature. In particular, in the strongly interacting regime, we predict a significant downshift of the breathing mode frequency, below the scale invariant value of $2{\ensuremath{\omega}}_{0}$, for temperatures of the order of the Fermi temperature.We examine the breathing mode of a strongly interacting two-dimensional Fermi gas and the role of temperature on the anomalous breaking of scale invariance. By calculating the equation of state with different many-body $T$-matrix theories and the virial expansion, we obtain a hydrodynamic equation of the harmonically trapped Fermi gas (with trapping frequency ${\ensuremath{\omega}}_{0}$) through the local density approximation. By solving the hydrodynamic equations, we determine the breathing mode frequencies as a function of interaction strength and temperature. We find that the breathing mode anomaly depends sensitively on both interaction strength and temperature. In particular, in the strongly interacting regime, we predict a significant downshift of the breathing mode frequency, below the scale invariant value of $2{\ensuremath{\omega}}_{0}$, for temperatures of the order of the Fermi temperature.

arXiv:1708.06978Physical Review AMay 17, 201816 citations

Harmonically trapped quasi-two-dimensional Fermi gases with synthetic spin-orbit coupling

JingKun Wang, Jinge Chen, Ke-Ji Chen +2 more

Science China Physics Mechanics and AstronomyJul 25, 20164 citations

Breathing mode of two-dimensional atomic Fermi gases in harmonic traps

Chao Gao, Zhenhua Yu

For two-dimensional (2D) atomic Fermi gases in harmonic traps, the SO(2,1) symmetry is broken by the interatomic interaction explicitly via the contact correlation operator. Consequently, the frequency of the breathing mode ${\ensuremath{\omega}}_{B}$ of the 2D Fermi gas can be different from $2{\ensuremath{\omega}}_{0}$, with ${\ensuremath{\omega}}_{0}$ the trapping frequency of harmonic potentials. At zero temperature, we use the sum rules of density correlation functions to yield upper bounds for ${\ensuremath{\omega}}_{B}$. We further calculate ${\ensuremath{\omega}}_{B}$ through the Euler equations in the hydrodynamic regime. The obtained value of ${\ensuremath{\omega}}_{B}$ satisfies the upper bounds and shows deviation from $2{\ensuremath{\omega}}_{0}$, which can be as large as about $8%$ .For two-dimensional (2D) atomic Fermi gases in harmonic traps, the SO(2,1) symmetry is broken by the interatomic interaction explicitly via the contact correlation operator. Consequently, the frequency of the breathing mode ${\ensuremath{\omega}}_{B}$ of the 2D Fermi gas can be different from $2{\ensuremath{\omega}}_{0}$, with ${\ensuremath{\omega}}_{0}$ the trapping frequency of harmonic potentials. At zero temperature, we use the sum rules of density correlation functions to yield upper bounds for ${\ensuremath{\omega}}_{B}$. We further calculate ${\ensuremath{\omega}}_{B}$ through the Euler equations in the hydrodynamic regime. The obtained value of ${\ensuremath{\omega}}_{B}$ satisfies the upper bounds and shows deviation from $2{\ensuremath{\omega}}_{0}$, which can be as large as about $8%$.

arXiv:1208.5640Physical Review AOct 9, 201241 citations

T

-matrix theories and the virial expansion, we obtain a hydrodynamic equation of the harmonically trapped Fermi gas (with trapping frequency ${\ensuremath{\omega}}_{0}$) through the local density approximation. By solving the hydrodynamic equations, we determine the breathing mode frequencies as a function of interaction strength and temperature. We find that the breathing mode anomaly depends sensitively on both interaction strength and temperature. In particular, in the strongly interacting regime, we predict a significant downshift of the breathing mode frequency, below the scale invariant value of $2{\ensuremath{\omega}}_{0}$, for temperatures of the order of the Fermi temperature.

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