arXiv:1608.02259

Temperature and interaction dependence of the moment of inertia of a rotating condensate boson gas

Ahmed S. Hassan, Azza M. El-Badry, Shemi S.M. Soliman

Published Aug 7, 2016• 0 citations

Abstract

In this paper, a developed Hartree-Fock semiclassical approximation is used to calculate the temperature and interaction dependence of the moment of inertia of a rotating condensate Boson gas. A fully classical and quantum mechanical treatment for the moment of inertia are given in terms of the normalized temperature. We found that the moment of inertia is considerably affected by the interaction. The present analysis, shows that the superfluid effects in the moment of inertia of a condensate Boson gas can be observed at temperatures $T > .25 T_0 $ and not dramatically smaller than $T_0$.

DOI: 10.48550/arxiv.1608.02259

Related papers

Moment of Inertia and Superfluidity of a Trapped Bose Gas

S. Stringari

The temperature dependence of the moment of inertia of a dilute Bose gas confined in a harmonic trap is determined. Deviations from the rigid value, due to the occurrence of Bose-Einstein condensation, reveal the superfluid behavior of the system. In the noninteracting gas these deviations become important at temperatures of the order of ${T}_{c}{N}^{\ensuremath{-}1/12}$. The role of interactions is also discussed.

arXiv:cond-mat/9509166Physical Review LettersFeb 26, 199663 citations

Moment of inertia of a trapped superfluid gas of Fermions

M. Farine, Peter Schuck, X. Viñas

The moment of inertia Q of a trapped superfluid gas of atomic Fermions (6Li) is calculated as a function of the temperature. At zero temperature the moment of inertia takes on the irrotational flow value. Only for T very close to Tc rigid rotation is attained. It is proposed that future measurements of the rotational energy will unambiguously reveal whether the system is in a superfluid state or not.

arXiv:cond-mat/0004006Apr 1, 20000 citations

Temperature dependence of the vortices number for rotating superfluid Bose-Einstein condensates in a two-dimensional lattice

Ahmed S. Hassan, Azza M. El-Badry, Adel M. Mohammedein +1 more

arXiv:2005.07763Jan 1, 20200 citations

Moment of inertia of a trapped superfluid gas of atomic fermions

M. Farine, Peter Schuck, X. Viñas

arXiv:cond-mat/9901241Physical Review AJun 16, 200029 citations

The moment of inertia and the scissors mode of a Bose-condensed gas

Onofrio M. Maragò, Gerald Hechenblaikner, E. Hodby +2 more

arXiv:cond-mat/0109193Journal of Physics Condensed MatterDec 24, 20018 citations

Rotational properties of trapped bosons

F. Brosens, J. T. Devreese, L. F. Lemmens

arXiv:cond-mat/0004208Physical Review AMar 1, 199712 citations

arXiv:1608.02259

Temperature and interaction dependence of the moment of inertia of a rotating condensate boson gas

Ahmed S. Hassan, Azza M. El-Badry, Shemi S.M. Soliman

Published Aug 7, 2016• 0 citations

arXiv HTML PDF

Abstract

T > .25 T_0

and not dramatically smaller than

T_0

DOI: 10.48550/arxiv.1608.02259

Related papers

Moment of Inertia and Superfluidity of a Trapped Bose Gas

S. Stringari

arXiv:cond-mat/9509166Physical Review LettersFeb 26, 199663 citations

Moment of inertia of a trapped superfluid gas of Fermions

M. Farine, Peter Schuck, X. Viñas

arXiv:cond-mat/0004006Apr 1, 20000 citations

Temperature dependence of the vortices number for rotating superfluid Bose-Einstein condensates in a two-dimensional lattice

Ahmed S. Hassan, Azza M. El-Badry, Adel M. Mohammedein +1 more

We developed an approach to investigate the temperature dependence of the vortices number for the rotating superfluid Bose-Einstein condensates in a two-dimensional lattice. Our approach enabled us to parametrize the thermal average of the quantum mechanics expectation value and the vortices number in terms of the thermodynamic potential $q(T)$ for the system under consideration. The effects of the interatomic interaction, the finite number of atoms, and optical potential depth on the vortices number are investigated. The calculated results show that the vortices number as a function of the rotation rate depends on the normalized temperature, interatomic interaction, optical potential depth, and the number of atoms in the ${\in situ}$ size. These results provide solid theoretical foundations for the measured experimental data for rotating condensate boson in optical lattice such as Williams et. al experiment [R. A. Williams, S. Al-Assam, and C. J. Foot, Phys. Rev. Lett. { 104} (2010) 050404.].We developed an approach to investigate the temperature dependence of the vortices number for the rotating superfluid Bose-Einstein condensates in a two-dimensional lattice. Our approach enabled us to parametrize the thermal average of the quantum mechanics expectation value and the vortices number in terms of the thermodynamic potential $q(T)$ for the system under consideration. The effects of the interatomic interaction, the finite number of atoms, and optical potential depth on the vortices number are investigated. The calculated results show that the vortices number as a function of the rotation rate depends on the normalized temperature, interatomic interaction, optical potential depth, and the number of atoms in the ${\in situ}$ size. These results provide solid theoretical foundations for the measured experimental data for rotating condensate boson in optical lattice such as Williams et. al experiment [R. A. Williams, S. Al-Assam, and C. J. Foot, Phys. Rev. Lett. { 104} (2010) 050404.].

arXiv:2005.07763Jan 1, 20200 citations

Moment of inertia of a trapped superfluid gas of atomic fermions

M. Farine, Peter Schuck, X. Viñas

The moment of inertia \ensuremath{\Theta} of a trapped superfluid gas of atomic fermions ${(}^{6}\mathrm{Li})$ is calculated as a function of the temperature. At zero temperature the moment of inertia takes on the irrotational-flow value. Only for T very close to ${T}_{c}$ is rigid rotation attained. It is proposed that future measurements of the rotational energy will unambiguously reveal whether the system is in a superfluid state or not.The moment of inertia \ensuremath{\Theta} of a trapped superfluid gas of atomic fermions ${(}^{6}\mathrm{Li})$ is calculated as a function of the temperature. At zero temperature the moment of inertia takes on the irrotational-flow value. Only for T very close to ${T}_{c}$ is rigid rotation attained. It is proposed that future measurements of the rotational energy will unambiguously reveal whether the system is in a superfluid state or not.

arXiv:cond-mat/9901241Physical Review AJun 16, 200029 citations

The moment of inertia and the scissors mode of a Bose-condensed gas

Onofrio M. Maragò, Gerald Hechenblaikner, E. Hodby +2 more

We relate the frequency of the scissors mode to the moment of inertia of a trapped Bose gas at finite temperature in a semi-classical approximation. We apply these theoretical results to the data obtained in our previous study of the properties of the scissors mode of a trapped Bose-Einstein condensate of $^{87}$ Rb atoms as a function of the temperature. The frequency shifts that we measured show quenching of the moment of inertia of the Bose gas at temperatures below the transition temperature - the system has a lower moment of inertia that of a rigid body with the same mass distribution, because of superfluidity.We relate the frequency of the scissors mode to the moment of inertia of a trapped Bose gas at finite temperature in a semi-classical approximation. We apply these theoretical results to the data obtained in our previous study of the properties of the scissors mode of a trapped Bose-Einstein condensate of $^{87}$Rb atoms as a function of the temperature. The frequency shifts that we measured show quenching of the moment of inertia of the Bose gas at temperatures below the transition temperature - the system has a lower moment of inertia that of a rigid body with the same mass distribution, because of superfluidity.

arXiv:cond-mat/0109193Journal of Physics Condensed MatterDec 24, 20018 citations

Rotational properties of trapped bosons

F. Brosens, J. T. Devreese, L. F. Lemmens

Based on the Hellman-Feynman theorem, it is shown that the average square radius of a cloud of interacting bosons in a parabolic well can be derived from their free energy. As an application, the temperature dependence of the moment of inertia of noninteracting bosons in a parabolic trap is determined as a function of the number of bosons. Well below the critical condensation temperature, the Bose-Einstein statistics are found to substantially reduce the moment of inertia of this system, as compared to a gas of ``distinguishable'' particles in a parabolic well.Based on the Hellman-Feynman theorem, it is shown that the average square radius of a cloud of interacting bosons in a parabolic well can be derived from their free energy. As an application, the temperature dependence of the moment of inertia of noninteracting bosons in a parabolic trap is determined as a function of the number of bosons. Well below the critical condensation temperature, the Bose-Einstein statistics are found to substantially reduce the moment of inertia of this system, as compared to a gas of ``distinguishable'' particles in a parabolic well.

arXiv:cond-mat/0004208Physical Review AMar 1, 199712 citations

T > .25 T_0

and not dramatically smaller than

T_0

q(T)

for the system under consideration. The effects of the interatomic interaction, the finite number of atoms, and optical potential depth on the vortices number are investigated. The calculated results show that the vortices number as a function of the rotation rate depends on the normalized temperature, interatomic interaction, optical potential depth, and the number of atoms in the

{\in situ}

size. These results provide solid theoretical foundations for the measured experimental data for rotating condensate boson in optical lattice such as Williams et. al experiment [R. A. Williams, S. Al-Assam, and C. J. Foot, Phys. Rev. Lett. { 104} (2010) 050404.].

The moment of inertia \ensuremath{\Theta} of a trapped superfluid gas of atomic fermions

{(}^{6}\mathrm{Li})

is calculated as a function of the temperature. At zero temperature the moment of inertia takes on the irrotational-flow value. Only for T very close to

{T}_{c}

is rigid rotation attained. It is proposed that future measurements of the rotational energy will unambiguously reveal whether the system is in a superfluid state or not.

^{87}

Rb atoms as a function of the temperature. The frequency shifts that we measured show quenching of the moment of inertia of the Bose gas at temperatures below the transition temperature - the system has a lower moment of inertia that of a rigid body with the same mass distribution, because of superfluidity.