Bose-Einstein Condensate Fundaments, Excitation and Turbulence Vanderlei Salvador Bagnato Instituto de Física de São Carlos – Universidade de São Paulo USHUAIA -2012
Jan 03, 2016
Bose-Einstein CondensateFundaments, 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?
VOLUME PRESSURE
(,,) = Extensive x Intensive
)()(
43
3
zgkT
kTP
3
1
V
)(
)(
3
4
zg
zgNkTPV
rd)r(U)r(n3
2P 3
30
Alternatively, we can use the famous Gibbs-Duhem relation:
The Gibbs-Duhem Relation
dV
NdT
V
SdP
),( TPP P is a fundamental quantity when expressed
in terms of T and - contains all the thermodynamics information of the system.
Taking T constant, N/VConsider an atomic gas of bosons of mass m in a trap
The Gibbs-Duhem Relation
221 ).()( rmrVext
The volume parameter is321
1
V
22
322
222
133
2
1)(
3
2zyxmrrdP
Where )(r is the density profile measured.
rdrrVrV
P ext3)()(.
3
1
To obtain P:
1.T Tc – Thermal Cloud2.T < Tc – Condesate fraction3.Extrapolation to T0
Measurements in three situations
TOFafter )(r
Measurement of situin )(r
Processing to obtain
Based on Y. Castin, and R. Dum: Phys. Rev. Lett. 77, 5315(1996).
rdrrVrV
P ext3)()(.
3
1
Double component velocity distribution
Thomas-Fermi profile for the center
Experimental data
Total fit
Gaussian fit for the wings
Overrall view across the transitionVarying the trapped number of atomssince is constant:variation of N variation of density
The transition line P vs T – Phase DiagramIt occurs from the discontinuity of the derivative of Pc vs Tc
0,0 0,1 0,2 0,3 0,4 0,5 0,6-2,00E-020
0,00E+000
2,00E-020
4,00E-020
6,00E-020
8,00E-020
1,00E-019
1,20E-019
1,40E-019
1,60E-019
1,80E-019
Pc
Pc
Tc
BEC + normal
normal
The relation Pc vs Tc is not like cc TP
Extrapolation T0
For zero temperature:
m
aUzyxm
UrTF
2
022
322
222
10
4where
2
11
density) (harmonic~ where
~157
1 yieldswhich
3
5/75/220
N
amP
Extrapolation T0
Taking the points after the transition we could extrapolate the curves to zero:
Dependence of P(T0) with Number
Finally we plot the zero temperature harmonic pressure as a function of N7/5:
Pressure T0
4,1 and
1,5 found wee wher
~say can ely weAlternativ
theory
0,30,2-
0
P
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:
0, Pzr
Perspectives
SNNVV T
V
T
PTC
,,
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 5,5ms 6ms 6,5ms
7ms 7,5ms 8ms 8,5ms
9ms 9,5ms 10ms 10,5ms
11ms 11,5ms 12ms
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, 043618 (2009)
How to form the vortices?