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arXiv:1707.09923 · Physical Review A

Color superfluidity of neutral ultracold fermions in the presence of color-flip and color-orbit fields

Dog̃a Murat Kürkçüog̃lu, C. A. R. Sá de Melo

Published Feb 22, 2018• 16 citations
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Abstract

We describe how color superfluidity is modified in the presence of color-flip and color-orbit fields in the context of ultracold atoms and discuss connections between this problem and that of color superconductivity in quantum chromodynamics. We study the case of $s$-wave contact interactions between different colors and we identify several superfluid phases, with five being nodal and one being fully gapped. When our system is described in a mixed-color basis, the superfluid order parameter tensor is characterized by six independent components with explicit momentum dependence induced by color-orbit coupling. The nodal superfluid phases are topological in nature and the low-temperature phase diagram of the color-flip field versus the interaction parameter exhibits a pentacritical point, where all five nodal color superfluid phases converge. These results are in sharp contrast to the case of zero color-flip and color-orbit fields, where the system has perfect U(3) symmetry and possesses a superfluid phase that is characterized by fully gapped quasiparticle excitations with a single complex order parameter with no momentum dependence and by inert unpaired fermions representing a nonsuperfluid component. In the latter case, just a crossover between a Bardeen-Cooper-Schrieffer and a Bose-Einstein-condensation superfluid occurs. Furthermore, we analyze the order parameter tensor in a total pseudospin basis, investigate its momentum dependence in the singlet, triplet, and quintet sectors, and compare the results with the simpler case of spin-1/2 fermions in the presence of spin-flip and spin-orbit fields, where only singlet and triplet channels arise. Finally, we analyze in detail spectroscopic properties of color superfluids in the presence of color-flip and color-orbit fields, such as the quasiparticle excitation spectrum, momentum distribution, and density of states to help characterize all the encountered topological quantum phases, which can be realized in fermionic isotopes of lithium, potassium, and ytterbium atoms with three internal states trapped.

DOI
10.1103/physreva.97.023632

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We describe how color superfluidity is modified in the presence of color-flip and color-orbit fields in the context of ultracold atoms and discuss connections between this problem and that of color superconductivity in quantum chromodynamics. We study the case of sss-wave contact interactions between different colors and we identify several superfluid phases, with five being nodal and one being fully gapped. When our system is described in a mixed-color basis, the superfluid order parameter tensor is characterized by six independent components with explicit momentum dependence induced by color-orbit coupling. The nodal superfluid phases are topological in nature and the low-temperature phase diagram of the color-flip field versus the interaction parameter exhibits a pentacritical point, where all five nodal color superfluid phases converge. These results are in sharp contrast to the case of zero color-flip and color-orbit fields, where the system has perfect U(3) symmetry and possesses a superfluid phase that is characterized by fully gapped quasiparticle excitations with a single complex order parameter with no momentum dependence and by inert unpaired fermions representing a nonsuperfluid component. In the latter case, just a crossover between a Bardeen-Cooper-Schrieffer and a Bose-Einstein-condensation superfluid occurs. Furthermore, we analyze the order parameter tensor in a total pseudospin basis, investigate its momentum dependence in the singlet, triplet, and quintet sectors, and compare the results with the simpler case of spin-1/2 fermions in the presence of spin-flip and spin-orbit fields, where only singlet and triplet channels arise. Finally, we analyze in detail spectroscopic properties of color superfluids in the presence of color-flip and color-orbit fields, such as the quasiparticle excitation spectrum, momentum distribution, and density of states to help characterize all the encountered topological quantum phases, which can be realized in fermionic isotopes of lithium, potassium, and ytterbium atoms with three internal states trapped.
We describe the emergence of color superfluidity in ultra-cold fermions induced by color-orbit and color-flip fields that transform a conventional singlet-pairing s-wave system into an unconventional non-s-wave superfluid with quintuplet pairing. We show that the tuning of interactions, color-orbit and color-flip fields transforms a momentum-independent scalar order parameter into an explicitly momentum-dependent tensor order parameter. We classify all unconventional superfluid phases in terms of the {\it loci} of zeros of their quasi-particle excitation spectrum in momentum space and we identify several Lifshitz-type topological transitions. Furthermore, when boundaries between phases are crossed, non-analyticities in the compressibility arise. We find a quintuple point, which is also pentacritical, where four gapless superfluid phases converge into a fully gapped superfluid phase.
We discuss topological phase transitions in ultracold Fermi superfluids induced by interactions and artificial spin-orbit fields. We construct the phase diagram for population-imbalanced systems at zero and finite temperatures, and analyze spectroscopic and thermodynamic properties to characterize various phase transitions. For balanced systems, the evolution from Bardeen-Cooper-Schrieffer to Bose-Einstein-condensate superfluids in the presence of spin-orbit effects is only a crossover as the system remains fully gapped, even though a triplet component of the order parameter emerges in the helicity basis. However, for imbalanced populations, spin-orbit fields induce a triplet component for the order parameter in the helicity basis, and may produce nodes in the quasiparticle excitation spectrum leading to bulk topological phase transitions of the Lifshitz type. Additionally a fully gapped phase exists, where a crossover from indirect to direct gap occurs, but a topological transition to a gapped phase possessing Majorana fermion edge states does not occur.
We describe the quantum phases of interacting three component fermions in the presence of spin-orbit coupling, as well as linear and quadratic Zeeman fields. We classify the emerging superfluid phases in terms of the loci of zeros of their quasi-particle excitation spectrum in momentum space, and we identify several Lifshitz-type topological transitions. In the particular case of vanishing quadratic Zeeman field, a quintuple point exists where four gapless superfluid phases with surface and line nodes converge into a fully gapped superfluid phase. Lastly, we also show that the simultaneous presence of spin-orbit and Zeeman fields transforms a momentum-independent scalar order parameter into an explicitly momentum-dependent tensor in the generalized helicity basis.
We study ultracold color fermions with three internal states, red, green, and blue, with SU(3)\mathrm{SU}(3)SU(3) symmetry in optical lattices, when color-orbit coupling and color-flip fields are present. This system corresponds to a generalization of two internal state fermions with SU(2)\mathrm{SU}(2)SU(2) symmetry in the presence of spin-orbit coupling and spin-flipping Zeeman fields. We investigate the eigenspectrum and Chern numbers to describe different topological phases that emerge in the phase diagrams of color-orbit coupled fermions in optical lattices. We obtain the phases as a function of artificial magnetic, color-orbit, and color-flip fields that can be independently controlled. For fixed artificial magnetic flux ratio, we identify topological quantum phases and phase transitions in the phase diagrams of chemical potential versus color-flip fields or color-orbit coupling, where the chirality and number of midgap edge states changes. The topologically nontrivial phases are classified in three groups: The first group has total nonzero chirality and exhibits only the quantum charge Hall effect; the second group has total nonzero chirality and exhibits both quantum charge and quantum color Hall effects; and the third group has total zero chirality but exhibits the quantum color Hall effect. These phases are generalizations of the quantum Hall and quantum spin Hall phases for charged spin-1/21/21/2 fermions. Lastly, we also describe the color density of states and a staircase structure in the total and color filling factors versus chemical potential for fixed color-orbit coupling, color-flip field, and magnetic flux ratio. We show the existence of incompressible states at rational filling factors precisely given by a gap labelling theorem that relates the filling factors to the magnetic flux ratio and topological quantum numbers.
Abstract The gapless Weyl superfluid has been widely studied in the three-dimensional ultracold fermionic superfluid. In contrast to Weyl superfluid, there exists another kind of gapless superfluid with topologically protected nodal lines, which can be regarded as the superfluid counterpart of nodal line semimetal in the condensed matter physics, just as Weyl superfluid with Weyl semimetal. In this paper we study the ground states of the cold fermionic gases in cubic optical lattices with one-dimensional spin-orbit coupling and transverse Zeeman field and map out the topological phase diagram of the system. We demonstrate that in addition to a fully gapped topologically trivial phase, some different nodal line superfluid phases appear when the Zeeman field is adjusted. The presence of topologically stable nodal lines implies the dispersionless zero-energy flat band in a finite region of the surface Brillouin zone. Experimentally these nodal line superfluid states can be detected via the momentum-resolved radio-frequency spectroscopy. The nodal line topological superfluid provide fertile grounds for exploring exotic quantum matters in the context of ultracold atoms.
We analyze the evolution of superfluidity for nonzero orbital angular momentum channels from the Bardeen-Cooper-Schrieffer (BCS) to the Bose-Einstein condensation (BEC) limit in three dimensions. First, we analyze the low-energy scattering properties of finite range interactions for all possible angular momentum channels. Second, we discuss ground-state (T=0)(T=0)(T=0) superfluid properties including the order parameter, chemical potential, quasiparticle excitation spectrum, momentum distribution, atomic compressibility, ground-state energy, and low-energy collective excitations. We show that a quantum phase transition occurs for nonzero angular momentum pairing, unlike the sss-wave case where the BCS to BEC evolution is just a crossover. Third, we present a Gaussian fluctuation theory near the critical temperature (T=Tc)(T={T}_{\mathrm{c}})(T=Tc​), and we analyze the number of bound, scattering, and unbound fermions as well as the chemical potential. Finally, we derive the time-dependent Ginzburg-Landau functional near Tc{T}_{\mathrm{c}}Tc​, and compare the Ginzburg-Landau coherence length with the zero-temperature average Cooper pair size.