Bose-Einstein Condensate Fundaments, Excitation and Turbulence

1. Bose-Einstein Condensate Fundaments, Excitation and Turbulence VanderleiSalvador Bagnato Instituto de Física de São Carlos – Universidade de São Paulo USHUAIA -2012

2. Lectures: • Basic concepts for BEC • Excitations – collective modes • Thermodynamics – Global variables • Vortices and Quantum turbulence • Future directions

3. BEC is a superfluid

5. VOLUME PRESSURE Can one make an analysis of tem Thermodynamics of an heterogeneous system using a single marcoscopic variable? (,,) = Extensive x Intensive

7. The Gibbs-Duhem Relation Alternatively, we can use the famous Gibbs-Duhem relation: P is a fundamental quantity when expressed in terms of T and  - contains all the thermodynamics information of the system.

8. The Gibbs-Duhem Relation Taking T constant, N/V Consider an atomic gas of bosons of mass m in a trap The volume parameter is Where is the density profile measured.

10. Measurements in three situations 1.T  Tc – Thermal Cloud 2.T < Tc – Condesate fraction 3.Extrapolation to T0 To obtain P: Processing to obtain Measurement of Based on Y. Castin, and R. Dum: Phys. Rev. Lett. 77, 5315 (1996).

11. Experimental data Gaussian fit for the wings Thomas-Fermi profile for the center Total fit Double component velocity distribution

12. Overrall view across the transition Varying the trapped number of atoms since  is constant: variation of N variation of density

13. The transition line P vs T – Phase Diagram It occurs from the discontinuity of the derivative of Pc vs Tc The relation Pc vs Tc is not like

14. Extrapolation T0 For zero temperature:

15. Extrapolation T0 Taking the points after the transition we could extrapolate the curves to zero:

16. Dependence of P(T0) with Number Finally we plot the zero temperature harmonic pressure as a function of N7/5:

17. Pressure T0

18. Perspectives 1-By knowing the equation of state one can measure the heat capacity at constant harmonic volume: This measurement requires the possibility to adiabatically change the harmonic volume, i.e., change the frequencies of the harmonic trap. This can be done in an optical trap since:

19. Perspectives 2-Another relevant quantity that could be measured is the isothermal compressibility: -both must diverge at the critical temperature.

20. EXCITATION BY OSCILLATION OF THE POTENTIAL ADDITION OF “SHAKING” COILS Displacement, Rotation and Deformation of the potential Atomic washing machine

21. QUADRUPOLE AND DIPOLE EXCITATIONS AND …….. 7,5ms 8ms 8,5ms 7ms 5,5ms 6ms 6,5ms 5ms 11,5ms 12ms 11ms Regular BEC 9,5ms 10ms 10,5ms 9ms

22. FORMATION OF VORTICES BY OSCILLATORY EXCITATION

26. Fluctuations at the surface of the BEC

28. BEC and thermal cloud counter flow

29. Phys. Rev. A 79, 043618 (2009)

30. How to form the vortices?