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Equation of state of the unitary gas in the normal phase : diagrammatic Monte Carlo versus cold atom experiments

Understanding and simulating a large number of quantum particles with strong interactions is a challenge which remains largely open, particularly for fermonic particles. Overcoming this challenge would greatly help the search for new materials with spectacular electronic properties.

A new direction is currently explored by an international collaboration of theorists, comprising a member of the group "ultracold Fermi gases" at LKB. The idea is to perform a random walk in a space of Feynman diagrams using a Monte Carlo method. Recall that the diagrammatic formalism allows to express physical quantities of interest as a series, each term being represented by a graph. An powerful aspect of the formalism is the possibility to use "dressed propagators" : The bold lines which are used as building blocks of the graphs then themselves stand for an infinite sum of elementary graphs. Because particles with attractive interactions tend to pair up, it is natural to also introduce a dressed propagator for the pairs of particles.

All this is included in the new algorithm, allowing to sum the contributions of billions of irreducible diagrams by a single self-consistent Monte Carlo process. Convergence of the diagrammatic series was not observed at low temperatures, and divergent-series summation methods were employed. Proving the applicability of these methods to the particular series of interest is an open mathematical challenge. But an accurate test was performed, comparing the first results obtained by the new method to new experimental measurements on a unitary gas of ultracold fermonic Lithium atoms. We recall that in a unitary gas, the effect of interatomic interactions is very important, as the scattering cross-section diverges as zero energy. A gas of Lithium atoms becomes unitary when one applies an external magnetic field and tunes its value to a so-called Feshbach resonance point, where the energy of an excited state of the Li2 molecule vanishes.

The equation of state computed by the new theoretical method [1] agrees excellently with the new experiments carried out at MIT in parallel with the calculation [1,2] as well as with the earlier experiments done at LKB [3]. The next comparisons with experiments will be about the polarized gas and the critical temperature below which the gas becomes superfluid. The question of the physical nature of the normal phase, currently under debate in the context of experimental results from LKB and JILA, will also be addressed, by looking for signatures of Landau quasi-particles or of a pseudogap in the dressed propagators.

Figure 1 : Density n of the unitary gas, normalized to the density n0 of the ideal gas, as a function of the ratio between temperature and chemical potential. Blue squares : bold diagrammatic Monte Carlo calculation [1]. Red circles : MIT experiment [1]. The red dotted lines indicate the experimental uncertainty coming from the error bar on the Feshbach resonance position. Black dashed line : third order high-temperature virial expansion [4].

Figure 2 : Pressure of the unitary gas. Black diamonds : LKB experiment [3]. Other symbols as in Figure 1.

[1] K. Van Houcke, F. Werner, E. Kozik, N. Prokofev, B. Svistunov, M. Ku, A. Sommer, L. W. Cheuk, A. Schirotzek, M. W. Zwierlein, Nature Physics (2012), doi:10.1038/nphys2273 [preprint ]
[2] Mark J. H. Ku, Ariel T. Sommer, Lawrence W. Cheuk, Martin W. Zwierlein, Science 335, 563 (2012)
[3] S. Nascimbène, N. Navon, K. J. Jiang, F. Chevy, C. Salomon, Nature, 463, 1057 (2010).
[4] X.-J. Liu, H. Hu, P. D. Drummond, Phys. Rev. Lett. 102, 160401 (2009)

Contact : Félix Werner

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