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Register a new userCollective modes of ultracold fermionic alkaline-earth gases with SU(N) symmetry
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We calculate the collective modes of ultracold trapped alkaline-earth fermionic atoms, which possess an SU($N$) symmetry of the nuclear spin degree of freedom, and a controllable $N$, with $N$ 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 $N$. 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 gases, as well as to lay the foundation for future work, for example on strongly interacting gases and SU($N$) spin modes.
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We measure collective excitations of a harmonically trapped two-dimensional (2D) SU($N$) Fermi gas of $^{173}$Yb confined to a stack of layers formed by a one-dimensional optical lattice. Quadrupole and breathing modes are excited and monitored in the collisionless regime $lvertln(k_F a_{2D})rvertgg 1$ with tunable spin. We observe that the quadrupole mode frequency decreases with increasing number of spin components due to the amplification of the interaction effect by $N$ in agreement with a theoretical prediction based on 2D kinetic equations. The breathing mode frequency, however, is measured to be twice the dipole oscillation frequency regardless of $N$. We also follow the evolution of collective excitations in the dimensional crossover from two to three dimensions and characterize the damping rate of quadrupole and breathing modes for tunable SU($N$) fermions, both of which reveal the enhanced inter-particle collisions for larger spin. Our result paves the way to investigate the collective property of 2D SU($N$) Fermi liquid with enlarged spin.
We discuss the collective modes in an alkaline-earth Fermi gas close to an orbital Feshbach resonance. Unlike the usual Feshbach resonance, the orbital Feshbach resonance in alkaline-earth atoms realizes a two-band superfluid system where the fermionic nature of both the open and the closed channel has to be taken into account. We show that apart from the usual Anderson-Bogoliubov mode which corresponds to the oscillation of total density, there also appears the long-sought Leggett mode corresponding to the oscillation of relative density between the two channels. The existence of the phonon and the Leggett modes and their evolution are discussed in detail. We show how these collective modes are reflected in the density response of the system.
Ultracold fermionic alkaline earth atoms confined in optical lattices realize Hubbard models with internal SU(N) symmetries, where N can be as large as ten. Such systems are expected to harbor exotic magnetic physics at temperatures below the superexchange energy scale. Employing quantum Monte Carlo simulations to access the low-temperature regime, we show that after adiabatically loading a weakly interacting gas into the strongly interacting regime of an optical lattice, the final temperature decreases with increasing N. Furthermore, we estimate the temperature scale required to probe correlations associated with low-temperature SU(N) magnetism. Our findings are encouraging for the exploration of exotic large-N magnetic states in ongoing experiments.
We investigate a species selective cooling process of a trapped $mathrm{SU}(N)$ Fermi gas using entropy redistribution during adiabatic loading of an optical lattice. Using high-temperature expansion of the Hubbard model, we show that when a subset $N_A < N$ of the single-atom levels experiences a stronger trapping potential in a certain region of space, the dimple, it leads to improvement in cooling as compared to a $mathrm{SU}(N_A)$ Fermi gas only. We show that optimal performance is achieved when all atomic levels experience the same potential outside the dimple and we quantify the cooling for various $N_A$ by evaluating the dependence of the final entropy densities and temperatures as functions of the initial entropy. Furthermore, considering ${}^{87}{rm Sr}$ and ${}^{173}{rm Yb}$ for specificity, we provide a quantitative discussion of how the state selective trapping can be achieved with readily available experimental techniques.
We investigate the existence of symmetry-protected topological phases in one-dimensional alkaline-earth cold fermionic atoms with general half-integer nuclear spin I at half filling. In this respect, some orbital degrees of freedom are required. They can be introduced by considering either the metastable excited state of alkaline-earth atoms or the p-band of the optical lattice. Using complementary techniques, we show that SU(2) Haldane topological phases are stabilised from these orbital degrees of freedom. On top of these phases, we find the emergence of topological phases with enlarged SU(2I+1) symmetry which depend only on the nuclear spin degrees of freedom. The main physical properties of the latter phases are further studied using a matrix-product state approach. On the one hand, we find that these phases are symmetry-protected topological phases, with respect to inversion symmetry, when I=1/2,5/2,9/2,..., which is directly relevant to ytterbium and strontium cold fermions. On the other hand, for the other values of I(=half-odd integer), these topological phases are stabilised only in the presence of exact SU(2I+1)-symmetry.
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