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arXiv:1508.06691 · Physical Review A

Pairing fluctuations and an anisotropic pseudogap phenomenon in an ultracold superfluid Fermi gas with plural p -wave superfluid phases

Daisuke Inotani, Yoji Ohashi

Published Dec 30, 2015• 12 citations
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Abstract

We investigate the superfluid properties of a one-component Fermi gas with a uniaxially anisotropic $p$-wave pairing interaction, ${U}_{x}>{U}_{y}={U}_{z}$ [where ${U}_{i}\phantom{\rule{0.28em}{0ex}}(i=x,y,z)$ is a ${p}_{i}$-wave pairing interaction]. This type of interaction is considered to be realized in a $^{40}\mathrm{K}$ Fermi gas. Including pairing fluctuations within a strong-coupling $T$-matrix theory, we determine the ${p}_{x}$-wave superfluid phase transition temperature ${T}_{\mathrm{c}}^{{p}_{x}}$, as well as the other phase transition temperature ${T}_{\mathrm{c}}^{{p}_{x}+i{p}_{y}}\phantom{\rule{0.28em}{0ex}}(<{T}_{\mathrm{c}}^{{p}_{x}})$, below which the superfluid order parameter has the ${p}_{x}+i{p}_{y}$-wave symmetry. In the normal state near ${T}_{\mathrm{c}}^{{p}_{x}}, {p}_{x}$-wave pairing fluctuations are shown to induce an anisotropic pseudogap phenomenon, where a dip structure in the angle-resolved density of states around $\ensuremath{\omega}=0$ is the most remarkable in the ${p}_{x}$ direction. In the ${p}_{x}$-wave superfluid phase $({T}_{\mathrm{c}}^{{p}_{x}+i{p}_{y}}<T\ensuremath{\le}{T}_{\mathrm{c}}^{{p}_{x}})$, while the pseudogap in the ${p}_{x}$ direction continuously changes to the superfluid gap, the pseudogap in the perpendicular direction to the ${p}_{x}$ axis is found to continue developing because of enhanced ${p}_{y}$-wave and ${p}_{z}$-wave pairing fluctuations around the node of the ${p}_{x}$-wave superfluid order parameter. Since pairing fluctuations are always suppressed in the isotropic $s$-wave superfluid state, this phenomenon is peculiar to an unconventional Fermi superfluid with a nodal superfluid order parameter. Since the $p$-wave Fermi superfluid is the most promising non-$s$-wave pairing state in an ultracold Fermi gas, our results would contribute to understanding how the anisotropic pairing fluctuations, as well as the existence of plural superfluid phases, affect many-body properties of this unconventional Fermi superfluid.

DOI
10.1103/physreva.92.063638

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We investigate the superfluid properties of a one-component Fermi gas with a uniaxially anisotropic ppp-wave pairing interaction, Ux>Uy=Uz{U}_{x}>{U}_{y}={U}_{z}Ux​>Uy​=Uz​ [where Ui(i=x,y,z){U}_{i}\phantom{\rule{0.28em}{0ex}}(i=x,y,z)Ui​(i=x,y,z) is a pi{p}_{i}pi​-wave pairing interaction]. This type of interaction is considered to be realized in a 40K^{40}\mathrm{K}40K Fermi gas. Including pairing fluctuations within a strong-coupling TTT-matrix theory, we determine the px{p}_{x}px​-wave superfluid phase transition temperature Tcpx{T}_{\mathrm{c}}^{{p}_{x}}Tcpx​​, as well as the other phase transition temperature Tcpx+ipy(<Tcpx){T}_{\mathrm{c}}^{{p}_{x}+i{p}_{y}}\phantom{\rule{0.28em}{0ex}}(<{T}_{\mathrm{c}}^{{p}_{x}})Tcpx​+ipy​​(<Tcpx​​), below which the superfluid order parameter has the px+ipy{p}_{x}+i{p}_{y}px​+ipy​-wave symmetry. In the normal state near Tcpx,px{T}_{\mathrm{c}}^{{p}_{x}}, {p}_{x}Tcpx​​,px​-wave pairing fluctuations are shown to induce an anisotropic pseudogap phenomenon, where a dip structure in the angle-resolved density of states around \ensuremathω=0\ensuremath{\omega}=0\ensuremathω=0 is the most remarkable in the px{p}_{x}px​ direction. In the px{p}_{x}px​-wave superfluid phase (Tcpx+ipy<T\ensuremath≤Tcpx)({T}_{\mathrm{c}}^{{p}_{x}+i{p}_{y}}<T\ensuremath{\le}{T}_{\mathrm{c}}^{{p}_{x}})(Tcpx​+ipy​​<T\ensuremath≤Tcpx​​), while the pseudogap in the px{p}_{x}px​ direction continuously changes to the superfluid gap, the pseudogap in the perpendicular direction to the px{p}_{x}px​ axis is found to continue developing because of enhanced py{p}_{y}py​-wave and pz{p}_{z}pz​-wave pairing fluctuations around the node of the px{p}_{x}px​-wave superfluid order parameter. Since pairing fluctuations are always suppressed in the isotropic sss-wave superfluid state, this phenomenon is peculiar to an unconventional Fermi superfluid with a nodal superfluid order parameter. Since the ppp-wave Fermi superfluid is the most promising non-sss-wave pairing state in an ultracold Fermi gas, our results would contribute to understanding how the anisotropic pairing fluctuations, as well as the existence of plural superfluid phases, affect many-body properties of this unconventional Fermi superfluid.
We investigate single-particle properties of a one-component Fermi gas with a tunable ppp-wave interaction. Including pairing fluctuations associated with this anisotropic interaction within a TTT-matrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature Tc{T}_{\mathrm{c}}Tc​. Starting from the weak-coupling regime, we show that the so-called pseudogap first develops in these quantities with increasing the interaction strength. However, when the interaction becomes strong to some extent, the pseudogap becomes obscure to eventually disappear in the intermediate coupling regime. In the strong-coupling regime, the excitation gap associated with the formation of tightly bound molecules again opens. This nonmonotonic interaction dependence of the excitation gap is quite different from the case of an sss-wave interaction, where the pseudogap simply develops with increasing the interaction strength, which continuously changes into the molecular excitation gap. The difference between the two cases is shown to originate from the momentum dependence of the ppp-wave interaction, which vanishes in the low momentum limit. We also identify the pseudogap regime in the phase diagram with respect to the temperature and the ppp-wave interaction strength. Since the pseudogap is a precursor phenomenon of the superfluid phase transition, our results would be useful for the research toward the realization of ppp-wave superfluid Fermi gases.
We investigate single-particle properties of a one-component Fermi gas with a tunable p-wave interaction. Including pairing fluctuations associated with this anisotropic interaction within a TTT-matrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature TcT_{\rm c}Tc​. Starting from the weak-coupling regime, we show that the so-called pseudogap first develops in these quantities with increasing the interaction strength. However, when the interaction becomes strong to some extent, the pseudogap becomes obscure to eventually disappear in the strong-coupling regime. This non-monotonic interaction dependence is quite different from the case of an s-wave interaction, where the pseudogap simply develops with increasing the interaction strength. The difference between the two cases is shown to originate from the momentum dependence of the p-wave interaction, which vanishes in the low momentum limit. We also identify the pseudogap regime in the phase diagram with respect to the temperature and the p-wave interaction strength. Since the pseudogap is a precursor phenomenon of the superfluid phase transition, our results would be useful for the research toward the realization of p-wave superfluid Fermi gases.
We investigate fluctuation effects in a single-component ultracold Fermi gas with a p-wave interaction. Within the framework of a strong-coupling T-matrix theory, we calculate the single-particle density of states (DOS) at the superfluid phase transition temperature Tc. Starting from the weak-coupling regime, we show that the so-called pseudogap structure develops in DOS, with increasing the strength of a pairing interaction. However, in contrast to the case of s-wave interaction (where the pseudogap size in DOS monotonically increases with increasing the interaction strength), the pseudogap structure is found to gradually disappear in the strong-coupling regime. We point out that this non-monotonic behavior of pseudogap originates from the momentum dependence of p-wave interaction. Our results clarify how the symmetry of pairing interaction affects pseudogap phenomena in strongly correlated fermion systems.
We investigate strong-coupling effects on normal-state properties of an ultracold Fermi gas. Within the framework of TTT-matrix approximation in terms of pairing fluctuations, we calculate the single-particle density of states (DOS), as well as the spectral weight, over the entire BCS--Bose-Einstein condensate (BEC) crossover region above the superfluid phase-transition temperature Tc{T}_{\text{c}}Tc​. Starting from the weak-coupling BCS regime, we show that the so-called pseudogap develops in DOS above Tc{T}_{\text{c}}Tc​, which becomes remarkable in the crossover region. The pseudogap structure continuously changes into a fully gapped one in the strong-coupling BEC regime, where the gap energy is directly related to the binding energy of tightly bound molecules. We determine the pseudogap temperature ${T}^{\ensuremath{\ast}}$ where the dip structure in DOS vanishes. The value of ${T}^{\ensuremath{\ast}}$ is shown to be very different from another characteristic temperature ${T}^{\ensuremath{\ast}\ensuremath{\ast}}$ where a BCS-type double-peak structure disappears in the spectral weight. While one finds ${T}^{\ensuremath{\ast}}>{T}^{\ensuremath{\ast}\ensuremath{\ast}}$ in the BCS regime, ${T}^{\ensuremath{\ast}\ensuremath{\ast}}$ becomes higher than ${T}^{\ensuremath{\ast}}$ in the crossover region and BEC regime. Including this, we determine the pseudogap region in the phase diagram of ultracold Fermi gases. Our results would be useful in the search for the pseudogap region in ultracold 6Li^{6}\text{L}\text{i}6Li and 40K^{40}\text{K}40K Fermi gases.
We investigate strong-coupling properties of a unitary Fermi gas consisting of two different species with different masses. Including pairing fluctuations within the self-consistent T -matrix approximation, we calculate the single-particle density of states in the normal state. We show that the pseudogap phenomenon, which is characterized by a dip structure in the density of states around ω = 0, appears more remarkably in the light mass component than in the heavy mass component. As a result, the pseudogap temperature, which is determined as the temperature at which the pseudogap disappears in the density of states, is higher in the former than in the latter. We also find that this different pseudogap temperatures lead to the existence of two kinds of pseudogap regions. That is, one is the ordinary pseudogap regime where the pseudogap appears in both the component, and the other case is that the light mass component only exhibits the pseudogap phenomenon. As the origin of these component- dependent pseudogap phenomena, we point out the importance of different Fermi temperatures between the two components. Since the formation of hetero-Cooper pairs and their condensation are expected in various systems, such as a 6 Li- 40 K Fermi gas mixture, an exciton (polariton) gas, as well as color superconductivity, our results would be useful for the understanding of strong-coupling properties of these novel Fermi condensates.
We investigate single-particle properties of a strongly interacting ultracold Fermi gas with mass imbalance. Using an extended TTT-matrix theory, we calculate the density of states, as well as the single-particle spectral weight, in the unitarity limit above the superfluid phase transition temperature TcT_{\rm c}Tc​. We show that the momentum regions where pairing fluctuations strongly affect single-particle excitations are different between light fermions and heavy fermions, reflecting the difference of the Pauli blocking effects between them. In addition, we obtain different pseudogap phenomena associated with pairing fluctuations in between the two components. Since the realization of a mass-imbalanced superfluid Fermi gas is an important challenge in this field, our results would contribute to the understanding of physical properties of the hetero-pairing state.