Journal of Chemical Biological and Physical Sciences

A theoretical study of super fluidity of an atomic Fermi gas near the unitary limit and evaluation of gap function as a function of K/KF in the unitary limit

Published Jan 1, 2017• 1 citation

Abstract

Using the theoretical formalism of S.De Palo etal (Laser Phys.15, 376 (2005)), we have theoretically studied super fluidity of an atomic Fermi gas near the unitarily limit.Our theoretically evaluated values of gap function (k)  as a function of F k k for different values of F g n / E show that the gap function has a damped oscillatory behaviour.Our theoretically evaluated results of the ratio 0 F

DOI: 10.24214/jcbps.c.7.4.82341

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Journal of Chemical Biological and Physical Sciences

A theoretical study of super fluidity of an atomic Fermi gas near the unitary limit and evaluation of gap function as a function of K/KF in the unitary limit

Published Jan 1, 2017• 1 citation

Publisher

Abstract

DOI: 10.24214/jcbps.c.7.4.82341

Related papers

A theoretical evaluation of momentum distribution, BCS pair function and BCS distribution function of atomic Fermi gas near the unitarity limit

Journal of Chemical Biological and Physical SciencesJan 1, 20171 citation

Thermodynamics of a trapped unitary Fermi gas

R. Haussmann, W. Zwerger

Thermodynamic properties of an ultracold Fermi gas in a harmonic trap are calculated within a local density approximation, using a conserving many-body formalism for the BCS to Bose-Einstein condensate crossover problem, which has been developed by Haussmann et al. [Phys. Rev. A 75, 023610 (2007)]. We focus on the unitary regime near a Feshbach resonance and determine the local density and entropy profiles and the global entropy $S(E)$ as a function of the total energy $E$ . Our results are in good agreement with both experimental data and previous analytical and numerical results for the thermodynamics of the unitary Fermi gas. The value of the Bertsch parameter at $T=0$ and the superfluid transition temperature, however, differ appreciably. We show that, well in the superfluid regime, removal of atoms near the cloud edge enables cooling far below temperatures that have been reached so far.Thermodynamic properties of an ultracold Fermi gas in a harmonic trap are calculated within a local density approximation, using a conserving many-body formalism for the BCS to Bose-Einstein condensate crossover problem, which has been developed by Haussmann et al. [Phys. Rev. A 75, 023610 (2007)]. We focus on the unitary regime near a Feshbach resonance and determine the local density and entropy profiles and the global entropy $S(E)$ as a function of the total energy $E$. Our results are in good agreement with both experimental data and previous analytical and numerical results for the thermodynamics of the unitary Fermi gas. The value of the Bertsch parameter at $T=0$ and the superfluid transition temperature, however, differ appreciably. We show that, well in the superfluid regime, removal of atoms near the cloud edge enables cooling far below temperatures that have been reached so far.

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We compute the shear viscosity of a superfluid atomic Fermi gas in the unitarity limit. The unitarity limit is characterized by a divergent scattering length between the atoms, and it has been argued that this will result in a very small viscosity. We show that in the low temperature $T$ limit the shear viscosity scales as ${\ensuremath{\xi}}^{5}∕{T}^{5}$, where the universal parameter $\ensuremath{\xi}$ relates the chemical potential and the Fermi energy, $\ensuremath{\mu}=\ensuremath{\xi}{\ensuremath{\epsilon}}_{F}$. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature ${T}_{c}$ . A na\"{\i}ve extrapolation indicates that the minimum value of the ratio of viscosity over entropy density is within a factor of $\ensuremath{\sim}5$ of the proposed bound $\ensuremath{\eta}∕s\ensuremath{\ge}\ensuremath{\hbar}∕(4\ensuremath{\pi}{k}_{B})$.We compute the shear viscosity of a superfluid atomic Fermi gas in the unitarity limit. The unitarity limit is characterized by a divergent scattering length between the atoms, and it has been argued that this will result in a very small viscosity. We show that in the low temperature $T$ limit the shear viscosity scales as ${\ensuremath{\xi}}^{5}∕{T}^{5}$, where the universal parameter $\ensuremath{\xi}$ relates the chemical potential and the Fermi energy, $\ensuremath{\mu}=\ensuremath{\xi}{\ensuremath{\epsilon}}_{F}$. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature ${T}_{c}$. A na\"{\i}ve extrapolation indicates that the minimum value of the ratio of viscosity over entropy density is within a factor of $\ensuremath{\sim}5$ of the proposed bound $\ensuremath{\eta}∕s\ensuremath{\ge}\ensuremath{\hbar}∕(4\ensuremath{\pi}{k}_{B})$.

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S. Giorgini, Лев П. Питаевский, S. Stringari

The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the $s$ -wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.The physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective. Emphasis is given to the effect of interactions that play a crucial role, bringing the gas into a superfluid phase at low temperature. In these dilute systems, interactions are characterized by a single parameter, the $s$-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.

arXiv:0706.3360Reviews of Modern PhysicsOct 2, 20081,997 citations

S(E)

as a function of the total energy

E

. Our results are in good agreement with both experimental data and previous analytical and numerical results for the thermodynamics of the unitary Fermi gas. The value of the Bertsch parameter at

T=0

and the superfluid transition temperature, however, differ appreciably. We show that, well in the superfluid regime, removal of atoms near the cloud edge enables cooling far below temperatures that have been reached so far.

T

limit the shear viscosity scales as ${\ensuremath{\xi}}^{5}∕{T}^{5}$, where the universal parameter $\ensuremath{\xi}$ relates the chemical potential and the Fermi energy, $\ensuremath{\mu}=\ensuremath{\xi}{\ensuremath{\epsilon}}_{F}$. Combined with the high temperature expansions of the viscosity our results suggest that the viscosity has a minimum near the critical temperature

{T}_{c}

. A na\"{\i}ve extrapolation indicates that the minimum value of the ratio of viscosity over entropy density is within a factor of $\ensuremath{\sim}5$ of the proposed bound $\ensuremath{\eta}∕s\ensuremath{\ge}\ensuremath{\hbar}∕(4\ensuremath{\pi}{k}_{B})$.

The thermodynamic and transport properties of the unitary Fermi gas at finite temperature

T

are governed by a quantum critical point at

T=0

and zero density. We compute the universal shear viscosity to entropy ratio $\ensuremath{\eta}/s$ in the high-temperature quantum critical regime $T\ensuremath{\gg}|\ensuremath{\mu}|$ and find that this strongly coupled quantum fluid comes close to perfect fluidity $\ensuremath{\eta}/s=\ensuremath{\hbar}/(4\ensuremath{\pi}{k}_{B})$. Using a controlled large-

N

expansion, we show that already at the first nontrivial order the equation of state and the Tan contact density

C

agree well with the most recent experimental measurements and theoretical Luttinger-Ward and bold diagrammatic Monte Carlo calculations.

s

-wave scattering length, whose value can be tuned using an external magnetic field near a broad Feshbach resonance. The BCS limit of ordinary Fermi superfluidity, the Bose-Einstein condensation (BEC) of dimers, and the unitary limit of large scattering length are important regimes exhibited by interacting Fermi gases. In particular, the BEC and the unitary regimes are characterized by a high value of the superfluid critical temperature, on the order of the Fermi temperature. Different physical properties are discussed, including the density profiles and the energy of the ground-state configurations, the momentum distribution, the fraction of condensed pairs, collective oscillations and pair-breaking effects, the expansion of the gas, the main thermodynamic properties, the behavior in the presence of optical lattices, and the signatures of superfluidity, such as the existence of quantized vortices, the quenching of the moment of inertia, and the consequences of spin polarization. Various theoretical approaches are considered, ranging from the mean-field description of the BCS-BEC crossover to nonperturbative methods based on quantum Monte Carlo techniques. A major goal of the review is to compare theoretical predictions with available experimental results.