Pairing in a three-component Fermi gas

Paananen, Tomi; Martikainen, Jani-Petri; Törmä, Païvi

doi:10.1103/physreva.73.053606

Cited by 66 publications

(73 citation statements)

References 32 publications

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“…Some recent works have investigated the relevant problem of imbalanced Fermi gases at finite temperature [16,17,18]. However, there are only few recent theoretical studies exploring, concomitantly, the temperature effects and the stability of population and mass imbalanced Fermi gases [14,19,20,21].…”

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Temperature effects in a Fermi gas with population imbalance

Caldas¹,

Mota²

2008

J. Stat. Mech.

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We investigate temperature effects in a Fermi gas with imbalanced spin populations. From the general expression of the thermal gap equation we find, in weak coupling limit, an analytical expression for the transition temperature Tc as a function of various possibilities of chemical potential and mass asymmetries between the two particle species. For a range of asymmetry between certain specific values, this equation always has two solutions for Tc which has been interpreted as a reentrant phenomena or a pairing induced by temperature effect. We show that the lower Tc is never related to a stable solution. The same results are obtained in strong coupling limit. The thermodynamical potential is carefully analyzed to avoid the consideration of the unstable solutions. We also obtain the tricritical points for the chemical potential and mass imbalanced cases, and beyond these points we properly minimize the thermodynamic potential to find the stable and metastable first order transition lines. The recent advances in experiments with ultracold fermionic atoms have provided the possibility for the understanding of superfluidity in several physical situations, from high temperature superconductivity to the pairing of quarks in the cores of neutron stars.When a two fermion species system have the same number of spin-up and spin-down particles, its ground state is described by the well known Bardeen-CooperSchrieffer (BCS) theory of superconductivity [1]. In this case, if the temperature is below a certain critical temperature (T c ), fermions with opposite spins interact near their common Fermi surface resulting in pair formation, even at arbitrarily weak coupling. For temperatures above T c the system is found to be in the normal state i.e., the fermions are unpaired. [6,7], and also the possibility of new coexisting phases in the BEC regime [8]. Other pairing mechanisms beyond BCS, such as P-wave superfluidity, have also been investigated [9]. Observation of phase separation between a fully paired superfluid core surrounded by the unpaired excess atoms, have been reported independently by the Rice [10,11] and MIT [12,13] groups. This phase separation can be viewed in terms of three phase transitions of different nature. Differently from the standard BCS thermodynamical phase transition we mentioned above, in an imbalanced system the phase * hcaldas@ufsj.edu.br † motaal@ufsj.edu.br transitions that may happen are: I. At zero temperature (T ), increasing the chemical potential or number asymmetry the system undergoes a (first-order) quantum phase transition to the normal state [6]; II. Still at T = 0, first order phase transitions occur from the normal to a phase separation (PS) phase, and from PS to a spatially homogeneous (magnetized) superfluid as the interaction parameter 1/k F a is varied [8,14], with a tricritical point sitting in the fully polarized line [14], and III. Lowering the temperature, a system with different and fixed number particles phase separates into a unpolarized superfluid core surrounded by a pol...

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Temperature effects in a Fermi gas with population imbalance

Caldas¹,

Mota²

2008

J. Stat. Mech.

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“…How will pairing occur in such a system: Will the individual components compete, and only two of them form pairs, while the third component remains a spectator, or will the lowest-energy state of the system be a three-body bound state [19,20,21]? There are predictions for a phase transition between a superfluid and trionic phase in optical lattices, which can be treated analogous to baryon formation in QCD [22].…”

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Collisional Stability of a Three-Component Degenerate Fermi Gas

et al. 2008

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We report on the creation of a degenerate Fermi gas consisting of a balanced mixture of atoms in three different hyperfine states of 6 Li. This new system consists of three distinguishable Fermions with different and tunable interparticle scattering lengths a12, a13 and a23. We are able to prepare samples containing 5 · 10 4 atoms in each state at a temperature of about 215 nK, which corresponds to T /TF ≈ 0.37. We investigated the collisional stability of the gas for magnetic fields between 0 and 600 G and found a prominent loss feature at 130 G. From lifetime measurements we determined three-body loss coefficients, which vary over nearly three orders of magnitude.

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“…Furthermore, pairing [23,28,29], stability [30], and breached pairing [31] have recently been studied in a three-component fermionic mixtures. However, these theoretical approaches did not consider situations directly relevant to ongoing experiments and also did not study how the many-body effects due to the presence of the third component influence the properties of the other two components.…”

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Induced Interactions and the Superfluid Transition Temperature in a Three-Component Fermi Gas

et al. 2009

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We study many-body contributions to the effective interaction between fermions in a threecomponent Fermi mixture. We find that effective interactions induced by the third component can lead to a phase diagram different from that predicted if interactions with the third component are neglected. As a result, in a confining potential a superfluid shell structure can arise even for equal populations of the components. We also find a critical temperature for the BCS transition in a 6 Li mixture which can deviate strongly from the one in a weakly interacting two-component system.By using Feshbach resonances to change the effective interaction between ultracold atoms several groups have probed the crossover from the Bardeen-CooperSchrieffer (BCS) superfluid to a Bose-Einstein condensate of molecules [1][2][3][4][5][6][7][8][9][10]. Studies of the crossover have provided important insights into fermionic superfluids around the unitarity limit of strong interactions. Importantly, it has become experimentally feasible to study also more complicated mixtures than Fermi gases with two different atomic internal states. Bose-Fermi mixtures [11,12] and Bose-Einstein condensates with many components have been created using many different setups [13,14]. Also, heteronuclear Fermi-Fermi mixtures [15,16] and even heteronuclear Fermi-Fermi-Bose mixtures [17] have been recently demonstrated. In yet another breakthrough a three-component Fermi mixture of atoms in the three lowest hyperfine states of 6 Li [18,19] has also been demonstrated. Such multicomponent systems have some intriguing similarities with quark matter counterparts where color superconductivity may appear [20].The purpose of this Letter is to explore how the induced interactions due to the third component modify the expected behavior of three-component mixtures. This is important because, depending on parameters, the many-body effects can change the effective interaction between atoms substantially and on occasion even change the relative magnitudes of couplings between different components. Such changes imply that phase diagrams predicted using only two-body scattering properties can be incorrect. Also, even when the corrections to the effective interactions are weak, they can cause large changes to the critical temperature for the BCS transition. Indeed, for a two component system Gorkov and MelikBarkhudarov (GM) showed [21] that the perturbative correction to the effective interaction can reduce the critical temperature by a constant factor of (4e) 1/3 ≈ 2.22 in the weak-coupling limit. Also in spin-density imbalanced systems such corrections have been shown to have a considerable effect [22]. Here we will analyze the effects of analogous corrections on the three component system and find important changes to the GM result. As an interesting consequence of these many-body corrections we predict in a spatially varying confining potential (typically harmonic trap) the appearance of superfluid shell structures even in the absence of population imbalance (polarization)...

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Pairing in a three-component Fermi gas

Cited by 66 publications

References 32 publications

Temperature effects in a Fermi gas with population imbalance

Temperature effects in a Fermi gas with population imbalance

Collisional Stability of a Three-Component Degenerate Fermi Gas

Induced Interactions and the Superfluid Transition Temperature in a Three-Component Fermi Gas

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