Simulation of two-flavor symmetry-locking phases in ultracold fermionic mixtures

Abstract

We describe an ultracold fermionic set-up where it is possible to synthesize a superfluid phase with symmetry obtained by locking independent invariance groups of the normal state. In this phase, named two-flavors symmetry-locking phase (TFSL), non-Abelian fractional vortices with semi-integer flux and gapless non-Abelian Goldstone modes localized on them appear. Considerations on the possible experimental realization of the TFSL are also provided. [3]. The possibility to synthesize Abelian and non-Abelian gauge fields, also in the presence of optical lattices [4][5][6][7][8][9], promises a better understanding of an increasing number of relevant physical systems and new phases of gauge field theories. In the non-Abelian case, hyperfine levels of suitable atoms are typically used as internal degrees of freedom where the gauge potential is defined: an advantageous proposal is given by earth-alkaline atoms [10]. To date, only static gauge fields have been experimentally simulated, but proposals for dynamical fields recently appeared in literature [11][12][13][14][15]. A further promising and challenging application of ultracold atoms and synthetic gauge fields is the emulation of relativistic models relevant to high energy physics: recent proposals focused on 2D [16][17][18][19][20][21][22][23] These intensive efforts are also expected to progress towards a better understanding of strongly coupled nonAbelian gauge theories, like quantum chromodynamics (QCD), and potentially to give new insights on the QCD phase diagram. Indeed in QCD various problems stay unsolved, like the origin of color confinement [32], chiral symmetry breaking (CSB), as well as the dynamics of nucleons, nuclear matter or quarks under extreme conditions [33,34]. In the light of the developments mentioned above, ultracold atoms can become a precious tool in the investigation of these important topics.

Phase diagram and non-Abelian symmetry locking for fermionic mixtures with unequal interactions

“…1 are rescaled by their values of U cf /t: in this way they all meet in the point U c = U f = U cf . In this point all the different Hamiltonians have a U (4) symmetry and the two phases TFSL and NTFSL can be mapped onto each other, signaling a transition point between the two phases, in agreement with [39].…”

“…A step forward towards the study of symmetry-locked states was presented in [39], based on multi-component fermionic mixtures: there a proposal for the synthesis of a superfluid phase locking two non-Abelian global symmetries has been presented. This state has been denoted as a two-flavour symmetry-locked (TSFL) state.…”

Effective Control of Chemical Potentials by Rabi Coupling with RF-Fields in Ultracold Mixtures

“…coincides with the mean-field Hamiltonian (33). Interestingly, this comparison sheds light on the physical meaning of the parameter γ, yielding indeed:…”

“…Summing up, we found that the relation in (35) for the mean-field parameter γ is imposed by the request of equality between the mean-field Hamiltonians in (33) and (34), a fact physically motivated, but not trivially implied, by the equivalence of the full Hamiltonians in (21) and (5).…”

Interorbital Interactions in an SU(2)xSU(6)-Symmetric Fermi-Fermi Mixture

“…Fermi gases with SU(N = 2I + 1)-symmetric interactions as realized with alkaline-earth(-like) atoms such as Yb (nuclear spin I = 1/2 and I = 5/2) [47,48] or Sr (I = 9/2) [9,49] allowed first groundbreaking experiments on thus far unexplored phenomena like SU(N ) quantum magnetism in 1D [50], the contact in a bulk SU (6) Fermi gas [51,52] or effects of spin degeneracy like Pomeranchuk cooling in SU(N ) Mott insulators [45,[53][54][55][56][57]. Isotope mixtures of SU(N )-symmetric Fermi gases [48,58] characterized by a competition between interand intraisotope interactions hold promise to exhibit exotic d-wave superfluidity [59] or two-flavor superfluid symmetry-locking phases [60,61].…”