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arXiv:1905.10815 · Physical Review Research

Collective excitations in two-dimensional SU( N ) Fermi gases with tunable spin

Chengdong He, Zejian Ren, Bo Song, Entong Zhao, Jeongwon Lee, Yi-Cai Zhang, Shizhong Zhang, Gyu-Boong Jo

Published Jan 27, 2020• 21 citations
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Abstract

The authors realize a two-dimensional gas of SU(N) fermions, and evaluate collective mode frequencies in the system. It includes the measurements of breathing and quadrupole mode frequencies, the latter of which decreases for larger spin component N due to the enhanced interaction. The paper provides a mean-field theory in good agreement with the observation. The dimensional evolution of collective excitations from two to three dimensions and the damping rate of collective modes provides an insight that the enhanced inter-particle collisions for larger spin are important in SU(N) fermions.

DOI
10.1103/physrevresearch.2.012028

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The authors realize a two-dimensional gas of SU(N) fermions, and evaluate collective mode frequencies in the system. It includes the measurements of breathing and quadrupole mode frequencies, the latter of which decreases for larger spin component N due to the enhanced interaction. The paper provides a mean-field theory in good agreement with the observation. The dimensional evolution of collective excitations from two to three dimensions and the damping rate of collective modes provides an insight that the enhanced inter-particle collisions for larger spin are important in SU(N) fermions.
Ultracold fermions with SU(N >2) symmetry offer a unique opportunity to study quantum dynamics and interaction effects in the large spin systems that have no analogue in condensed matter physics. In this poster, we present a set of experiments on the measurement of contact parameters and collective excitations with a SU(N) Fermi gas of 173Yb atoms. First, we explore the short-range interaction effect via Tan’s contact parameters in a multi-component Fermi gas with SU(N >2) symmetry. The s-wave contact parameter is experimentally measured by recording the high-momentum tail of weakly interacting fermions. For a tunable number of spin component N with a fixed number of atoms per component, we verify the linear increase in the contact with N providing experimental confirmation of SU(N) interactions. Furthermore, we explore the momentum distribution of SU(N) fermions at the low momentum regime. Next, we measure collective excitations of a harmonically trapped twodimensional SU(N) Fermi gas. Various collective modes are investigated with a tunable number of spin component N showing a decrease in the ratio of quadruple and dipole mode with N. Our work will pave the way for the experimental study of interacting SU(N) Fermi gases with large spin.
We calculate the collective modes of ultracold trapped alkaline-earth-metal fermionic atoms, which possess an SU(N\mathrm{SU}(NSU(N) symmetry of the nuclear spin degree of freedom and a controllable NNN, with NNN as large as 10. We calculate the breathing and quadrupole modes of two-dimensional and three-dimensional harmonically trapped gases in the normal phase. We particularly concentrate on two-dimensional gases, where the shift is more accessible experimentally, and the physics has special features. We present results as a function of temperature, interaction strength, density, and NNN. We include calculations across the collisionless to hydrodynamic crossover. We assume the gas is interacting weakly, such that it can be described by a Boltzmann-Vlasov equation that includes both mean-field terms and the collision integral. We solve this with an approximate scaling ansatz, taking care in two dimensions to preserve the scaling symmetry of the system. We predict the collective-mode frequency shifts and damping, showing that these are measurable in experimentally relevant regimes. We expect these results to furnish powerful tools to characterize interactions and the state of alkaline-earth-metal gases, as well as to lay the foundation for future work, for example, on strongly interacting gases and SU(N)\mathrm{SU}(N)SU(N) spin modes.
We derive analytical expressions for the frequency and damping of the lowest collective modes of a two-dimensional Fermi gas using kinetic theory. For strong coupling, we furthermore show that pairing correlations overcompensate the effects of Pauli blocking on the collision rate for a large range of temperatures, resulting in a rate which is larger than that of a classical gas. Our results agree well with experimental data, and they recover the observed crossover from collisionless to hydrodynamic behavior with increasing coupling for the quadruple mode. Finally, we show that a trap anisotropy within the experimental bounds results in a damping of the breathing mode which is comparable to what is observed, even for a scale-invariant system.
We investigate collective excitations of a harmonically trapped two-dimensional Fermi gas from the collisionless (zero sound) to the hydrodynamic (first sound) regime. The breathing mode, which is sensitive to the equation of state, is observed with an undamped amplitude at a frequency 2 times the dipole mode frequency for a large range of interaction strengths and different temperatures. This provides evidence for a dynamical SO(2,1) scaling symmetry of the two-dimensional Fermi gas. Moreover, we investigate the quadrupole mode to measure the shear viscosity of the two-dimensional gas and study its temperature dependence.
In a recent experiment [Vogt et al., Phys. Rev. Lett. 108, 070404 (2012)], quadrupole and breathing modes of a two-dimensional Fermi gas were studied. We model these collective modes by solving the Boltzmann equation via the method of phase-space moments up to fourth order, including in-medium effects on the scattering cross section. In our analysis, we use a realistic Gaussian potential deformed by the presence of gravity and magnetic field gradients. We conclude that the origin of the experimentally observed damping of the quadrupole mode, especially in the weakly interacting (or even noninteracting) case, cannot be explained by these mechanisms.
Due to Pauli blocking of intermediate states, the scattering matrix (or TTT matrix) of two fermionic atoms in a Fermi gas becomes different from that of two atoms in free space. This effect becomes particularly important near a Feshbach resonance, where the interaction in free space is very strong but becomes effectively suppressed in the medium. We calculate the in-medium TTT matrix in ladder approximation and study its effects on the properties of collective modes of a trapped gas in the normal-fluid phase. We introduce the in-medium interaction on both sides of the Boltzmann equation, namely, in the calculation of the mean field and in the calculation of the collision rate. This allows us to explain the observed upward shift of the frequency of the quadrupole mode in the collisionless regime. By including the mean field, we also improve considerably the agreement with the measured temperature dependence of frequency and damping rate of the scissors mode, whereas the use of the in-medium cross section deteriorates the description, in agreement with previous work.