arXiv:1703.00585 · Journal of the Physical Society of Japan

Specific Heat and Effects of Uniaxial Anisotropy of ap-Wave Pairing Interaction in a Strongly Interacting Ultracold Fermi Gas

Daisuke Inotani, Pieter van Wyk, Yoji Ohashi

Published Mar 3, 2017• 2 citations

Abstract

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 Nozières 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.

DOI: 10.7566/jpsj.86.044301

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arXiv:1703.00585 · Journal of the Physical Society of Japan

Specific Heat and Effects of Uniaxial Anisotropy of ap-Wave Pairing Interaction in a Strongly Interacting Ultracold Fermi Gas

Daisuke Inotani, Pieter van Wyk, Yoji Ohashi

Published Mar 3, 2017• 2 citations

arXiv HTML PDF

Abstract

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 Nozières 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.

DOI: 10.7566/jpsj.86.044301

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Strong-Coupling Properties of ap-Wave Interacting Fermi Gas on the Viewpoint of Specific Heat at Constant Volume

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We theoretically investigate the specific heat $C_V$ at constant volume in the normal state of a $p$ -wave interacting Fermi gas. Including fluctuations in the $p$ -wave Cooper channel within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we clarify how $C_V$ as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime, $C_V$ is shown to be enhanced by $p$ -wave pairing fluctuations, near the superfluid phase transition temperature $T_{\rm c}$ . Similar enhancement of $C_V(T\simeq T_{\rm c})$ is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of $p$ -wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the $p$ -wave molecular Bose gas regime, and (3) the region between the two, where $p$ -wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a $p$ -wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above $T_{\rm c}$ .We theoretically investigate the specific heat $C_V$ at constant volume in the normal state of a $p$-wave interacting Fermi gas. Including fluctuations in the $p$-wave Cooper channel within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we clarify how $C_V$ as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime, $C_V$ is shown to be enhanced by $p$-wave pairing fluctuations, near the superfluid phase transition temperature $T_{\rm c}$. Similar enhancement of $C_V(T\simeq T_{\rm c})$ is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of $p$-wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the $p$-wave molecular Bose gas regime, and (3) the region between the two, where $p$-wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a $p$-wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above $T_{\rm c}$.

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Daisuke Inotani, Ryota Watanabe, Manfred Sigrist +1 more

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 $T$ -matrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature $T_{\rm c}$ . 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 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 $T$-matrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature $T_{\rm c}$. 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.

arXiv:1202.5353Journal of Physics Conference SeriesDec 17, 20121 citation

We investigate the specific heat

C_V

at constant volume and effects of uniaxial anisotropy of a

p

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.

We theoretically investigate the specific heat

C_V

at constant volume in the normal state of a

p

-wave interacting Fermi gas. Including fluctuations in the

p

-wave Cooper channel within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink, we clarify how

C_V

as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime,

C_V

is shown to be enhanced by

p

-wave pairing fluctuations, near the superfluid phase transition temperature

T_{\rm c}

. Similar enhancement of

C_V(T\simeq T_{\rm c})

is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of

p

-wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the

p

-wave molecular Bose gas regime, and (3) the region between the two, where

p

-wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a

p

-wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above

T_{\rm c}

We investigate the specific heat

C_V

at constant volume in the normal state of a

p

-wave interacting Fermi gas. Including

p

-wave pairing fluctuations within the strong-coupling theory developed by Nozières and Schmitt-Rink, we show that, in the weak-coupling side,

C_V

exhibits a dip-hump behavior as a function of the temperature. While the dip is associated with the pseudogap phenomenon near

T_{\rm c}

, the hump structure is found to come from the suppression of Fermi quasiparticle scattering into a

p

-wave molecular state in the Fermi degenerate regime. Since the latter phenomenon does not occur in the ordinary

s

-wave interacting Fermi gas, it may be viewed as a characteristic phenomenon associated with a

p

-wave pairing interaction.

We investigate the specific heat at constant volume

{C}_{V}

in the Bardeen-Cooper-Schrieffer--Bose-Einstein-condensate (BCS-BEC)-crossover regime of an ultracold Fermi gas above the superfluid phase transition temperature

{T}_{\mathrm{c}}

. Within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we show that this thermodynamic quantity is sensitive to the stability of preformed Cooper pairs. That is, while ${C}_{V}(T\ensuremath{\gtrsim}{T}_{\mathrm{c}})$ in the unitary regime is remarkably enhanced by metastable preformed Cooper pairs or pairing fluctuations, it is well described by that of an ideal Bose gas of long-lived stable molecules in the strong-coupling BEC regime. Using these results, we identify the region where the system may be viewed as an almost ideal Bose gas of stable pairs, as well as the pseudogap regime where the system is dominated by metastable preformed Cooper pairs, in the phase diagram of an ultracold Fermi gas with respect to the strength of a pairing interaction and the temperature. We also show that the calculated specific heat agrees with the recent experiment on a

^{6}\text{Li}

unitary Fermi gas. Since the formation of preformed Cooper pairs is a crucial key in the BCS-BEC-crossover phenomenon, our results would be helpful in considering how fluctuating preformed Cooper pairs appear in a Fermi gas to eventually become stable as one passes through the BCS-BEC-crossover region.

We investigate theoretically strong-coupling and finite-temperature effects on the

p

-wave contacts, as well as the asymptotic behavior of the momentum distribution in the 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}_{\mathrm{c}}

from the adiabatic energy relations. We show that, while the

p

-wave contact related to the scattering volume monotonically increases with increasing interaction strength, the one related to the effective range depends nonmonotonically on interaction strength and its sign changes in the intermediate-coupling regime. The nonmonotonic 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 effective range. We also analyze the asymptotic form of the momentum distribution in the 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 are not related to the thermodynamic properties, appear. Furthermore, in the high-temperature region, we find that the extra terms dominate the subleading 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, while our model qualitatively explains the dependence on the interaction strength of the

p

-wave contacts, there are some quantitative disagreements between our theory and recent experiment; for example, the peak position of the

p

-wave contact related to the effective range. Since the

p

-wave contacts connect the microscopic properties to the thermodynamic properties of the system, our results would be helpful for further understanding many-body properties of this anisotropic interacting Fermi gas in the normal phase.

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

T

-matrix theory, we calculate the single-particle density of states, as well as the spectral weight, above the superfluid transition temperature

T_{\rm c}

. 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.