Finite-Size Effects in Strongly-Interacting Fermionic Systems
Final Report Abstract
Throughout a vast range of scales, from ultracold atomic clouds to the hot plasmas of relativistic heavy-ion collisions, strongly coupled dynamics dominates the physics. And yet, we are largely unable to describe such behaviour numerically from first principles for a variety of reasons. With respect to lattice Monte Carlo (MC) calculations, this is related to the often dubbed “infamous” sign problem. This issue, now understood as a formidable signal-to-noise problem, appears in practice as our inability to design a positive-definite probability measure needed for the computation, and it often turns up in cases of non-zero spin polarization, mass imbalance, finite quark density, and nearly every other situation of interest. Within this project, we have developed techniques to surmount this problem and used those to compute the equation of state of spin- and mass-imbalanced unitary Fermi gases from first principles for the first time. In particular, the experimental search for inhomogeneous phases in terms of the search for (stable) solitonic solutions has attracted a lot of attention very recently. Many new experimental studies of many-body phenomena with mixtures of a variety of fermion species with different masses (such as 6Li, 40K, 161Dy, 163Dy, and 167Er) are within reach in the near future, giving us an unprecedented opportunity to better our understanding of spin- and mass imbalances in strongly coupled Fermi gases and push our understanding of more exotic phenomena such as the emergence of inhomogeneous phases to a whole new level. From the theory point of view, the equation of state plays a key role for our understanding of such phenomea as it describes the dynamics of ultracold Fermi gases and presently still underlies mostly our understanding of the dynamics of these gases in the presence of confining geometries. It was a key feature of this project to use a multi-tier strategy from a technical and phenomenological point of view which eventually allowed us to better our understanding of ultracold gases under extreme conditions by combining the complementary strengths and the awareness of individual draw-backs of several approaches. In particular, we have found that exotic phases associated with inhomogeneous condensates form for mass ratios of the spin-down and spin-up fermions greater than three and that the extent of the inhomogeneous phase in parameter space increases with increasing mass imbalance, already representing a testable prediction for future experiments. Together with our novel MC setup, we are now in a position to further refine these predictions and, based on our results for the EOS, to come up with quantitative predictions for the phase structure of ultracold Fermi gases and the fate of exotic phases in confining geometries.
Publications
- Finite-size and Particle-number Effects in an Ultracold Fermi Gas at Unitarity, Phys. Rev. A 84, 063616 (2011)
J. Braun, S. Diehl and M. M. Scherer
- Fermion Interactions and Universal Behavior in Strongly Interacting Theories, J. Phys. G 39, 033001 (2012)
J. Braun
(See online at https://doi.org/10.1088/0954-3899/39/3/033001) - On the Phase Structure of QCD in a Finite Volume, Phys. Lett. B 713, 216 (2012)
J. Braun, B. Klein and B. J. Schaefer
(See online at https://doi.org/10.1016/j.physletb.2012.05.053) - Imaginary polarization as a way to surmount the sign problem in Ab Initio calculations of spin-imbalanced Fermi gases, Phys. Rev. Lett. 110, 130404 (2013)
J. Braun, J. W. Chen, J. Deng, J. E. Drut, B. Friman, C. T. Ma and Y. D. Tsai
(See online at https://doi.org/10.1103/PhysRevLett.110.130404) - Fermi gases with imaginary mass imbalance and the sign problem in Monte Carlo calculations, J. Phys. G 41, 055110 (2014)
D. Roscher, J. Braun, J. W. Chen and J. E. Drut
(See online at https://doi.org/10.1088/0954-3899/41/5/055110) - Phases of spin- and mass-imbalanced ultracold Fermi gases in harmonic traps, Phys. Rev. A 89, no. 5, 053613 (2014)
J. Braun, J. E. Drut, T. Jahn, M. Pospiech and D. Roscher
(See online at https://doi.org/10.1103/PhysRevA.89.053613) - Phase structure of mass- and spin-imbalanced unitary Fermi gases, Phys. Rev. A 91, no. 5, 053611 (2015)
D. Roscher, J. Braun and J. E. Drut
(See online at https://doi.org/10.1103/PhysRevA.91.053611) - Zero-temperature equation of state of mass-imbalanced resonant Fermi gases, Phys. Rev. Lett. 114, no. 5, 050404 (2015)
J. Braun, J. E. Drut and D. Roscher
(See online at https://doi.org/10.1103/PhysRevLett.114.050404)
