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arXiv:cond-mat/0607138 · Physical Review Letters

Color Superfluidity and “Baryon” Formation in Ultracold Fermions

Ákos Rapp, Gergely Zaránd, Carsten Honerkamp A, Walter Hofstetter

Published Apr 18, 2007• 221 citations
arXivHTMLPDF

Abstract

We study fermionic atoms of three different internal quantum states (colors) in an optical lattice, which are interacting through attractive on site interactions, U<0. Using a variational calculation for equal color densities and small couplings, |U|<|UC|, a color superfluid state emerges with a tendency to domain formation. For |U|>|UC|, triplets of atoms with different colors form singlet fermions (trions). These phases are the analogies of the color superconducting and baryonic phases in QCD. In ultracold fermions, this transition is found to be of second order. Our results demonstrate that quantum simulations with ultracold gases may shed light on outstanding problems in quantum field theory.

DOI
10.1103/physrevlett.98.160405

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arXiv:0910.0648•Physical Review A•Oct 14, 2009•41 citations
We study fermionic atoms of three different internal quantum states (colors) in an optical lattice, which are interacting through attractive on site interactions, U<0. Using a variational calculation for equal color densities and small couplings, |U|<|UC|, a color superfluid state emerges with a tendency to domain formation. For |U|>|UC|, triplets of atoms with different colors form singlet fermions (trions). These phases are the analogies of the color superconducting and baryonic phases in QCD. In ultracold fermions, this transition is found to be of second order. Our results demonstrate that quantum simulations with ultracold gases may shed light on outstanding problems in quantum field theory.
To investigate ultracold fermionic atoms of three internal states (colors) in an optical lattice, subject to strong attractive interaction, we study the attractive three-color Hubbard model in infinite dimensions by using a variational approach. We find a quantum phase transition between a weak-coupling superconducting phase and a strong-coupling trionic phase where groups of three atoms are bound to a composite fermion. We show how the Gutzwiller variational theory can be reformulated in terms of an effective field theory with three-body interactions and how this effective field theory can be solved exactly in infinite dimensions by using the methods of dynamical mean field theory.
We investigate three-component (colors) fermionic atoms with anisotropic attractive interactions in optical lattices at half filling using the dynamical mean field theory. In the weakly interacting region the color superfluid (CSF) state emerges, where atoms with two of three colors form the Cooper pairs. As the interaction is increased, a first-order quantum phase transition to the trionic state occurs, where singlet bound states of three different color atoms are formed. We show that the trionic state survives up to a fairly large anisotropic region. The phase diagram for the CSF and trionic states is obtained.
In optical lattices attractive ultracold fermions with three hyperfine-spin components (colors) can form three fermionic configurations depending on the interactions---unbound fermions, on-site trions, and off-site trions---leading to the coexistence of multiple fermionic species in the ordered phase, which demonstrates that the attractive three-color fermions are unique from other correlated fermion systems and may host intriguing phases and phase transitions. At temperatures below the superexchange energy scale, we employ the determinant quantum Monte Carlo (QMC) method to investigate the phases and phase transitions in the half-filled attractive three-color Hubbard model on a honeycomb lattice where the Hubbard interactions are color dependent (anisotropic interactions) and the coupling between color 3 and colors (1, 2) serves as a control parameter. In the coupling regime where on-site and off-site trions coexist, our QMC simulations demonstrate coexisting N\'eel and charge density wave (CDW) orders which are common in condensed matter but rare in ultracold atoms. At weak coupling where the color superfluid (CSF) order is scattered by color-3 fermions, we find that very small coupling of color 3 with colors (1, 2) can destroy the CSF order and that the vanishing of the CSF order is not immediately accompanied by the emergence of the on-site trionic phase, which strikingly disagrees with the prevalent results of dynamical mean-field theory. The underlying mechanisms of the coexisting N\'eel/CDW orders and of the CSF order breaking are also presented based on intuitive physical pictures.
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.
Abstract. We study the phase diagram of an SU(3)-symmetric mixture of three-component ultracold fermions with attractive interactions in an optical lattice, including the additional effect on the mixture of an effective three-body constraint induced by three-body losses. We address the properties of the system in D ≥ 2 by using dynamical mean-field theory and variational Monte Carlo techniques. The phase diagram of the model shows a strong interplay between magnetism and superfluidity. In the absence of the three-body constraint (no losses), the system undergoes a phase transition from a color superfluid phase to a trionic phase, which shows additional particle density modulations at half-filling. Away from the particle-hole symmetric point the color superfluid phase is always spontaneously magnetized, leading to the formation of different color superfluid domains in systems where the total number of particles of each species is conserved. This can be seen as the SU(3) symmetric realization of a more general tendency to phase-separation in three-component Fermi mixtures. The three-body constraint strongly disfavors the trionic phase, stabilizing a (fully magnetized) color superfluid also at strong coupling. With increasing temperature we observe a transition to a non-magnetized SU(3) Fermi liquid phase.ar X iv
We investigate the finite-temperature properties of attractive three-component (colors) fermionic atoms in optical lattices using a self-energy functional approach. As the strength of the attractive interaction increases in the low-temperature region, we observe a second-order transition from a Fermi liquid to a color superfluid (CSF), where atoms from two of the three colors form Cooper pairs. In the strong attractive region, we observe a first-order transition from a CSF to a trionic state, where three atoms with different colors form singlet bound states. A crossover between a Fermi liquid and a trionic state is observed in the high-temperature region. We present a phase diagram covering zero to finite temperatures. We demonstrate that the CSF transition temperature is enhanced by the anisotropy of the attractive interaction.