We calculate the Bose-Einstein-condensate (BEC) occupation statistics vs the interparticle interaction in a dilute gas with a nonuniform condensate in a box trap within the Bogoliubov approach. The results are compared against the previously found BEC-occupation statistics in (i) an ideal gas and (ii) a weakly interacting gas with a uniform condensate. In particular, we reveal and explicitly describe an appearance of a nontrivial transition from the ideal gas to the Thomas-Fermi regime. The results include finding the main regimes of the BEC statistics---the anomalous non-Gaussian thermally dominated fluctuations and the Gaussian quantum-dominated fluctuations---as well as a crossover between them and their manifestations in a mesoscopic system. Remarkably, we show that the effect of the boundary conditions, imposed at the box trap, on the BEC fluctuations does not vanish in the thermodynamic limit of a macroscopic system even in the presence of the interparticle interactions. Finally, we discuss a challenging problem of an experimental verification of the theory of the BEC fluctuations addressing a much deeper level of the many-body statistical physics than usually studied quantities related to the mean condensate occupation.We calculate the Bose-Einstein-condensate (BEC) occupation statistics vs the interparticle interaction in a dilute gas with a nonuniform condensate in a box trap within the Bogoliubov approach. The results are compared against the previously found BEC-occupation statistics in (i) an ideal gas and (ii) a weakly interacting gas with a uniform condensate. In particular, we reveal and explicitly describe an appearance of a nontrivial transition from the ideal gas to the Thomas-Fermi regime. The results include finding the main regimes of the BEC statistics---the anomalous non-Gaussian thermally dominated fluctuations and the Gaussian quantum-dominated fluctuations---as well as a crossover between them and their manifestations in a mesoscopic system. Remarkably, we show that the effect of the boundary conditions, imposed at the box trap, on the BEC fluctuations does not vanish in the thermodynamic limit of a macroscopic system even in the presence of the interparticle interactions. Finally, we discuss a challenging problem of an experimental verification of the theory of the BEC fluctuations addressing a much deeper level of the many-body statistical physics than usually studied quantities related to the mean condensate occupation.

arXiv:2007.15753Physical Review AOct 13, 202014 citations

Reentrant behavior of breathing mode in one-dimensional Bose gas

Andrii Gudyma, G. E. Astrakharchik, Mikhail B. Zvonarev

We calculate the breathing mode frequency $\omega$ in a one-dimensional Bose gas confined to a harmonic trap of frequency $\omega_z$ . We predict a smooth crossover from Thomas-Fermi Bose-Einstein condensate (BEC) regime ( $\omega = \sqrt{3} \omega_z$ ) to Gaussian BEC regime ( $\omega = 2 \omega_z$ ) using Hartree approximation and sum rules approach, adopted to small system sizes. Local density approximation (LDA) correctly captures the crossover from Tonks-Girardeau ( $\omega = 2 \omega_z$ ) to Thomas-Fermi BEC ( $\omega = \sqrt{3} \omega_z$ ) regimes. Predictions from local density and Hartree approximations can be continuously matched for $N>25$ particles, providing a complete zero-temperature description for large number of particles and resulting in a non-monotonic reentrant behavior of the breathing frequency. For smaller number of particles (ranging from $N=2$ to $N=25$ ) we perform extensive diffusion Monte Carlo simulations. This permits us to obtain a complete picture, applicable to arbitrary number of particles and any repulsive interaction strength. We provide perturbative analysis for both weak and strong coupling regimes. We revisit Innsbruck group experiment [Science 325, 1224 (2009)], analyzing the measurements done in Thomas-Fermi - Gaussian BEC crossover, and demonstrate that the breathing frequency follows a reentrant behavior as a function of the interaction strength in full agreement with our theory.We calculate the breathing mode frequency $\omega$ in a one-dimensional Bose gas confined to a harmonic trap of frequency $\omega_z$. We predict a smooth crossover from Thomas-Fermi Bose-Einstein condensate (BEC) regime ($\omega = \sqrt{3} \omega_z$) to Gaussian BEC regime ($\omega = 2 \omega_z$) using Hartree approximation and sum rules approach, adopted to small system sizes. Local density approximation (LDA) correctly captures the crossover from Tonks-Girardeau ($\omega = 2 \omega_z$) to Thomas-Fermi BEC ($\omega = \sqrt{3} \omega_z$) regimes. Predictions from local density and Hartree approximations can be continuously matched for $N>25$ particles, providing a complete zero-temperature description for large number of particles and resulting in a non-monotonic reentrant behavior of the breathing frequency. For smaller number of particles (ranging from $N=2$ to $N=25$) we perform extensive diffusion Monte Carlo simulations. This permits us to obtain a complete picture, applicable to arbitrary number of particles and any repulsive interaction strength. We provide perturbative analysis for both weak and strong coupling regimes. We revisit Innsbruck group experiment [Science 325, 1224 (2009)], analyzing the measurements done in Thomas-Fermi - Gaussian BEC crossover, and demonstrate that the breathing frequency follows a reentrant behavior as a function of the interaction strength in full agreement with our theory.

Dec 14, 20140 citations

Statistical fluctuations and quasi phase transition of mesoscopic Bose–Einstein condensation in anharmonic trap

Sangita Bera, M. L. Lekala, Gaotsiwe Joel Rampho +2 more

Physica A Statistical Mechanics and its ApplicationsApr 11, 20192 citations

Vortex lattices in Bose-Einstein condensates: From the Thomas-Fermi regime to the lowest-Landau-level regime

Marco Cozzini, S. Stringari, C. Tozzo

We consider a periodic vortex lattice in a rotating Bose-Einstein-condensed gas, where the centrifugal potential is exactly compensated by the external harmonic trap. By introducing a gauge transformation which makes the Hamiltonian periodic, we numerically solve the two-dimensional (2D) Gross-Pitaevskii equation finding the exact mean field ground state. In particular, we explore the crossover between the Thomas-Fermi regime, holding for large values of the coupling constant, and the lowest Landau level limit, corresponding to the weakly interacting case. Explicit results are given for the equation of state, the vortex core size, as well as the elastic shear modulus, which is crucial for the calculation of the Tkachenko frequencies.We consider a periodic vortex lattice in a rotating Bose-Einstein-condensed gas, where the centrifugal potential is exactly compensated by the external harmonic trap. By introducing a gauge transformation which makes the Hamiltonian periodic, we numerically solve the two-dimensional (2D) Gross-Pitaevskii equation finding the exact mean field ground state. In particular, we explore the crossover between the Thomas-Fermi regime, holding for large values of the coupling constant, and the lowest Landau level limit, corresponding to the weakly interacting case. Explicit results are given for the equation of state, the vortex core size, as well as the elastic shear modulus, which is crucial for the calculation of the Tkachenko frequencies.

arXiv:cond-mat/0509559Physical Review AFeb 22, 200619 citations

Quantum phase transition in one-dimensional Bose-Einstein condensates with attractive interactions

Hiroki Saito

Jan 1, 20030 citations

We calculate the breathing mode frequency

\omega

in a one-dimensional Bose gas confined to a harmonic trap of frequency

\omega_z

. We predict a smooth crossover from Thomas-Fermi Bose-Einstein condensate (BEC) regime (

\omega = \sqrt{3} \omega_z

) to Gaussian BEC regime (

\omega = 2 \omega_z

) using Hartree approximation and sum rules approach, adopted to small system sizes. Local density approximation (LDA) correctly captures the crossover from Tonks-Girardeau (

\omega = 2 \omega_z

) to Thomas-Fermi BEC (

\omega = \sqrt{3} \omega_z

) regimes. Predictions from local density and Hartree approximations can be continuously matched for

N>25

particles, providing a complete zero-temperature description for large number of particles and resulting in a non-monotonic reentrant behavior of the breathing frequency. For smaller number of particles (ranging from

N=2

N=25

) we perform extensive diffusion Monte Carlo simulations. This permits us to obtain a complete picture, applicable to arbitrary number of particles and any repulsive interaction strength. We provide perturbative analysis for both weak and strong coupling regimes. We revisit Innsbruck group experiment [Science 325, 1224 (2009)], analyzing the measurements done in Thomas-Fermi - Gaussian BEC crossover, and demonstrate that the breathing frequency follows a reentrant behavior as a function of the interaction strength in full agreement with our theory.