Order and Correlations in Asymmetric Superfluid Matter
Final Report Abstract
Ultracold Fermi gases have attracted considerable interest for more than 20 years by now. The high level of activity in this field can be traced back to the fact that quantum many-body phenomena, ranging from Bose-Einstein condensation (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluidity, have become accessible to experiments in a clean and very versatile way. The (experimental) control parameters are the density and the s-wave scattering length, which sets the strength of the interaction. The latter can be essentially tuned at will by an external magnetic field in the presence of a Feshbach resonance. For a sufficiently dilute Fermi gas, the range of the interaction effectively represents the smallest length scale in this many-body problem. Of particular interest is then the strongly coupled “unitary" limit associated with an infinite s-wave scattering length. Except for the density, as in a non-interacting gas, the system is scale-free in this limit. In these gases, pairing of spin-up and spin-down fermions at diametrically opposite points of the Fermi surface (i.e., Cooper pairing) typically leads to a superfluid phase at low enough temperatures, accompanied by the opening of an energy gap in the quasiparticle spectrum. In addition to the occurrence of a (homogeneous) surperfluid phase, crystalline phases (“supersolid phase") may emerge at low temperatures and finite polarizations. It is indeed still not settled whether such crystalline phases really exist in the phase diagram of the unitary Fermi gas in the plane spanned by the temperature and the polarization. From the standpoint of theory, the lack of a comprehensive understanding of this aspect is related to the so-called sign problem at finite polarization which hinders (or, at least complicates) stochastic ab initio computations of the underlying path integral. Within this project, we employed the so-called Complex-Langevin approach to surmount this problem and perform ab initio studies of correlation functions which allow to analyze pairing patterns at finite polarization and to search for indications of the existence of crystalline phases. We were able to place non-perturbative, ab initio bounds on the possible locations of crystalline phases. To be specific, for the temperatures and polarizations considered in this project, our results for the pair-momentum distribution only indicate the formation of a conventional superfluid as associated with standard BCS-type pairing. However, our results for so-called shot-noise correlations suggest that the clear signature for BCS-type pairing is washed out when the polarization is increased and other pairing channels may become increasingly favorable. This may be viewed as a precursor for the formation of crystalline phases. Our results for the pair-momentum distribution as well as the shot-noise correlations represent experimentally accessible predictions. In fact, shot-noise correlations have already been measured in two-dimensional Fermi gases. Of course, our findings do not exclude the existence of crystalline phases at even higher polarizations and lower temperatures than considered in this project. However, ab initio studies of this regime require further developments of our Complex-Langevin framework. Our novel pairing-field formalism may provide a suitable basis for these developments in the future.
Publications
-
Complex Langevin and other approaches to the sign problem in quantum many-body physics. Physics Reports, 892, 1-54.
Berger, C.E.; Rammelmüller, L.; Loheac, A.C.; Ehmann, F.; Braun, J. & Drut, J.E.
-
Pairing and the spin susceptibility of the polarized unitary Fermi gas in the normal phase. Physical Review A, 103(4).
Rammelmüller, Lukas; Hou, Yaqi; Drut, Joaquín E. & Braun, Jens
-
Pairing patterns in polarized unitary Fermi gases above the superfluid transition. Physical Review A, 105(6).
Attanasio, Felipe; Rammelmüller, Lukas; Drut, Joaquín E. & Braun, Jens
-
A lattice pairing-field approach to ultracold Fermi gases. SciPost Physics, 16(4).
Ehmann, Florian; Drut, Joaquín E. & Braun, Jens
