global thermodynamic variables for trapped quantum … gases _… · and understanding of...
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GLOBAL THERMODYNAMIC VARIABLES FOR TRAPPED QUANTUM SYSTEM
&QUANTUM TURBULENCE
V. S. Bagnato
University of São Paulo
Brazil
http://cepof.ifsc.usp.br
QUANTUM TURBULENCE
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cepof.ifsc.usp.br
2
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Diffusion
Innovation
Innovation with Social responsibility
http://cepof.ifsc.usp.br
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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
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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)
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Brazilian Atomic Clock
Bobinas de Compensação
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BEC
OPTICSCONDENSED MATTER
FLUIDSLASERS
ATOMIC PHYS.
SUPERFLUID
FLUIDS
FIELD THEORY
STAT. PHYS.
MAGNETISM.
LASERS
QUANT. VORTICES
TURBULENCE
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T > Tc T < Tc T << Tc
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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
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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
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:
Critical temperature:
3/194.0 NTk hoCB ⋅⋅= ωh
Thermodynamic limit: ∞→N constT hoc =
Volume parameter:
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Pressure conjugated to volume….
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Isodensity curves:
Phys. Rev. A, v. 85, 023632, 2012.
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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
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In He:
λλλλ transition He-I => He-II
Heat Capacity
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With the macroscopic parameters:
(pure thermal)
(pure BEC)
R.F. Shiozaki et al., Phys. Rev. A. (2014)
(pure BEC)
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S. Grossmann and M. Holthaus, Phys. Lett. A, v. 208, p. 188, 1995
Effect of interactions.
Phys. Rev. A 90, 043640 (2014)
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Normalized CV:
S. Giorgini et al., J. Low Temp. Phys.,
v. 109, 309, 1997.
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Results
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., Phys. Rev. A, v. 85, 023632, 2012.
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Limit of N 0 and T 0
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HEISEMBERG LIMITTED STATE EQUATION
SOLID LINE SOLID LINE
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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……..”
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NEAR CRITICAL TEMPERATURE
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PROBLEM WITH LDA - TECHNICAL RESOLUTION
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turbulent regime in superfluids
1955: Feynman proposed that “superfluid turbulence” consists of a tangle of quantized vortices.
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-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)
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Displacement,
Rotation and
Deformation of the potential
ADDITION OF “SHAKING” COILS
EXCITATION BY OSCILLATION OF THE POTENTIAL
Atomicwashing machine
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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
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Vortex formation
COLLECTIVE MODES
Phys. Rev. A 79, 043618 (2009)
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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
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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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Tangle vortices region
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Las. Phys. Lett. 8,691(2011)
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K-3
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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)
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