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

Abstract

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...

BCS-BEC crossovers and unconventional phases in dilute nuclear matter

“…On the contrary, one finds d∆(T )/dT < 0 for the LOFF branch, as is the case in ordinary (symmetrical) BCS theory [41]. It should be mentioned that the "anomalous" behavior of the BCS gap below the point of bifurcation leading to the LOFF state gives rise to a number of anomalies in thermodynamic quantities, such as negative superfluid density or excess entropy of the superfluid [42]. These anomalies are absent in the LOFF state [43].…”

Cooling and thermometry of atomic Fermi gases

“…Such a state is named, from its proponents, the LOFF (or FFLO) state. This is an example of a series of alternative pairing mechanisms proposed, including Sarma superfluidity [43][44][45], deformed Fermi-sphere superconductivity [46][47][48], and breached pairing superconductivity [49].…”

Thermal evolution of massive compact objects with dense quark cores

“…In this paper, we shall concentrate on simple ud-quark condensates and explore the possibility that these condensates are in one of the gapless phases with broken spatial symmetry [13][14][15][16][17][18][19][20][21]. The homogeneous gapless color superconductors are not treated because they develop tachionic instabilities in the ground state [22] and their specific heat has anomalous temperature dependence [23].…”

“…A homogenous red-green condensate, when in the gapless BCS regime, develops tachionic instabilities, which manifest themselves in negative Meissner masses [22]. Furthermore, the thermodynamic quantities of a homogeneous gapless superconductor are generally anomalous at low temperatures; in particular, for large enough asymmetries the gap disappears at a lower critical temperature and the specific heat experiences a jump [19,23]. Recent studies show that a realization of inhomogeneous superconductors, the Fulde-Ferrell phase, is preferred in color superconducting quark matter to the homogenous BCS phase at sufficiently low temperature and weak coupling for arbitrary flavor asymmetries [20] as well as when color and charge neutrality are enforced [21].…”