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arXiv:1406.4632 · Physical Review Letters

Peltier Cooling of Fermionic Quantum Gases

Charles Grenier, Antoine Georges, Corinna Kollath

Published Nov 12, 2014• 30 citations
arXivHTMLPDF

Abstract

We propose a cooling scheme for fermionic quantum gases, based on the principles of the Peltier thermoelectric effect and energy filtering. The system to be cooled is connected to another harmonically trapped gas acting as a reservoir. The cooling is achieved by two simultaneous processes: (i) the system is evaporatively cooled, and (ii) cold fermions from deep below the Fermi surface of the reservoir are injected below the Fermi level of the system, in order to fill the "holes" in the energy distribution. This is achieved by a suitable energy dependence of the transmission coefficient connecting the system to the reservoir. The two processes can be viewed as simultaneous evaporative cooling of particles and holes. We show that both a significantly lower entropy per particle and faster cooling rate can be achieved in this way than by using only evaporative cooling.

DOI
10.1103/physrevlett.113.200601

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We propose a cooling scheme for fermionic quantum gases, based on the principles of the Peltier thermoelectric effect and energy filtering. The system to be cooled is connected to another harmonically trapped gas acting as a reservoir. The cooling is achieved by two simultaneous processes: (i) the system is evaporatively cooled, and (ii) cold fermions from deep below the Fermi surface of the reservoir are injected below the Fermi level of the system, in order to fill the "holes" in the energy distribution. This is achieved by a suitable energy dependence of the transmission coefficient connecting the system to the reservoir. The two processes can be viewed as simultaneous evaporative cooling of particles and holes. We show that both a significantly lower entropy per particle and faster cooling rate can be achieved in this way than by using only evaporative cooling.
This brief review presents the emerging field of mesoscopic physics with cold atoms, with an emphasis on thermal and ‘thermoelectric’ transport, i.e. coupled transport of particles and entropy. We review in particular the comparison between theoretically predicted and experimentally observed thermoelectric effects in such systems. We also show how combining well-designed transport properties and evaporative cooling leads to an equivalent of the Peltier effect with cold atoms, which can be used as a new cooling procedure with improved cooling power and efficiency compared to the evaporative cooling currently used in atomic gases. This could lead to a new generation of experiments probing strong correlation effects of ultracold fermionic atoms at low 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.
The evaporative cooling of a two-component mixture of trapped atomic fermions into quantum degeneracy is investigated using the semiclassical Boltzmann equation for fermions. The influence of Fermi blocking for temperatures well below the Fermi temperature is discussed. Comparison between collisional and relaxation rates for a Fermi degenerate gas are made, and the similarities and differences between the cooling kinetics of the Fermi gas mixture and a mixture of classical gases is investigated, and discussed using a simple model. The latter also serves to clarify the processes which terminate the cooling in the quantum degenerate regime. Finally, a brief discussion of mean-field effects is given.
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.
Summary form only given. Magnetic trapping and evaporative cooling have been employed to cool a million /sup 40/K atoms to below the Fermi temperature, T/sub P/. Simultaneous evaporation of spin-mixed samples is used to overcome the lack of s-wave collisions between spin-polarized fermionic atoms at these ultralow temperatures. By releasing the gas from the magnetic trap and allowing it to expand, the energy and momentum distributions of this quantum degenerate gas were measured. Consistent with Fermi-Dirac (FD) quantum statistics, the total energy in the gas is higher than the classical expectation at the same temperature. Further, the momentum distribution was shown to be non-Gaussian (non-classical) and also congruent with FD statistics.
The collective Raman cooling of trapped one- and two-component Fermi gases is considered. We obtain the quantum master equation that describes laser cooling in the festina lente regime, for which the heating due to photon reabsorption can be neglected. For the two-component case the collisional processes are described within the formalism of the quantum Boltzmann master equation. The inhibition of the spontaneous emission can be overcome by properly adjusting the spontaneous Raman rate during the cooling. Our numerical results, based on Monte Carlo simulations of the corresponding rate equations, show that three-dimensional temperatures of the order of 0.08 T F (single component) and 0.03 T F (two components) can be achieved. We investigate the statistical properties of the equilibrium distribution of the laser-cooled gas, showing that the number fluctuations are enhanced compared with the thermal distribution close to the Fermi surface. Finally, we analyse the heating related to the background losses, concluding that our laser-cooling scheme should maintain the temperature of the gas without significant additional losses.