Pairing and Phase Separation in a Polarized Fermi Gas

Partridge, Guthrie B.; Li, Wenhui; Kamar, Ramsey I.; Liao, Yunxiang; Hulet, Randall G.

doi:10.1126/science.1122876

Cited by 952 publications

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“…The atom-dimer scattering is strongly affected by the mass asymmetry [12] and the ultimate fate of a Fermi liquid in presence of the Efimov effect is currently an open question being actively investigated [13]. All these theoretical considerations are strongly motivated by cold-atom experiments which have recently achieved degeneracy of Fermi gases with different masses [6] and spin-imbalanced two-component fermionic gases [14].…”

Section: Introductionmentioning

confidence: 99%

Multimer formation in one-dimensional two-component gases and trimer phase in the asymmetric attractive Hubbard model

2011

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We consider two-component one-dimensional quantum gases at special imbalanced commensurabilities which lead to the formation of multimer (multiparticle bound-states) as the dominant order parameter. Luttinger liquid theory supports a mode-locking mechanism in which mass (or velocity) asymmetry is identified as the key ingredient to stabilize such states. While the scenario is valid both in the continuum and on a lattice, the effects of umklapp terms relevant for densities commensurate with the lattice spacing are also mentioned. These ideas are illustrated and confronted with the physics of the asymmetric (mass-imbalanced) fermionic Hubbard model with attractive interactions and densities such that a trimer phase can be stabilized. Phase diagrams are computed using density-matrix renormalization group techniques, showing the important role of the total density in achieving the latter phase. The effective physics of the trimer gas is studied as well. Last, the effect of a parabolic confinement and the emergence of a crystal phase of trimers are briefly addressed. This model has connections with the physics of imbalanced two-component fermionic gases and Bose-Fermi mixtures as the latter gives a good phenomenological description of the numerics in the strong-coupling regime.

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Section: Introductionmentioning

confidence: 99%

Multimer formation in one-dimensional two-component gases and trimer phase in the asymmetric attractive Hubbard model

2011

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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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“…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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Pairing and Phase Separation in a Polarized Fermi Gas

Cited by 952 publications

References 37 publications

Multimer formation in one-dimensional two-component gases and trimer phase in the asymmetric attractive Hubbard model

Multimer formation in one-dimensional two-component gases and trimer phase in the asymmetric attractive Hubbard model

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

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

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