Fermionic Superfluidity with Imbalanced Spin Populations

Zwierlein, Martin; Schirotzek, André; Schunck, Christian H.; Ketterle, Wolfgang

doi:10.1126/science.1122318

Cited by 876 publications

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“…Ss, 03.75.Hh,74.25.Dw Recent advances in the experiments of ultracold Fermi gases have shown great potential for elucidating longstanding problems in many different fields of physics related to strongly correlated Fermions. For instance, in recent experiments [1,2,3,4,5] spin-density imbalanced, or polarized, Fermi gases were considered. Such systems make it possible to study pairing with mismatched Fermi surfaces, potentially leading to non-standard phases such as that appearing in FFLO-states [6,7] or BP-states [8] (Sarma-states).…”

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Finite-Temperature Phase Diagram of a Polarized Fermi Gas in an Optical Lattice

et al. 2007

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We present phase diagrams for a polarized Fermi gas in an optical lattice as a function of temperature, polarization, and lattice filling factor. We consider the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO), Sarma or breached pair (BP), and BCS phases, and the normal state and phase separation. We show that the FFLO phase appears in a considerable portion of the phase diagram. The diagrams have two critical points of different nature. We show how various phases leave clear signatures to momentum distributions of the atoms which can be observed after time of flight expansion.PACS numbers: 03.75. Ss, 03.75.Hh,74.25.Dw Recent advances in the experiments of ultracold Fermi gases have shown great potential for elucidating longstanding problems in many different fields of physics related to strongly correlated Fermions. For instance, in recent experiments [1,2,3,4,5] spin-density imbalanced, or polarized, Fermi gases were considered. Such systems make it possible to study pairing with mismatched Fermi surfaces, potentially leading to non-standard phases such as that appearing in FFLO-states [6,7] or BP-states [8] (Sarma-states). These possibilities have been considered extensively in condensed-matter, nuclear, and highenergy physics [9]. The experiments in trapped gases have shown clear evidence of the separation of the gas into a BCS core region and a normal state shell around it, i.e. phase separation. Although an FFLO-type state has been predicted to appear in these systems as well [10,11], it is likely to be difficult to observe since it appears in the edges of the trap except for large polarizations.Recent experiments [12,13] on Fermi gases confined in optical lattices have already demonstrated the potential of these systems for a multitude of studies of new phases, dimensionality effects, and dynamics. In this letter, we calculate the phase diagram for an attractively interacting Fermi gas in an optical lattice at zero and finite temperatures. In particular, we consider the possibility of the single mode FFLO-phase, where the order parameter is space-dependent, and of the BCS-BP phase, where compared to the standard BCS phase the excess polarization is carried by additional Bogoliubov excitations. We investigate their competition with the phase separation (PS) of the gas into normal and BCS superfluid regions. Our results reveal that a typical phase diagram as a function of polarization and temperature is as shown in Fig. 1: phase separation is expected for small polarizations and temperatures, whereas at zero temperature the FFLO state appears after some critical polarization. At a finite temperature, the FFLO-phase competes with the BCS-BP phase. As the temperature increases the BCS-BP phase becomes energetically favorable, and as the temperature is increased even further the BCS-BP phase gives way to a normal polarized Fermi gas.Furthermore, the phase diagrams reveal a Lifshitz point which is surrounded by the normal, FFLO, and BCS-BP phases. The transitions around this point are of second order, but the FFLO ph...

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Finite-Temperature Phase Diagram of a Polarized Fermi Gas in an Optical Lattice

et al. 2007

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“…However, recent experiments [18] on these systems did not show explicit evidence of the BP state or the LOFF state, rather they produced strong evidence of the phase separation at moderate mismatch. We explain in this letter that the BP state or the FF state maybe prevented to form there because of the Higgs instability induced by the mismatch.…”

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Higgs instability in gapless superfluidity/superconductivity

et al. 2007

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In this letter we explore the Higgs instability in the gapless superfluid/superconducting phase. This is in addition to the (chromo)magnetic instability that is related to the fluctuations of the Nambu-Goldstone bosonic fields. While the latter may induce a single-plane-wave LOFF state, the Higgs instability favors spatial inhomogeneity and cannot be removed without a long range force. In the case of the g2SC state the Higgs instability can only be partially removed by the electric Coulomb energy. But this does not exclude the possibility that it can be completely removed in other exotic states such as the gCFL state. 12.38.Aw, 26.60.+c Superfluidity or superconductivity with mismatched Fermi momenta appears in many systems such as the charge neutral dense quark matter, the asymmetric nuclear matter, and in imbalanced cold atomic gases. The mismatch plays the role of breaking the Cooper pairing. But it is not understood how a BCS superconductor is destroyed as the mismatch is increased. It was proposed in the 1960s that the competition between the pair breaking and the pair condensation would induce an unconventional superconducting phase, the Larkin-OvchinnikovFulde-Ferrel (LOFF) state [1]. Recently it was found that if the mismatch is larger than the gap magnitude, a gapless superconducting phase [2,3] or a breached pairing (BP) [4] can be formed in a charge neutral quark matter or in a constrained imbalanced cold atom system, respectively. Another scenario for the ground state at moderate mismatch is the phase separation[5] between of superfluid/superconducting and normal phases.Both gapless superconducting and BP phases exhibit instabilities. The former exhibits a chromomagnetic instability [6,7] while the latter a superfluid density instability [8]. Recent studies have demonstrated that this type of instability is related to the local phase fluctuation of the superconducting order parameter, i.e., the Nambu-Goldstone boson fields [9,10,11,12]. This type of instability induces the formation of the single-planewave FF-like state [13,14,15,16,17].The imbalanced cold atom systems such as the 40 K and 6 Li offer an intriguing experimental opportunity to understand the pair breaking states. However, recent experiments [18] on these systems did not show explicit evidence of the BP state or the LOFF state, rather they produced strong evidence of the phase separation at moderate mismatch. We explain in this letter that the BP state or the FF state maybe prevented to form there because of the Higgs instability induced by the mismatch. The Higgs instability is related to the magnitude fluctuation of the superconducting order parameter, i.e., the Higgs field. It causes spatial inhomogeneity that may lead to phase separation. The Higgs instability was also considered in [20], where it was named "amplitude instability".The Higgs instability is an inhomogeneous extension of the Sarma instability against a homogeneous variation of the order parameter. Consider a system described by the Hamiltonian H with a spontaneous ...

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“…Since the experiments are carried out in finite geometries, finite-size corrections need to be taken into account in a more complete analysis. Recent experiments [1,2] which have measured the density profiles of trapped gases with population imbalance demonstrate the importance of these effects in determining the ground state structure of the condensate [29,30]. Related work on finite temperature phase diagram of ASC appeared in Refs.…”

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“…Recent experiments [1,2] on ultracold dilute gases of fermionic atoms trapped an unequal number of fermions in two different hyperfine states. These experiments started addressing some of the long-standing problems in the theory of asymmetric superconductors (ASCs) that are of interest in a variety of fields including metallic superconductors [3,4], nuclear systems [5][6][7] and high density QCD [8][9][10][11].…”

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Anomalous Specific-Heat Jump in a Two-Component Ultracold Fermi Gas

2006

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The thermodynamic functions of a Fermi gas with spin population imbalance are studied in the temperature-asymmetry plane in the BCS limit. The low-temperature domain is characterized by an anomalous enhancement of the entropy and the specific heat above their values in the unpaired state, decrease of the gap and eventual unpairing phase transition as the temperature is lowered. The unpairing phase transition induces a second jump in the specific heat, which can be measured in calorimetric experiments. While the superfluid is unstable against a supercurrent carrying state, it may sustain a metastable state if cooled adiabatically down from the stable high-temperature domain. In the latter domain the temperature dependence of the gap and related functions is analogous to the predictions of the BCS theory. DOI: 10.1103/PhysRevLett.97.140404 PACS numbers: 05.30.Fk, 03.75.Hh, 03.75.Ss, 74.20.Fg Recent experiments [1,2] on ultracold dilute gases of fermionic atoms trapped an unequal number of fermions in two different hyperfine states. These experiments started addressing some of the long-standing problems in the theory of asymmetric superconductors (ASCs) that are of interest in a variety of fields including metallic superconductors [3,4], nuclear systems [5][6][7] and high density QCD [8][9][10][11]. The unprecedented control over the many-body systems achieved in the experiments with ultracold dilute fermions combined with the possibility of tuning the interactions via the Feshbach resonance mechanism provide for the first time a realistic perspective of testing the predictions of the theories of ASC in the context of dilute fermionic systems. The realizations of various phases of ASC of dilute fermions have been intensively studied on the theoretical front; the simplest realizations are the isotropic, homogeneous phases that are characterized either by a Zeeman splitting of Fermi levels [12 -14] or by pairing between light and heavy fermions [15,16]. At large asymmetries the phases with broken space symmetries [17][18][19][20][21][22][23][24] and the mixed phases [25,26] become energetically more favorable. Alternatives include pairing in higher angular momentum states [27,28]. Finite-size and trap geometry introduce an additional complication to the problem and may qualitatively affect the comparison between the theory and experiment [29,30]. A number of related problems of interest are the nature of phase transitions between the various phases and their relation to the topology of Fermi surfaces [31,32] as well as the features of the BCS-BEC crossover [33][34][35] under population imbalance.The population asymmetry in ASC can be characterized either in terms of the difference (mismatch) in the chemical potentials or the difference in the densities of the species. The first case arises when the ''chemical'' equilibrium between populations admits transmutation between the different spin states, as, e.g., under the equilibrium with respect to the weak interactions in cold dense hadronic or quark matter. We sha...

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Fermionic Superfluidity with Imbalanced Spin Populations

Cited by 876 publications

References 36 publications

Finite-Temperature Phase Diagram of a Polarized Fermi Gas in an Optical Lattice

Finite-Temperature Phase Diagram of a Polarized Fermi Gas in an Optical Lattice

Higgs instability in gapless superfluidity/superconductivity

Anomalous Specific-Heat Jump in a Two-Component Ultracold Fermi Gas

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