GLOBAL THERMODYNAMIC VARIABLES FOR TRAPPED QUANTUM SYSTEM

&QUANTUM TURBULENCE

V. S. Bagnato

University of São Paulo

Brazil

http://cepof.ifsc.usp.br

QUANTUM TURBULENCE

cepof.ifsc.usp.br

2

Diffusion

Innovation

Innovation with Social responsibility

http://cepof.ifsc.usp.br

FacultE. HeennS.R. Muniz

ResearchersK.. MagalhãesG. TellesM. CaracanhasPost-Doc

G. StudentP. CastilhoP. TavaresR. PoliseliE. PedrosoF. VivancoA. SmairaA. FritschPost-Doc

M.TsatusF. Poveda-Cuevas

http://cepof.ifsc.usp.br

BEC project

A. FritschA. Cidrin

Three BEC experiments:

BEC1 – QT ( Rb-87)

BEC2 – Thermodynamic and SQUID ( Rb -87 and now Rb-85)

BEC3 – Na/K – vortices transference

COLLABORATORS:G. ROATI ( ITALY)A. FETTER ( USA)M. TSUBOTA ( JAPAN)V. ROMERO-ROCHIN ( MEXICO)V. YUKALOV( RUSSIA)

Brazilian Atomic Clock

Bobinas de Compensação

BEC

OPTICSCONDENSED MATTER

FLUIDSLASERS

ATOMIC PHYS.

SUPERFLUID

FLUIDS

FIELD THEORY

STAT. PHYS.

MAGNETISM.

LASERS

QUANT. VORTICES

TURBULENCE

T > Tc T < Tc T << Tc

Turbulence in BEC

Introduction – General remarks

Generation of vortices/anti-vortices

Proliferation of vortices to tangle configuration

TURBULENCE

Road m

ap

TURBULENCE

Decay of turbulence Evolution to Granulation

Properties of Turbulent cloud

Hydrodynamics ThermodynamicsTransition to Weak QT

Experiments and Theoretical aspects

THERMODYNAMICS WITH GLOBAL VARIABLES FOR COLD TRAPPED ATOMS

Can we describe the trapped system with global variables , in steady of local variables?

Volume – Extensive variablePressure - Intensive variablePressure - Intensive variable

ΩΩΩΩ(µµµµ,ΤΤΤΤ,ωωωω) = Extensive x Intensive

For extensive: √√√√ λ√λ√λ√λ√ N λλλλNE λλλλES λλλλS

:

Critical temperature:

3/194.0 NTk hoCB ⋅⋅= ωh

Thermodynamic limit: ∞→N constT hoc =

Volume parameter:

Pressure conjugated to volume….

Isodensity curves:

Phys. Rev. A, v. 85, 023632, 2012.

The transition line P vs T – Phase DiagramIt occurs from the discontinuity of the derivative of Pc vs Tc

1,00E-019

1,20E-019

1,40E-019

1,60E-019

1,80E-019

Pc

BEC

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-020Pc

Tc

+ normal

normal

δα cc TP

In He:

λλλλ transition He-I => He-II

Heat Capacity

With the macroscopic parameters:

(pure thermal)

(pure BEC)

R.F. Shiozaki et al., Phys. Rev. A. (2014)

(pure BEC)

S. Grossmann and M. Holthaus, Phys. Lett. A, v. 208, p. 188, 1995

Effect of interactions.

Phys. Rev. A 90, 043640 (2014)

Normalized CV:

S. Giorgini et al., J. Low Temp. Phys.,

v. 109, 309, 1997.

Results

., Phys. Rev. A, v. 85, 023632, 2012.

Limit of N 0 and T 0

HEISEMBERG LIMITTED STATE EQUATION

SOLID LINE SOLID LINE

Bohr´s remarkers in his 1930 Faraday Lecture concerning complementarity between pairs of thermodynamics variables: P and V. One infers a kind of thermodynamics uncertainty principle .

C. Moller – Matematisk –Fysiske Meddelelser 87, 4 C. Moller – Matematisk –Fysiske Meddelelser 87, 4 (1969)“ ….pressure is complementary to volume, in much the same way that momentum and position…. It is true tha t for systems of ponderable size where N is very larg e, the complemmentary character of the mentioned quantities is usually not apparent, but in principle……..”

NEAR CRITICAL TEMPERATURE

PROBLEM WITH LDA - TECHNICAL RESOLUTION

turbulent regime in superfluids

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

-In comparison with many other areas, our knowledge and understanding of Turbulence ( classical and quantum ) is primitive

-The topic is placed as a challenges for present decade

Energy is injected at large scale ( vortex filaments) QT

Special configuration

( Turbulence )

Reconnection allow energy to flow to small scale ( Kelvin cascade)

Phonon Emission ( equivalent to effective kinematic viscosity)

Displacement,

Rotation and

Deformation of the potential

ADDITION OF “SHAKING” COILS

EXCITATION BY OSCILLATION OF THE POTENTIAL

Atomicwashing machine

GENERATION OF VORTICESFORMATIONS OF VORTICES CLUSTERSEMERGENCE OF TURBULENCESELF-SIMILAR EXPANSIONDIAGRAM OF EXCITATIONSFINITE SIZE EFFECTSECOND SOUND EXCITATIONGRANULATION

GENERALIZED THERMODYNAMICS

2009

Sequence of works

GENERALIZED THERMODYNAMICS

NEW TECHNIQUE FOR VISUALIZATION

KINETIC ENERGY SPECTRUM

TWO SUPERFLUIDSGIANT VORTEX DECAY

VISUALIZATION OF VORTICES LINES ( DUBNA)

20132014

Vortex formation

COLLECTIVE MODES

Phys. Rev. A 79, 043618 (2009)

Increasing amplitude or time of excitation : Explosion and proliferation of many vortices but no regular pattern and hard to count

Vortices to tangle vortices

“TURBULENCE”

J Low Temp Phys (2010) 158: 435–442

Phys. Rev. Lett. 103, 045301 (2009)

NON REGULAR – MANY POSITIONS

ORIENTATIONS AND LENGTH

Vortices and anti-vortices are together)

Three-vortex configurations in trapped Bose-Einstein

Phys. Rev. A 82 ,033616(2010)

Tangle vortices region

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

K-3

Turbulent cloud

Thermal BEC Turbulent

Cloud expansion

( hydrodynamics)

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 r

atio

TOF (ms)

Thermal BEC Turbulent

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