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Bose-Einstein CondensateFundaments, Excitation and
Turbulence
Vanderlei Salvador Bagnato
Instituto de Física de São Carlos – Universidade de São Paulo
USHUAIA -2012
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Lectures:
1) Basic concepts for BEC
2) Excitations – collective modes
Thermodynamics – Global variables
3) Vortices and Quantum turbulence
Future directions
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BEC
OPTICSCONDENSED MATTER
FLUIDS
FIELD THEORY
STAT. PHYS.
MAGNETISM.
LASERS
ATOMIC PHYS.
SUPERFLUID
QUANT. VORTICES
TURBULENCE
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Quantum turbulence has recently become one of the most important branches in low temperature physics.
Quantum turbulence has been studied thoroughly in superfluid 4He and 3He, but never addressed in atomic Bose-Einstein condensates.
BECs may be a nice system for QT
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Vortex lattice Vortex tangleSuperfluid He
Atomic BEC
There are two main cooperative phenomena of quantized vortices; Vortex lattice under rotation and Vortex tangle (Quantum turbulence).
None
3.
1. QT in a trapped BEC
M. Tsubota
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How to form the vortices?
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Main aspect of vortex in the superfluid quantized
(1) Circulation
(2)core size is very small.
v s ds nStability => n = 1
r
h / m
Healing length = ( 8π ρ a ) -1/2
MIT
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BEC is a superfluid
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Idea of turbulent regime in superfluids
1955: Feynman proposed that “superfluid turbulence” consists of a tangle of quantized vortices.
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Liquid Helium1955 – 1957: Vinen observed “superfluid turbulence”.Mutual friction between the vortex tangle and the normal fluid causes dissipation of the flow.
Hard to see individual components in the turbulent fluidObservations are indirectly done
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T > Tc T < Tc T << Tc
Turbulence Thermodynamics Magnetism Finite Temperature
Mixture of BECs: K,Na
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Ωx
Ωz
Vortex lattice
Vorte
x la
ttice
Vortex tangle
?0
ωx×ωz
From M. Tsubota
Original motivation:
Vortex lines are subject to many effects: oscillations, reconnections, etc…
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GENERATION OF VORTICES
FORMATIONS OF VORTICES CLUSTERS
EMERGENCE OF TURBULENCE
SELF-SIMILAR EXPANSION
DIAGRAM OF EXCITATIONS
FINITE SIZE EFFECT
GRANULATION
GENERALIZED THERMODYNAMICS
MODEL FOR SELF-SIMILAR EXPANSION
SECOND SOUND EXCITATION (COUNTER FLOW )
KINETIC ENERGY SPECTRUM
2009
2012
Sequence of works
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BEC
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Displacement, Rotation andDeformation of the potential
ADDITION OF “SHAKING” COILS
EXCITATION BY OSCILLATION OF THE POTENTIAL
Atomic washing machine
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E. A. L. Henn et al., J. Low Temp. Phys. 158, 435 (2010)
Total potential
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PRODUCING BEC ( 1 MIN )
EXCITATION ( 0 TO 70 ms )Time and amplitude
Rest ( 20 ms)
TOF FOLLOWED BY ABSORPTION IMAGE
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VARYING AMPLITUDE AND TIME OF EXCITATION WE OBSERVE
Oscillatory bending
vortices
Phys. Rev. A 79, 043618 (2009)
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Vortices and anti-vortices are together)
Three-vortex configurations in trapped Bose-Einstein
Phys. Rev. A 82,033616(2010)
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Looking at stable three-vortex configurations we know that our excitation is able to create vortices and anti-vortices at the same time.
J.A. Seman, et al. Phys. Rev. A 82, 033616 (2010)
BEC-I: results
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PROLIFERATION
0 50 100 150 200 250 300-2
0
2
4
6
8
10
12
14
16
18
20
Excitation Time
20 ms 40 ms 50 ms
Num
ber o
f Vor
tices
Amplitude (mV)
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Vortices to tangle vortices
“TURBULENCE”
J Low Temp Phys (2010) 158: 435–442Phys. Rev. Lett. 103, 045301 (2009)
Increasing amplitude or time of excitation: Explosion and proliferation of many vortices but no regular pattern and hard to count
NON REGULAR – MANY POSITIONSORIENTATIONS AND LENGTH
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Tangle vortices region
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KELVIN MODESVortex breaking and reconnecting
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4 6 8 10 12 14 16
0,6
0,8
1,0
1,2
1,4 Turbulent cloud Regular BEC cloud Thermal cloud
Aspe
ct ra
tio
TOF (ms)
Thermal BEC Turbulent
Cloud expansion( hydrodynamics)
J. Phys. Conf.Ser.264,012004(2011)
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A FEW VORTICES DOES NOT CAUSE SELF SIMILAR EXPANSION
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0 5 10 15 20 25 30 35
0
1
2
3
4
5
6
7
As
pect
Ratio
Time (ms)
N= 0 N = 5 N = 10 N = 15
JLTP 166, 49-58 (2012
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Las. Phys. Lett. 8,691(2011)
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0 20 40 60 800
40
80
120
160
Am
plitu
de o
f Exc
itatio
n ( m
G/c
m)
Time of Excitation ( ms)
Vortices( TURBULENCE)
Vortices( NO TURBULENCE)
CRITICAL LINE ------ Fitting: A+Ao = C/t
Finite size effects on the QT
Laser Phys. Lett. 8,393(2011)
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EXCITATION RATE
DEPENDS ON AMPLITUDE
OVERPOPULATION OF VORTICES IN THE CLOUD
0~ lNN cvort
TURBULENCE
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SIMPLE MODEL BASED ON ENERGY BALANCE
0I
0I Rate of energy transferred to the cloud
tI .0 ( Energy Coupled to the cloud )
.. vortEEvorticeFirst
0
20
2
ln lml
Evort
ml 0
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vortvortENtI 0 ( Number of vortices formed)
Turbulence takes place when vortices densely fill the trap:
0~ lNN cvort
a
81
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vortc EltI0.
tElI vort
c
.0
There is a “kind “ of critical number of vortices introduced in the cloud before it gets to be turbulentDetermination of the board between non-turbulent
and turbulentFor our conditions we calculated around 20 vortices
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Simulation by Tsubota, Kasamatsu and Kobayashi - Japan
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i r
t
2
2 1
2x
2
r2 x
2 y 2
u2D
2 z sin t Lz
Needs dissipation
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Vortex array Vortex tangleSuperfluid He
Atomic BEC
Conclusions:
2.
3.
Intrinsic difficulties
Hope
The wider significance of QT rises interesting questions. I believe that many aspects of it are applicable in other fields. Grigory Volovick ( Finland ) suggests, for example that QT might have been important in the evolution of cosmic strings in the early universe. Certainly QT may throw light on many unsolved problems. The contribution of BEC for all that is in the very beginning……..
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