We present two gapless mean-field theories for trapped Bose-Einstein condensates, and compare them to the better known Hartree-Fock-Bogoliubov (HFB)-Popov approach. The proposed theories are based on suitable inclusion of the simplest anomalous average of the Bose field operator. This leads to an effective interaction between two atoms which is both temperature and density dependent, as opposed to the HFB-Popov approach, for which it is constant. These theories are compared to the HFB-Popov approach for a trapped one-dimensional condensate of 2000 atoms. The density profiles and excitation frequencies of the proposed theories differ from the corresponding HFB-Popov ones by at most a few percent.We present two gapless mean-field theories for trapped Bose-Einstein condensates, and compare them to the better known Hartree-Fock-Bogoliubov (HFB)-Popov approach. The proposed theories are based on suitable inclusion of the simplest anomalous average of the Bose field operator. This leads to an effective interaction between two atoms which is both temperature and density dependent, as opposed to the HFB-Popov approach, for which it is constant. These theories are compared to the HFB-Popov approach for a trapped one-dimensional condensate of 2000 atoms. The density profiles and excitation frequencies of the proposed theories differ from the corresponding HFB-Popov ones by at most a few percent.

Physical Review ASep 1, 199861 citations

Bose-Einstein Condensation of Pairons

Kluwer Academic Publishers eBooksJan 27, 20061 citation

Collective excitations of Bose-Einstein-condensed gases at finite temperatures

R. J. Dodd, Mark Edwards, Charles W. Clark +1 more

We have applied the Popov version of the Hartree-Fock-Bogoliubov (HFB) approximation to calculate the finite-temperature excitation spectrum of a Bose-Einstein condensate (BEC) of ${}^{87}\mathrm{Rb}$ atoms. For lower values of the temperature, we find excellent agreement with recently published experimental data for the JILA time-averaged orbiting potential trap. In contrast to recent comparison of the results of HFB-Popov theory with experimental condensate fractions and specific heats, there is disagreement of the theoretical and recent experimental results near the BEC phase transition temperature.We have applied the Popov version of the Hartree-Fock-Bogoliubov (HFB) approximation to calculate the finite-temperature excitation spectrum of a Bose-Einstein condensate (BEC) of ${}^{87}\mathrm{Rb}$ atoms. For lower values of the temperature, we find excellent agreement with recently published experimental data for the JILA time-averaged orbiting potential trap. In contrast to recent comparison of the results of HFB-Popov theory with experimental condensate fractions and specific heats, there is disagreement of the theoretical and recent experimental results near the BEC phase transition temperature.

arXiv:cond-mat/9708139Physical Review AJan 1, 1998119 citations

Theory of magnetic-field-induced Bose-Einstein condensation of triplons in Ba3Cr2O8

Tyler Dodds, Bohm‐Jung Yang, Yong Baek Kim

Motivated by recent experiments on ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ , a new spin-dimer compound with spin-1/2 moments of ${\text{Cr}}^{5+}$ ions, we theoretically investigate the field-induced magnetic ordering in this material in view of the Bose-Einstein condensation (BEC) of triplet excitations (triplons). We apply the self-consistent Hartree-Fock-Popov (HFP) approach to a microscopic Hamiltonian, using the realistic triplon dispersion measured in an inelastic neutron-scattering experiment. In particular, we ask to what extent the BEC of dilute triplons near the critical field can explain the magnetic ordering in this material. For example, we investigate the temperature range where the BEC picture of triplons can be applied via the HFP approach. We also determine the temperature regime where a quadratic approximation of the triplon dispersion works. It is found that the strength of the effective repulsive interaction between triplons is much weaker in ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ than in the canonical spin-dimer compound ${\text{TlCuCl}}_{3}$ . Small effective repulsive interaction in combination with the narrow band of triplons leads to higher density of triplons ${n}_{\text{cr}}$ at the critical point. The combined effect points to a bigger HFP correction $U{n}_{\text{cr}}$ in ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ than in ${\text{TlCuCl}}_{3}$ . Nonetheless, the HFP approach provides a reasonable explanation of the transverse magnetization and the specific-heat data of ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ .Motivated by recent experiments on ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$, a new spin-dimer compound with spin-1/2 moments of ${\text{Cr}}^{5+}$ ions, we theoretically investigate the field-induced magnetic ordering in this material in view of the Bose-Einstein condensation (BEC) of triplet excitations (triplons). We apply the self-consistent Hartree-Fock-Popov (HFP) approach to a microscopic Hamiltonian, using the realistic triplon dispersion measured in an inelastic neutron-scattering experiment. In particular, we ask to what extent the BEC of dilute triplons near the critical field can explain the magnetic ordering in this material. For example, we investigate the temperature range where the BEC picture of triplons can be applied via the HFP approach. We also determine the temperature regime where a quadratic approximation of the triplon dispersion works. It is found that the strength of the effective repulsive interaction between triplons is much weaker in ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ than in the canonical spin-dimer compound ${\text{TlCuCl}}_{3}$. Small effective repulsive interaction in combination with the narrow band of triplons leads to higher density of triplons ${n}_{\text{cr}}$ at the critical point. The combined effect points to a bigger HFP correction $U{n}_{\text{cr}}$ in ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$ than in ${\text{TlCuCl}}_{3}$. Nonetheless, the HFP approach provides a reasonable explanation of the transverse magnetization and the specific-heat data of ${\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}$.

arXiv:0910.0247Physical Review BFeb 9, 201013 citations

We have applied the Popov version of the Hartree-Fock-Bogoliubov (HFB) approximation to calculate the finite-temperature excitation spectrum of a Bose-Einstein condensate (BEC) of

{}^{87}\mathrm{Rb}

atoms. For lower values of the temperature, we find excellent agreement with recently published experimental data for the JILA time-averaged orbiting potential trap. In contrast to recent comparison of the results of HFB-Popov theory with experimental condensate fractions and specific heats, there is disagreement of the theoretical and recent experimental results near the BEC phase transition temperature.

Motivated by recent experiments on

{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}

, a new spin-dimer compound with spin-1/2 moments of

{\text{Cr}}^{5+}

ions, we theoretically investigate the field-induced magnetic ordering in this material in view of the Bose-Einstein condensation (BEC) of triplet excitations (triplons). We apply the self-consistent Hartree-Fock-Popov (HFP) approach to a microscopic Hamiltonian, using the realistic triplon dispersion measured in an inelastic neutron-scattering experiment. In particular, we ask to what extent the BEC of dilute triplons near the critical field can explain the magnetic ordering in this material. For example, we investigate the temperature range where the BEC picture of triplons can be applied via the HFP approach. We also determine the temperature regime where a quadratic approximation of the triplon dispersion works. It is found that the strength of the effective repulsive interaction between triplons is much weaker in

{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}

than in the canonical spin-dimer compound

{\text{TlCuCl}}_{3}

. Small effective repulsive interaction in combination with the narrow band of triplons leads to higher density of triplons

{n}_{\text{cr}}

at the critical point. The combined effect points to a bigger HFP correction

U{n}_{\text{cr}}

{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}

than in

{\text{TlCuCl}}_{3}

. Nonetheless, the HFP approach provides a reasonable explanation of the transverse magnetization and the specific-heat data of

{\text{Ba}}_{3}{\text{Cr}}_{2}{\text{O}}_{8}