Fabrizio Larcher BEC Center Trento & JQC Durham-Newcastle I-K. - - PowerPoint PPT Presentation

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Fabrizio Larcher BEC Center Trento & JQC Durham-Newcastle I-K. - - PowerPoint PPT Presentation

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Generation & dynamics of solitonic defects: Kibble-Zurek in reduced dimensionality Fabrizio Larcher BEC Center Trento & JQC Durham-Newcastle I-K. Liu, P . Comaron, S. Serafini, M. Barbiero, M. Debortoli, S. Donadello, G. Lamporesi, G.

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SLIDE 1

Generation & dynamics of solitonic defects: Kibble-Zurek in reduced dimensionality

National Changhua University of Education

Fabrizio Larcher

BEC Center Trento & JQC Durham-Newcastle I-K. Liu, P . Comaron, S. Serafini, M. Barbiero, M. Debortoli, S. Donadello,

  • G. Lamporesi, G. Ferrari, S.-C. Gou, I. Carusotto , F

. Dalfovo and N. P . Proukakis 616th WE-Heraeus Seminar, 12 May 2016 Bad Honnef - Germany

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SLIDE 2

Outline

  • Kibble-Zurek Mechanism;
  • a relevant experiment (Nat. Phys. 9, 2013);
  • solitons vs “solitonic” vortices (PRL 113, 2014);
  • stochastic defect generation;
  • solitonic vortex dynamics and interactions (PRL 115,

2015);

  • quenches in a 2D system (BKT corrections).
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SLIDE 3

The system evolution slows down at the phase transition. Fast enough quenches could result in defect creation.

Kibble-Zurek Mechanism

equilibrium critical exponents

Defect number

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SLIDE 4

Weiler-Davis et al. Nature 455, 948 (2008) Dalibard Nat. Comm. (2015)

1D: Soliton Formation Quasi-2D / 3D: Vortex Formation Ring Trap: Persistent Current

Experiment: Dalibard/Beugnon PRL 113, 135302 (2014)

Brand et al. PRL 110, 215302 (2013) Davis et al PRL 107, 230402 (2011) Zurek et al. Sci. Rep (2012)

Hadzibabic et al, Science 347 (2015)

Dalibard et al., Nat. Comm. Critical Exponents Experimentally Characterised in a Box-like T rap

Zurek et al. PRL 102, 105702 (2009) PRL 104, 160404 (2010) Engels / Schmiedmayer et al.

Kibble-Zurek in cold atoms

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SLIDE 5

Quench with different rates

Slow Fast

Solitons?

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SLIDE 6

The lifetime puzzle

  • Click to edit Master text styles
  • Second level
  • Third level
  • Fourth level
  • Fifth level

Solitons in 3D are expected to undergo two kinds of instability:

  • Thermal (unless at )
  • Dynamical (snaking

instability) Why do they live for such a long time?

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SLIDE 7

Are they really solitons?

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SLIDE 8

Solitonic vortices

  • Vortex oriented perpendicularly to the

axis of an axisymmetric elongated trap.

  • Quantized vorticity
  • Anisotropic phase pattern - Planar

density depletion

  • M. Tylutki et al., EPJ-ST 224, 577 (2015)
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SLIDE 9

Random orientation

  • Click to edit Master text styles
  • Second level
  • Third level
  • Fourth level
  • Fifth level

TOF

  • S. Donadello et al., Phys. Rev. Lett. 113, 065302 (2
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SLIDE 10

Scaling and aspect ratio

  • power-law scaling for slow

ramps

  • aspect ratio dependent

exponent

  • at plateau for fast ramps
  • plateau independent on

aspect ratio Experiments show some intriguing behaviour, how to get some more information? Zurek, PRL 102, 105702 (2009) Del Campo et al., NJP 13, 083022 New on arXiv::1605.02982

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SLIDE 11

Simulations:

Stochastic Projected Gross-Pitaevskii equation:

  • represents the condensate

and a number of thermal modes.

  • Condensate

extracted by numerical diagonalisation [Penrose-Onsager].

Experimental data matched through: Blakie et al., Adv. in Phys., 57 (2008)

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SLIDE 12

Quench:

I-K. Liu et al, in preparation.

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SLIDE 13
  • Click to edit Master text styles
  • Second level
  • Third level
  • Fourth level
  • Fifth level

I-K. Liu et al, in preparation.

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SLIDE 14

Scaling exponent for the defect density

Qualitative agreement with the experiments:

  • Plateau for fast quenches
  • Power decay for slower

quenches

  • Lowering with waiting time

The number of defects goes down as the waiting time increases. ms A.R.= I-K. Liu et al, in preparation.

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SLIDE 15

Long term evolution

  • f solitonic vortices

Quasi-non destructive stroboscopic imaging:

  • Magnetic harmonic trap in with Hz;
  • ms of expansion in , with RF refocusing dressing;
  • Up to 20 consecutive extractions.

Serafini et al., Phys. Rev. Lett. 115, 170402 (2015)

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SLIDE 16
  • Click to edit Master text styles
  • Second level
  • Third level
  • Fourth level
  • Fifth level
  • Expansion in the

anti-trapped state

  • Optical levitation
  • Imaging of the
  • utcoupled part
  • nly

Serafini et al., Phys. Rev. Lett. 115, 170402 (2015)

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SLIDE 17

Vortex dynamics

  • A straight vortex line should precess in an

inhomogeneous non-rotating condensate

  • It follows equipotential elliptical orbits around

the centre. Orbital period: being: the axial trapping frequency; the maximum amplitude; the condensate healing length.

z

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SLIDE 18

The extraction procedure changes the number of particles in time:

Vortex dynamics

Decay without extraction Decay with extraction

Hence, the period itself should depend

  • n time:

Vortex dynamics

Serafini et al., Phys. Rev. Lett. 115, 1704 (2015)

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SLIDE 19

Period decay

  • Click to edit Master text styles
  • Second level
  • Third level
  • Fourth level
  • Fifth level

Serafini et al., Phys. Rev. Lett. 115, 1704 (2015)

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SLIDE 20

Vortex interactions?

  • Click to edit Master text styles
  • Second level
  • Third level
  • Fourth level
  • Fifth level

Destructive absorption images show random

  • rientation of vortex lines

The experimental system seems a good benchmark for studying in real time vortex decay processes and reconnections, if only an axial non-destructive

  • bservation method is developed.
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SLIDE 21

Vortex crossings

  • Click to edit Master text styles
  • Second level
  • Third level
  • Fourth level
  • Fifth level

Observations:

  • Unperturbed trajectory or
  • Change in visibility and/or
  • Trajectory phase shift.
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SLIDE 22

Bouncing

  • L. Galantucci and C. Barenghi, in
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SLIDE 23

Reconnections

Single Double

  • L. Galantucci and C. Barenghi, in
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SLIDE 24
  • Click to edit Master text st
  • Second level
  • Third level
  • Fourth level
  • Fifth level

T wo-dimensional systems

  • L. Chomaz et al., Nat. Comm.

6, 2015

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SLIDE 25
  • Click to edit Master text st
  • Second level
  • Third level
  • Fourth level
  • Fifth level

T wo-dimensional systems

  • L. Chomaz et al., Nat. Comm.

6, 2015

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SLIDE 26

Vortex decay vs in polaritons

  • A. Jelić et al., J. Stat. Mech.

Fit according to P . Comaron et al., in

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SLIDE 27

Newcastle upon Tyne (UK)

conferences.ncl.ac.uk/jqcma cro/ Registration deadline: 30th June, 2016 Multicomponent Atomic Condensates & ROtational dynamics Keynote speakers include:

  • V. Bagnato, N. Berloff, H.

Rubinsztein-Dunlop, I. Spielman, M. Ueda ultiple contributed talk slots available to applicants. Thank you!

Happy soliton

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SLIDE 28

Backslides

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SLIDE 29

Power law scaling: coherence length relaxation time If the quench is linear ”Freezing” time: domain size: defect density:

Kibble-Zurek Mechanism

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SLIDE 30

Scaling exponents

ν, z: critical exponents D: system dimension d: defect dimension Dimensionality has a role in scaling! Zurek, PRL 102, 105702 (2009 Del Campo et al., NJP 13, 083022 (2011)

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SLIDE 31

Scaling exponent

The number of defects is expected to follow a power-law as a function of the quench time (fixed size of the system) where is determined by the critical exponents of the phase transition.

  • F-model prediction

for solitons in 3D:

Zurek, W. H. Phys. Rev. Lett. 102, 105702 (2009).

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SLIDE 32

Other period characterisations

Click to edit Master text styles

  • Second level
  • Third level
  • Fourth level
  • Fifth level

Serafini et al., Phys. Rev. Lett. 115, 1704 (2015)

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SLIDE 33

A quench is performed simultaneously in temperature and in chemical potential (inset). P-O mode growth. is the ramp time. I-K. Liu et al, in preparation.

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SLIDE 34

Vortex length

Vortex line density scales as

  • r (quantum turbulence

regime?). P . M. Walmsley and A. I. Golov, Phys. Rev. 100, 245301

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SLIDE 35

Vortex decay

Single vortex lifetime is limited by scattering with thermal excitations.

is compatible for , but not for Does this mean that two-vortex interactions are suppressed?

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SLIDE 36

BKT free vortices give a correction in the predicted vortex density for KZM:

  • T

wo-dimensional KZM

  • A. Jelić et al., J. Stat. Mech.

2011(02), 2011

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SLIDE 37

Polaritons

loss rate; pumping strength; saturation density; A steady state is reached when the system equilibrates between driving and dissipation.

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SLIDE 38

Vortex number decay

  • Click to edit Master text styles
  • Second level
  • Third level
  • Fourth level
  • Fifth level

P . Comaron et al., in

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SLIDE 39

T wo-dimensional KZM

BKT phase transition:

  • Due to the Mermin-Wagner theorem, no condensation in an

infinite 2D system for any

  • However, a superfluid transition occurs at finite
  • Berezinskii-Kosterlitz-Thouless (BKT) at
  • For vortices of opposite circulation are coupled in pairs.
  • For they gradually become free.