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

Lectures: 1)Basic concepts for BEC 2)Excitations – collective modes Thermodynamics – Global variables 3)Vortices and Quantum turbulence Future directions

BEC is a superfluid

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

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

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

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

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

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

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

Extrapolation T  0 For zero temperature:

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

Dependence of P(T  0) with Number Finally we plot the zero temperature harmonic pressure as a function of N 7/5 :

Pressure T  0

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: Perspectives

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

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

Regular BEC 5ms 5,5ms6ms6,5ms 7ms 7,5ms8ms8,5ms 9ms 9,5ms10ms10,5ms 11ms 11,5ms12ms QUADRUPOLE AND DIPOLE EXCITATIONS AND ……..

FORMATION OF VORTICES BY OSCILLATORY EXCITATION

Fluctuations at the surface of the BEC

BEC and thermal cloud counter flow

Phys. Rev. A 79, (2009)

How to form the vortices?