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arXiv:1702.02772 · Physical Review A

Thermometry of a deeply degenerate Fermi gas with a Bose-Einstein condensate

Rianne S. Lous, Isabella Fritsche, Michael Jag, Bo Huang, Rudolf Grimm

Published May 23, 2017• 39 citations
arXivHTMLPDF

Abstract

We measure the temperature of a deeply degenerate Fermi gas, by using a weakly interacting sample of heavier bosonic atoms as a probe. This thermometry method relies on the thermalization between the two species and on the determination of the condensate fraction of the bosons. In our experimental implementation, a small sample of $^{41}\mathrm{K}$ atoms serves as the thermometer for a $^{6}\mathrm{Li}$ Fermi sea. We investigate the evaporative cooling of a $^{6}\mathrm{Li}$ spin mixture in a single-beam optical dipole trap and observe how the condensate fraction of the thermometry atoms depends on the final trap depth. From the condensate fraction, the temperature can be readily extracted. We show that the lowest temperature of 5.9(5)% of the Fermi temperature is obtained, when the decreasing trap depth closely approaches the Fermi energy. To understand the systematic effects that may influence the results, we carefully investigate the role of the number of bosons and the thermalization dynamics between the two species. Our thermometry approach provides a conceptually simple, accurate, and general way to measure the temperature of deeply degenerate Fermi gases. Since the method is independent of the specific interaction conditions within the Fermi gas, it applies to both weakly and strongly interacting Fermi gases.

DOI
10.1103/physreva.95.053627

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We measure the temperature of a deeply degenerate Fermi gas, by using a weakly interacting sample of heavier bosonic atoms as a probe. This thermometry method relies on the thermalization between the two species and on the determination of the condensate fraction of the bosons. In our experimental implementation, a small sample of 41K^{41}\mathrm{K}41K atoms serves as the thermometer for a 6Li^{6}\mathrm{Li}6Li Fermi sea. We investigate the evaporative cooling of a 6Li^{6}\mathrm{Li}6Li spin mixture in a single-beam optical dipole trap and observe how the condensate fraction of the thermometry atoms depends on the final trap depth. From the condensate fraction, the temperature can be readily extracted. We show that the lowest temperature of 5.9(5)% of the Fermi temperature is obtained, when the decreasing trap depth closely approaches the Fermi energy. To understand the systematic effects that may influence the results, we carefully investigate the role of the number of bosons and the thermalization dynamics between the two species. Our thermometry approach provides a conceptually simple, accurate, and general way to measure the temperature of deeply degenerate Fermi gases. Since the method is independent of the specific interaction conditions within the Fermi gas, it applies to both weakly and strongly interacting Fermi gases.
This thesis presents studies of quantum degenerate atomic gases of fermionic 6Li and bosonic 7Li. Degeneracy is reached by evaporative cooling of 7Li in a strongly confining magnetic trap. Since at low temperatures direct evaporative cooling is not possible for a polarized fermionic gas, 6Li is sympathetically cooled by thermal contact with 7Li. In a first series of experiments both isotopes are trapped in their low-field seeking higher hyperfine states. A Fermi degeneracy of is achieved for 105 fermions. For more than ~300 atoms, the 7Li condensate collapses, due to the attractive interatomic interaction in this state. This limits the degeneracy reached for both species. To overcome this limit, in a second series of experiments 7Li and 6Li atoms are transferred to their low field seeking lower hyperfine states, where the boson-boson interaction is repulsive but weak. The inter-isotope collisions are used to thermalize the mixture. A 7Li Bose-Einstein condensate (BEC) of 104 atoms immersed in a Fermi sea is produced. The BEC is quasi-one-dimensional and the thermal fraction can be negligible. The measured degeneracies are . The temperature is measured using the bosonic thermal fraction, which vanishes at the lowest temperatures, limiting our measurement sensitivity. In a third series of experiments, the bosons are transferred into an optical trap and their internal state is changed to , the lowest energy state. A Feshbach resonance is detected and used to produce a BEC with tunable atomic interactions. When the effective interaction between atoms is tuned to be small and attractive, we observe the formation of a matter-wave bright soliton. Propagation of the soliton without spreading over a macroscopic distance of 1.1~mm is observed.
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.
We compare strategies for evaporative and sympathetic cooling of two-species Fermi-Bose mixtures in single-color and two-color optical dipole traps. We show that in the latter case a large heat capacity of the bosonic species can be maintained during the entire cooling process. This could allow one to efficiently achieve a deep Fermi degeneracy regime having at the same time a significant thermal fraction for the Bose gas, crucial for a precise thermometry of the mixture. Two possible signatures of a superfluid phase transition for the Fermi species are discussed.
Abstract We report a new apparatus for the study of two-species quantum degenerate mixture of 41 K and 6 Li atoms. We develop and combine several advanced cooling techniques to achieve both a large atom number and high phase space density of the two-species atom clouds. Furthermore, we build a high efficiency two-species magnetic transport system to transfer atom clouds from the 3D magneto-optical-trap chamber to a full glass science chamber of an extreme high vacuum environment and good optical access. We perform a forced radio-frequency evaporative cooling for 41 K atoms while the 6 Li atoms are sympathetically cooled in an optically plugged magnetic trap. Finally, we achieve the simultaneous quantum degeneracy for the 41 K and 6 Li atoms. The Bose–Einstein condensate of 41 K has 1.4 × 10 5 atoms with a condensate fraction of about 62%, while the degenerate Fermi gas of 6 Li has a total atom number of 5.4 × 10 5 at 0.25 Fermi temperature.
Experimental methods of laser and evaporative cooling, used in the production of atomic Bose-Einstein condensates have recently been extended to realize quantum degeneracy in trapped Fermi gases. Fermi gases are a new rich system to explore the implications of Pauli exclusion on scattering properties of the system, and ultimately fermionic superfluidity. We have produced a new macroscopic quantum system, in which a degenerate Li-6 Fermi gas coexists with a large and stable Na-23 BEC. This was accomplished using inter-species sympathetic cooling of fermionic 6Li in a thermal bath of bosonic Na-23. We have achieved high numbers of both fermions (less than 10(exp 5) and bosons (less than 10(exp 6), and Li-6 quantum degeneracy corresponding to one half of the Fermi temperature. This is the first time that a Fermi sea was produced with a condensate as a "refrigerator".
Thermometry is essential for studying many-body physics with ultracold atoms. Accurately measuring low temperatures in these systems, however, remains a significant challenge due to the absence of a universal thermometer. Most widely applicable methods, such as fitting of in situ density profiles, are limited by the requirement of global thermal equilibrium and inapplicability to homogeneous systems. In this Letter, we introduce a novel in situ thermometry for quantum gases, leveraging single-atom-resolved measurements via quantum gas microscopy, and demonstrate it on an ideal Fermi gas. By analyzing number fluctuations in probe volumes containing as little as one atom on average, we extract both global and local temperatures over a broad dynamic range. Our method does not rely on the fluctuation-dissipation theorem and is based instead on the exact relationship between number fluctuations and density-density correlations. In the low-temperature regime, it allows us to observe significant deviations from fluctuation-dissipation predictions, uncovering subextensive fluctuations. Our method is applicable to systems with arbitrary trapping potentials, requiring neither precise trap calibration nor global thermal equilibrium. This thermometer for quantum gases overcomes key limitations of existing techniques, paving the way for more accurate and versatile temperature measurements in ultracold quantum systems.