The Birth (and Death) of a Superfluid€¦ · 1985: Wojciech Zurek: quantized vortices can be spontaneously created in a superfluid transition. ... “Superfluid Turbulence” model

BP Anderson, Lorne 2008, 20-Nov-2008

The Birth (and Death) of a Superfluid(experiment)

Experiment(Univ. Arizona)

Chad WeilerTyler NeelyCarlo SamsonDavid SchererBPA

Theory/Simulations(Univ. Queensland)

Matthew DavisAshton Bradley

(Univ. Otago)


Outline

Kibble-Zurek mechanism: model for describing topological defect formation during a continuous phase transition

Vortices by BEC merging

Superfluid turbulence

Experimental and numerical observations, comparisons

Next step #1: vortex observations vs BEC formation times

(Next step #2: examining the transition to superfluid turbulence)

Conclusions

Project GoalTo gain a detailed microscopic understanding of how BECs form.

- How is coherence achieved? (and how is coherence lost?)- How does the BEC phase transition relate to general continuous phase transitions?


1970’s. Tom Kibble (cosmologist): In the phase transition of the universe that occurred just after the Big

Bang, isolated regions may have independently proceeded through the transition

regions merged together formation of cosmic strings

Do cosmic strings exist? Not yet detected.

Kibble-Zurek mechanism

1985: Wojciech Zurek: quantized vortices can be spontaneously created in a superfluid transition.

“Kibble-Zurek mechanism”: spontaneous formation and trapping of topological defects in a system undergoing a continuous phase transition.

Faster transition more defects.


Two physical aspects to the KZ mechanism regarding BECs

1. Do uncorrelated regions form as a gas is cooled through the BEC phase transition?

2. Are vortices spontaneously created when uncorrelated regions merge together?


(1) 3 uncorrelated BECs grow during evaporative cooling in a triple-well potential

(2) BECs merge togetherwhen barriers removed. Interference between matter waves leads to phase gradient, directional fluid flow.

Merging and Interference region

Fluid flow? Depends on relative phases.

Given random relative phases between BECs, there is a 25% chance of vortex formation when BECs slowly merge.

Vortices by BEC merging (Caloundra, 2007)


Optical barrier Barrier: 170 mW, kB x 26 nKMerging by lowering barrier

Experiment sequence

Merging experiment

• Turn on optical potential, splits trap into 3 wells• Make 3 uncorrelated BECs by evaporative cooling• Remove optical barriers, BECs merge• Turn off trap, cloud expands (vortex cores expand)• Image cloud (by absorption)

Our standard BEC formation• 4x105 87Rb atoms in TOP trap, ~7 Hz (radial) x 14 Hz (axial) trap• μ ~ kB x 8 nK

Scherer, Weiler, Neely, and Anderson, PRL 98, 110402 (2007).


Two physical aspects to the KZ mechanism regarding BECs

1. Do uncorrelated regions form as a gas is cooled through the BEC phase transition?

2. Are vortices spontaneously created when uncorrelated regions merge together?


Kibble-Zurek mechanismKibble, J Phys A 9, 1387(1976) [spont. defect formation during evolution of Universe],Zurek, Nature 317, 505 (1985) [spont. vortex formation in superfluids], Anglin & Zurek, PRL 83,1707 (1999) [spont. vortex formation in BECs]

2π

0

+ξ

Transition is not smooth: Isolated regions of coherence, merging as BEC grows

Random relative phases

Correlation length: smaller for faster BEC formation.

Vortices may form. Smaller ξ = more vortices

Numerical estimate: appearance and merging of uncorrelated regions?

Realistic? Accurate? Primarily a useful model?

For our BECs, ξ ~ aSHO /5


Kagan & Svistunov, PRL 79, 3331 (1997),Svistunov, J. Mosc. Phys. Soc 1, 373 (1991),Kagan et al, Sov. Phys. JETP 75, 387 (1992),Kagan & Svistunov, Sov. Phys. JETP 78, 187 (1994),Berloff & Svistunov, PRA 66, 013603 (2002).

3 stages in condensation of trapped Bose gas(1) Many low-energy modes of the trap occupied as cooling proceeds.

Mode interference – nodes in the total field.(2) Quasi-condensate forms, nodes of the total field become vortices(3) Eventually vortices annihilate/damp, true condensation is achieved.

More accurate quantum mechanical description of BEC evolution

No simple numerical estimate of vortex density (like with KZ), but basic ideas can be examined in simulations.

“Superfluid Turbulence” model of vortex formation


Numerical and Experimental Approaches

Numerical approach: Stochastic GPE simulations

SGPE formalism (more from Matt Davis)• Model low-energy modes of trapped gas as a complex field (superfluid turbulence)• Evolution of field based on a modified GPE• Incorporate field-thermal bath interactions and scattering, random and complex field noise• Randomness, noise in initial conditions: single simulation runs analogous to single expt. runs.

Experimental ApproachMake BECs, determine statistics of vortex formation.

(1) Start with equilibrium state, T > Tc(2) Change T, μ to initiate BEC formation.(3) Watch BEC form(4) Look for vortices.(5) Repeat.(6) Determine statistics of vortex formation.(7) Compare with experimental results…


Temperature quench, BEC growth

“Quench B”Sudden RF jump

“Quench A”RF ramp

Numerical parameters: match experimental parameters for BEC growth.

Start: at t = 0, T > Tc, weak trap (νz ~ 15 Hz, νr ~ 8 Hz) [Top trap]


Experimental data: Images 1-30 (of a 90-image set)


Experiment (59 ms expansion, absorption)

Numerics – state of the BEC after formation

Numerics (phase)

Column density images

Image comparisons


Observation statistics

Overall, statistics between Quench A and Quench B are nearly the same.

Very different RF trajectories, but similar BEC growth rates, so not surprising. (Temperature quench should not be associated with evaporation trajectories!)

Main Results


Conclusions so far:

The usual “BEC creation myth” is not as simple as descriptions often imply. There are complex dynamics in BEC formation, even at these ultracold temperatures.

Simulations and experimental results in good quantitative agreement –demonstration of the power and utility of the numerical methods.

Spontaneous vortices in the formation of BECs.C. Weiler, T. Neely, D. Scherer, A. Bradley, M. Davis, and B. Anderson,

Nature 455, p. 948, 16 October, 2008

Significance:Details in the dynamics of phase transitions and turbulence may be testable

with experiments and corresponding simulations based in microscopic physics.

1. Can we test the KZ mechanism using microscopic observations, theory?

2. Can we understand a wide range of superfluid turbulence dynamics from microscopic studies?

3. How is coherence established in the growth of a superfluid?


1. Testing the KZ mechanism: vortices vs BEC formation time.

Faster condensation = more vortices?

Test in a highly oblate (pancake-shaped) BEC. Easier to condense faster, easier to see vortices.

Highly oblate trap: TOP trap + red-detuned laser beam.

Vertical (z) imaging

Cylindrical lens (focus in z direction)

1090 nm, ~2 WOblate trap:

ωr/2π = 8 Hzωz/2π = 90 Hz


50 μm

Procedure: load thermal atoms into oblate trap, then condense

Thermal cloud, side view

BEC, side view

BEC, top-down view

Phase contrast, in situ images


Fast condensation: ~250 ms formation time (~10% to ~90% of final N0)

Many more vortices!

Example expansion images


Vortices visible 100 ms after first signs of BEC (where do these vortices come from?)

Magnitude of previous TOP trap results

Highly oblate trap, ~250 ms BEC formation time.

Plot: average number of vortices vs time after condensate starts to form

Vortices in the birth of a superfluid


0

1

2

3

4

0 500 1000 1500 2000

Next data point is falling somewhere in here.

BEC formation time (ms)

Average number of vortices

Highly oblate trap: vortices vs BEC formation time

Previous data from TOP trap

Vortices vs BEC growth time


2: Death of a superfluid? Transition to turbulence from below

How is coherence lost as a system approaches the phase transition from ~zero temperature?

Highly oblate harmonic trap.Modulate the trapping frequency.

Vortices near edges of BEC


Vertical (z) imaging

Cylindrical lens (focus in z direction)

1090 nm, ~2 W

Add blue-detuned optical potential along z axis (λ = 650 nm, w0 ~ 13 μm)

Turbulence in an annular trap?

BEC in annular potential (not expansion)

Side view

Top-down view


Modulating the frequency of harmonic part of confinement

Modulation time

t = 0

t = 0.1 τ

t = 0.5 τ

t = 2.5 ττ = harmonic trap oscillation period

Transition to turbulence


MUCH easier to excite BEC into a turbulent state in annular trap!

Questions, tasks:

What is the key element of the annular trap that makes turbulence appear more easily than harmonic trap? (stirring-type mechanism within the BEC?)

Compare with simulations (in progress, A. Bradley).

How to characterize the resulting turbulent states? Counting vortices won’t work.

Re-thermalization measurable? Timescales? Temperatures?


The usual “BEC creation myth” is not as simple as descriptions often imply. There are complex dynamics in BEC formation, even at these ultracoldtemperatures.

Simulations and experimental results in good quantitative agreement –demonstration of the power and utility of the numerical methods.

Faster BEC formation = more vortices. For testing KZ mechanism, need to figure out how to deal with finite size of system (non-trivial)

Studying dyanimcs of the transition to a superfluid turbulent state appears possible. Means of understanding how coherence is lost?

Final Conclusions


BEC dynamics theory, simulationsU. Arizona BEC group

Tyler Neely Chad Weiler

BPA

David Scherer

Matt Davis Ashton BradleyU. Queensland Univ. Otago

Spontaneous vortices in the formation of BECs.

C. Weiler, T. Neely, D. Scherer,A. Bradley, M. Davis, and B. Anderson,Nature 455, p. 948, 16 October, 2008

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The Birth (and Death) of a Superfluid€¦ · 1985: Wojciech Zurek: quantized vortices can be spontaneously created in a superfluid transition. ... “Superfluid Turbulence” model