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

OPTICSCONDENSED MATTER

FLUIDS

FIELD THEORY

STAT. PHYS.

MAGNETISM.

LASERS

ATOMIC PHYS.

SUPERFLUID

QUANT. VORTICES

TURBULENCE

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

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

How to form the vortices?

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

BEC is a superfluid

Idea of turbulent regime in superfluids

1955: Feynman proposed that “superfluid turbulence” consists of a tangle of quantized vortices.

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 fluid

Observations are indirectly done

T > Tc T < Tc T << Tc

Turbulence Thermodynamics Magnetism Finite Temperature

Mixture of BECs: K,Na

Ωx

Ωz

Vortex lattice

Vor

tex

latt

ice

Vortex tangle

?

0

ωx×ωz

From M. Tsubota

Original motivation:

Vortex lines are subject to many effects: oscillations, reconnections, etc…

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

BEC

Displacement,

Rotation and

Deformation of the potential

ADDITION OF “SHAKING” COILS

EXCITATION BY OSCILLATION OF THE POTENTIAL

Atomic washing machine

E. A. L. Henn et al., J. Low Temp. Phys. 158, 435 (2010)

Total potential

PRODUCING BEC ( 1 MIN )

EXCITATION ( 0 TO 70 ms )

Time and amplitude

Rest ( 20 ms)

TOF FOLLOWED BY ABSORPTION IMAGE

VARYING AMPLITUDE AND TIME OF EXCITATION WE OBSERVE

Oscillatory bending

vortices

Phys. Rev. A 79, 043618 (2009)

Vortices and anti-vortices are together)

Three-vortex configurations in trapped Bose-Einstein

Phys. Rev. A 82,033616(2010)

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

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

of V

ortic

es

Amplitude (mV)

Vortices to tangle vortices

“TURBULENCE”

J Low Temp Phys (2010) 158: 435–442

Phys. 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 POSITIONS

ORIENTATIONS AND LENGTH

Tangle vortices region

KELVIN MODESVortex breaking and reconnecting

4 6 8 10 12 14 16

0,6

0,8

1,0

1,2

1,4 Turbulent cloud Regular BEC cloud Thermal cloud

Asp

ect ra

tio

TOF (ms)

Thermal BEC Turbulent

Cloud expansion

( hydrodynamics)

J. Phys. Conf.Ser.264,012004(2011)

A FEW VORTICES DOES NOT CAUSE SELF

SIMILAR EXPANSION

0 5 10 15 20 25 30 35

0

1

2

3

4

5

6

7

A

spect

Ratio

Time (ms)

N= 0 N = 5 N = 10 N = 15

JLTP 166, 49-58 (2012

Las. Phys. Lett. 8,691(2011)

0 20 40 60 800

40

80

120

160

Am

plit

ude

of E

xcita

tion

( 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)

EXCITATION RATE

DEPENDS ON AMPLITUDE

OVERPOPULATION OF VORTICES IN THE CLOUD

0~l

NN cvort

TURBULENCE

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

lnl

mlEvort

ml

0

vortvortENtI 0 ( Number of vortices formed)

Turbulence takes place when vortices densely fill the trap:

0~l

NN cvort

a

8

1

vortc El

tI0.

t

ElI vortc

.0

There is a “kind “ of critical number of vortices introduced in the cloud before it gets to be turbulent

Determination of the board between non-turbulent and turbulent

For our conditions we calculated around 20 vortices

Simulation by Tsubota, Kasamatsu and Kobayashi - Japan

i r

t

2

2 1

2

x2

r2x 2 y 2

u2D

2 z sin t Lz

Needs dissipation

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……..