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arXiv:2102.08656 · Physical Review A

State selective cooling of SU(N) Fermi gases

Aaron Merlin Müller, Miklós Lajkó, Florian Schreck, Frédéric Mila, Jiří Minář

Published Jul 6, 2021• 4 citations
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Abstract

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 an $\mathrm{SU}({N}_{A})$ 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 $^{87}\mathrm{Sr}$ and $^{173}\mathrm{Yb}$ for specificity, we provide a quantitative discussion of how the state selective trapping can be achieved with readily available experimental techniques.

DOI
10.1103/physreva.104.013304

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We investigate a species selective cooling process of a trapped SU(N)\mathrm{SU}(N)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 NA<N{N}_{A}<NNA​<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 an SU(NA)\mathrm{SU}({N}_{A})SU(NA​) 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 NA{N}_{A}NA​ by evaluating the dependence of the final entropy densities and temperatures as functions of the initial entropy. Furthermore, considering 87Sr^{87}\mathrm{Sr}87Sr and 173Yb^{173}\mathrm{Yb}173Yb for specificity, we provide a quantitative discussion of how the state selective trapping can be achieved with readily available experimental techniques.
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We calculate experimentally relevant properties of trapped fermionic alkaline-earth-metal atoms in an optical lattice, modeled by the SU(N)(N)(N) Hubbard model. We employ a high-temperature expansion that is accurate when the temperature is larger than the tunneling rate, similar to current regimes in ultracold atom experiments. In addition to exploring the Mott insulator-metal crossover, we calculate final temperatures achieved by the standard experimental protocol of adiabatically ramping from a noninteracting gas, as a function of initial gas temperature. Of particular experimental interest, we find that increasing NNN for fixed particle numbers and initial temperatures gives substantially colder Mott insulators after the adiabatic ramping, up to more than a factor of 5 for relevant parameters. This cooling happens for all NNN, fixing the initial entropy, or for all $N\ensuremath{\lesssim}20$ (the exact value depends on dimensionality), at fixed, experimentally relevant initial temperatures.
The standard approach for generating deeply degenerate quantum gases is evaporative or sympathetic cooling in a harmonic trap, after which the gas has reached its minimum entropy. All subsequent state transformations rely on adiabatic changes of a closed system, and coupling to the environment or non-adiabatic processes monotonically increase the entropy. Here, we demonstrate that this experimental paradigm can be bypassed by utilizing species-selective trapping with a low-dissipation optical tune-out trap in a dual-species mixture. We successfully reduce the entropy of a two-component fermionic quantum gas via isothermal compression within a bosonic bath, reaching deep quantum degeneracy of T/TF=0.024+0.007T/T_F = 0.024^{+0.007}T/TF​=0.024+0.007, with TFT_FTF​ the Fermi temperature. By characterizing the cross-dimensional relaxation and thermalization, we demonstrate that cooling light fermions with heavy bosons remains efficient and fast, even deep in the degenerate regime, where the thermalization time is found to be independent of T/TFT/T_FT/TF​. Our results pave the way for direct cooling within optical lattices, box traps, or other complex potentials, thereby eliminating the reliance on adiabatic state transformations to reach strongly interacting many-body regimes.
We discuss the cooling efficiency of ultracold Fermi-Bose mixtures in species-selective traps using a thermodynamical approach. The dynamics of evaporative cooling trajectories is analyzed in the specific case of bichromatic optical dipole traps also taking into account the effect of partial spatial overlap between the Fermi gas and the thermal component of the Bose gas. We show that large trapping frequency ratios between the Fermi and the Bose species allow for the achievement of a deeper Fermi degeneracy, consolidating in a thermodynamic setting earlier arguments based on more restrictive assumptions. In particular, we confirm that the minimum temperature of the mixture is obtained at the crossover between boson and fermion heat capacities, and that below such a temperature sympathetic cooling vanishes. When the effect of partial overlap is taken into account, optimal sympathetic cooling of the Fermi species may be achieved by properly tuning the relative trapping strength of the two species in a time-dependent fashion. Alternatively, the dimensionality of the trap in the final stage of cooling can be changed by increasing the confinement strength, which also results in a crossover of the heat capacities at deeper Fermi degeneracies. This technique may be extended to Fermi-Bose degenerate mixtures in optical lattices.
The study of low density, ultracold atomic Fermi gases is a promising avenue to understand fermion superfluidity from first principles. One technique currently used to bring Fermi gases in the degenerate regime is sympathetic cooling through a reservoir made of an ultracold Bose gas. We discuss a proposal for trapping and cooling of two-species Fermi-Bose mixtures into optical dipole traps made from combinations of laser beams having two different wavelengths. In these bichromatic traps it is possible, by a proper choice of the relative laser powers, to selectively trap the two species in such a way that fermions experience a stronger confinement than bosons. As a consequence, a deep Fermi degeneracy can be reached having at the same time a softer degenerate regime for the Bose gas. This leads to an increase in the sympathetic cooling efficiency and allows for higher precision thermometry of the Fermi - Bose mixture.
Summary form only given. Evaporative cooling of atoms in an optical trap has recently received renewed attention as a means for obtaining degeneracy in an optically trapped bosonic Cs vapor as well as a fermionic Li gas. We have developed a new model describing the evaporative cooling process for atoms confined in a time-dependent optical potential formed by a single focused Gaussian laser beam. We find that a substantial increase in the phase-space density can be obtained by adiabatically reducing the trap laser power and thereby the trap well depth as a function of time. Since we are specifically interested in the evaporative cooling of fermionic /sup 6/Li atoms, we have included the effect of Fermi statistics in the model. Although the collision rate is suppressed as the temperature T is reduced below the Fermi temperature T/sub F/, we find that values of T/T/sub F//spl Lt/1 can be achieved for suitable initial conditions.