36 research outputs found

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

We investigate superfluid properties of a one-component Fermi gas with a
uniaxially anisotropic $p$-wave pairing interaction, $U_x>U_y=U_z$ (where $U_i$
($i=x,y,z)$ is a $p_i$-wave pairing interaction). This type of interaction is
considered to be realized in a $^{40}$K Fermi gas. Including pairing
fluctuations within a strong-coupling $T$-matrix theory, we determine the
$p_x$-wave superfluid phase transition temperature $T^{p_x}_{\rm c}$, as well
as the other phase transition temperature $T_{\rm c}^{p_x+ip_y}$ ($<T_{\rm
c}^{p_x}$), below which the superfluid order parameter has the $p_x+ip_y$-wave
symmetry. In the normal state near $T^{p_x}_{\rm c}$, $p_x$-wave pairing
fluctuations are shown to induce an anisotropic pseudogap phenomenon, where a
dip structure in the angle-resolved density of states around $\omega=0$ is the
most remarkable in the $p_x$ direction. In the $p_x$-wave superfluid phase
($T_{\rm c}^{p_x+ip_y}<T\le T_{\rm c}^{p_x}$), 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.Comment: 27 pages, 11 figure

### Closed-channel contribution in the BCS-BEC crossover regime of an ultracold Fermi gas with an orbital Feshbach resonance

We theoretically investigate strong-coupling properties of an ultracold Fermi
gas with an orbital Feshbach resonance (OFR). Including tunable pairing
interaction associated with an OFR within the framework of the strong-coupling
theory developed by Nozi\`eres and Schmitt-Rink (NSR), we examine the
occupation of the closed channel. We show that, although the importance of the
closed channel is characteristic of the system with an OFR, the occupation
number of the closed channel is found to actually be very small at the
superfluid phase transition temperature $T_{\rm c}$, in the whole BCS
(Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region,
when we use the scattering parameters for an ultracold $^{173}$Yb Fermi gas.
The occupation of the closed channel increases with increasing the temperature
above $T_{\rm c}$, which is more remarkable for a stronger pairing interaction.
We also present a prescription to remove effects of an experimentally
inaccessible deep bound state from the NSR formalism, which we meet when we
theoretically deal with a $^{173}$Yb Fermi gas with an OFR

### Evolution of Cooper pairs with zero-center-of-mass momentum and their first-order correlation function in a two-dimensional ultracold Fermi gas near the observed Berezinskii-Kosterlitz-Thouless transition

We investigate the center-of-mass momentum distribution $n_{\boldsymbol Q}$
of Cooper pairs and their first-order correlation function $g_1(r)$ in a
strongly interacting two-dimensional Fermi gas. Recently, the BKT
(Berezinskii-Kosterlitz-Thouless) transition was reported in a two-dimensional
$^6$Li Fermi gas, based on (1) the observations of anomalous enhancement of
$n_{{\boldsymbol Q}={\boldsymbol 0}}$ [M. G. Ries, et. al., Phys. Rev. Lett.
114, 230401 (2015)], as well as (2) a power-law behavior of $g_1(r)$ [P. A.
Murthy, et. al., Phys. Rev. Lett. 115, 010401 (2015)]. However, including
pairing fluctuations within a $T$-matrix approximation (TMA), we show that
these results can still be explained as strong-coupling properties of a
normal-state two-dimensional Fermi gas. Our results indicate the importance of
further experimental observations, to definitely confirm the realization of the
BKT transition in this system. Since the BKT transition has been realized in a
two-dimensional ultracold Bose gas, our results would be useful for the
achievement of this quasi-long range order in an ultracold Fermi gas.Comment: 22 pages, 7 figure

### Superfluid theory of a gas of polarized dipolar Fermi molecules

We present a superfluid theory of a polarized dipolar Fermi gas. For two
dipolar molecules each of which consists of two atoms with positive charge and
negative charge, we derive an effective dipole-dipole pairing interaction.
Using this pairing interaction, we show that the resulting BCS gap equation is
not suffered from the well-known ultraviolet divergence, so that one can
quantitatively predict superfluid properties of a dipolar Fermi gas. Using this
cutoff-free superfluid theory, we examine the symmetry of the superfluid order
parameter at T=0. We also discuss the deformation of the Fermi surface,
originating from the anisotropy of the dipole-dipole interaction.Comment: 7 pages, 5 figure

### Specific Heat and Effects of Uniaxial Anisotropy of a $p$-wave Pairing Interaction in a Strongly Interacting Ultracold Fermi Gas

We investigate the specific heat $C_V$ at constant volume and effects of
uniaxial anisotropy of a $p$-wave attractive interaction in the normal state of
an ultracold Fermi gas. Within the framework of the strong-coupling theory
developed by Nozi\`eres and Schmitt-Rink, we evaluate this thermodynamic
quantity as a function of temperature, in the whole interaction regime. While
the uniaxial anisotropy is not crucial for $C_V$ in the weak-coupling regime,
$C_V$ is found to be sensitive to the uniaxial anisotropy in the
strong-coupling regime. This originates from the population imbalance among
$p_i$-wave molecules ($i=x,y,z$), indicating that the specific heat is a useful
observable to see which kinds of $p$-wave molecules dominantly exist in the
strong-coupling regime when the $p$-wave interaction has uniaxial anisotropy.
Using this strong point, we classify the strong-coupling regime into some
characteristic regions. Since a $p$-wave pairing interaction with uniaxial
anisotropy has been discovered in a $^{40}$K Fermi gas, our results would be
useful in considering strong-coupling properties of a $p$-wave interacting
Fermi gas, when the interaction is uniaxially anisotropic.Comment: 21 pages, 7 figure

### Single-particle Excitations and Effects of Hetero-pairing Fluctuations in a Bose-Fermi Mixture with a Feshbach Resonance

We theoretically investigate normal-state properties of a gas mixture of
single-component bosons and fermions with a hetero-nuclear Feshbach resonance.
Including strong hetero-pairing fluctuations associated with the Feshbach
resonance, we calculate single-particle density of states, as well as the
spectral weight at various interaction strengths. For this purpose, we employ
an improved T-matrix approximation (TMA), where the bare Bose Green's function
in the non-selfconsistent TMA self-energy is modified so as to satisfy the
Hugenholtz-Pines relation at the Bose-Einstein condensation (BEC) temperature
$T_{\rm BEC}$. In the unitary regime at $T_{\rm BEC}$, we show that
hetero-pairing fluctuations couple Fermi atomic excitations with Fermi
molecular excitations, as well as with Bose atomic excitations. Although a
similar coupling phenomenon by pairing fluctuations is known to give a
pseudo-gapped density of states in the unitary regime of a two-component Fermi
gas, such a dip structure is found to not appear even in the unitary limit of a
Bose-Fermi mixture. It only appears in the strong-coupling regime. Instead, a
spectral peak along the molecular dispersion appears in the spectral weight.We
also clarify how this coupling phenomenon is seen in the Bose channel. Since a
hetero-nuclear Feshbach resonance, as well as the formation of Bose-Fermi
molecules, have been realized, our results would be useful for the study of
strong-coupling properties of this unique quantum gas

### A possible method to confirm $\pm s$-wave pairing state using the Riedel anomaly in Fe-pnictide superconductors

We theoretically propose a method to identify $\pm s$-wave order parameter in
recently discovered Fe-pnictide superconductors. Our idea uses the Riedel
anomaly in ac-Josephson current through an SI($\pm$ S) (single-band s-wave
superconductor/insulator/$\pm$s-wave two-band superconductor) junction. We show
that the Riedel peak effect leads to vanishing ac-Josephson current at some
values of biased voltage. This phenomenon does not occur in the case when the
$\pm s$-wave superconductor is replaced by a conventional s-wave one, so that
the observation of this vanishing Josephson current would be a clear signature
of $\pm s$-wave pairing state in Fe-pnictide superconductors.Comment: 4 pages, 3 figure

### Strong coupling effects on specific heat in the BCS-BEC crossover

We theoretically investigate strong-coupling effects on specific heat at
constant volume $C_{\rm V}$ in a superfluid Fermi gas with a tunable
interaction associated with Feshbach resonance. Including fluctuations of the
superfluid order parameter within the strong-coupling theory developed by
Nozi\`eres and Schmitt-Rink, we calculate the temperature dependence of $C_{\rm
V}$ at the unitarity limit in the superfluid phase. We show that, in the low
temperature region, $T^3$-behavior is shown in the temperature dependence of
$C_{\rm V}$. This result indicates that the low-lying excitations are dominated
by the gapless Goldstone mode, associated with the phase fluctuations of the
superfluid order parameter. Since the Goldstone mode is one of the most
fundamental phenomena in the Fermionic superfluidity, our results are useful
for further understanding how the pairing fluctuations affects physical
properties in the BCS-BEC crossover physics below the superfluid transition
temperature.Comment: 8 pages, 4 figure

### Pseudogap regime of a two-dimensional uniform Fermi gas

We investigate pseudogap phenomena in a two-dimensional Fermi gas. Including
pairing fluctuations within a self-consistent $T$-matrix approximation, we
determine the pseudogap temperature $T^*$ below which a dip appears in the
density of states $\rho(\omega)$ around the Fermi level. Evaluating $T^*$, we
identify the pseudogap region in the phase diagram of this system. We find
that, while the observed BKT (Berezinskii-Kosterlitz-Thouless) transition
temperature $T^{\rm exp}_{\rm BKT}$ in a $^6$Li Fermi gas is in the pseudogap
regime, the detailed pseudogap structure in $\rho(\omega)$ at $T^{\rm exp}_{\rm
BKT}$ still differs from a fully-gapped one, indicating the importance of
amplitude fluctuations in the Cooper channel there. Since the observed $T^{\rm
exp}_{\rm BKT}$ in the weak-coupling regime cannot be explained by the recent
BKT theory which only includes phase fluctuations, our results may provide a
hint about how to improve this BKT theory. Although $\rho(\omega)$ has not been
measured in this system, we show that the assessment of our results is still
possible by using the observable Tan's contact.Comment: 23 pages, 9 figure

### Strong-Coupling and Finite Temperature Effects on $p$-wave Contacts

We theoretically investigate strong-coupling and finite temperature effects
on the p-wave contacts, as well as the asymptotic behavior of the momentum
distribution in large momentum region in a one-component Fermi gas with a
tunable p-wave interaction. Including p-wave pairing fluctuations within a
strong-coupling theory, we calculate the p-wave contacts above the superfluid
transition temperature $T_{\rm c}$ from the adiabatic energy relations. We show
that while the p-wave contacts related to the scattering volume monotonically
increases with increasing the interaction strength, one related to the
effective range non-monotonically depends on interaction strength and its sign
changes in the intermediate-coupling regime. The non-monotonic interaction
dependence of these quantities is shown to originate from the competition
between the increase of the cutoff momentum and the decrease of the coupling
constant of the p-wave interaction with increasing the effective range. We also
analyze the asymptotic form of the momentum distribution in large momentum
region. In contrast to the conventional s-wave case, we show that the
asymptotic behavior cannot be completely described by only the p-wave contacts,
and the extra terms, which is not related to the thermodynamic properties,
appear. Furthermore, in high temperature region, we find that the extra terms
dominate the sub-leading term of the large-momentum distribution. We also
directly compare our results with the recent experimental measurement, by
including the effects of a harmonic trap potential within the local density
approximation. We show that our model explains the dependence on the
interaction strength of the p-wave contacts.Comment: 26 pages, 12 figure