Yong P. ChenQuantum Matter and Devices Lab

Department of Physics andSchool of Electrical and Computer Engineering and

Birck Nanotechnology CenterPurdue University <yongchen@purdue.edu>

Expanding Atomic Quantum Gaseswith tunable interaction and disorder

---emulating dynamics and fluctuations in superfluids … and nuclear matter?

Brookhaven National Laboratory May 23, 2008

Nuclear Physics & RIKEN Theory Seminar

My question

Promising systems (studied in my lab): • Graphene --- Dirac/chiral fermions: Coulomb collapse, Klein paradox…..

• Ultracold quantum gases (Bose-Einstein condensates; degenerate fermions/BEC-BCS;Bose-fermi mixtures;….)

Advantages: Tunable system parameters (customer-designed Hamiltonians): You can watch the system (probe both density and phase) to evolve!

How can we design condensed matter experiments to emulate nuclear/high energy physics phenomena?(esp. those difficult to test in real NP/HEP experiments, i.e. accelerators)

Emulational physics?

Talk outline

• Brief review of cold atoms & BEC---examples of NP/HEP connection

• Tunable interaction and expanding BEC• Disordered BEC:

superfluid to insulator transitionevolution of quantum and density

fluctuations

Please stop me for questions!

Bose-Einstein Condensate

~1μK 50nK

[7Li]

[6Li][7Li]

Meet Our Atom: Lithium-77Li -- boson(3p+, 4n) + 3e-

6Li -- fermion(3p+, 3n) + 3e-

E

r(continuum)

Bose-EinsteinCondensation

(1)

(mF=2)

(0)(-1)

(-2)

(-1)(0)(1)

F=2

F=1

22S1/2

(Feshbach Resonance)of 7Li in (1,1) state

Tunable Interaction

“mean field” interaction ∝ a0

repulsive

attractive

rf evaporationN~few 106

T~10 μK

Magnetic trap (2,2) state [a<0]

~700K

Zeeman Slowing --------------> MOT ------>

N~few 1010

T~1mKlaser cooling:

ω(671nm)

υ ωF=-kυ B(1,1)

(2,2)Uoptical pumping --->

Experimental Creation of BEC

<---------------optical evaporation<-----------------

(1, 1) statego to high B

1 μK300 nK

BEC!

80nK N~105-106

z

(1030nm)

optical trap U

• in-situ imaging of cloud-- probe ground state wavefunction

• free expansion: momentum space translates into real space---probe phase coherence/fluctuation

•(“restricted-fly”) evolution dynamics in selective potentials

• excite and collective mode

How to Experimentally Probe an Atomic Gas

“sit”

“fly”

“kick”

Just watch it!

A golden decade of quantum gases of cold atomic quantum gases --- some highlights• Bose-Einstein Condensate (BEC) [1995] now in most alkali, H, He* and Yb, Cr

(Nobel prize, 2001)

• Fermionic Condensate/BCS-BEC crossover [2004-2005]2-

body

Inte

r.

B

BEC(bosonicmolecules)

BCS(cooperpairs)

kF|a| > 1“Feshbach Resonance”

(from Ketterle’05)

•atoms in optical lattices (eg., BEC/superfluid-Mott insulator) [2002-]

•atoms in optical disorder potential [2005-]

(Mott insulator)

M. Greiner et al., (2002)

(Anderson insulator)

Tunable System Parameters• interaction (repulsive, attractive, short

range, long range,isotropic/anisotropic)• random and period potentials• dimensionality (1-3D) and spatial

structure• quantum and density fluctuations • time-dependent perturbations……

Emulator for Quantum Systems [Feynman/DARPA]

NP/HEP Connections?• Expansion of quantum gases and

hydrodynamics [Thomas, Grimm, …] • Instabilities due to interaction ----

condensate collapse: “Bosenova”; dipolar collapse

• Bose-Fermi mixture and supersymmetry, “Goldstino” modes (K.Yang’08); models for string theory (Stoof’05)…

• Sound wave propagation: models for cosmology

Interaction and Expansion of BEC

200

150

100

50

0

-50

-100

Scat

terin

g Le

ngth

(a B)

1000800600400

Magnetic Field (G)

Li-7 in (1,1) state

(b) B=717G

(c) B=551G

(d) B=544G

(a)

0.005ms

0.3ms

1ms

3ms

6ms

9ms

11ms

544G: a<0 TOF images

0.5ms

1ms

3ms

6ms

9ms

11ms

551G: a<~1aB

TOF images

Dipolar Interaction and Dipolar Collapse at a>0

• Cr-52 BEC: a dipolar BEC (Pfau’05)

Disordered BEC, fluctuations

Collaborators: James Hitchcock, Dan Dries, Mark Junker, Chris Welford and Randy Hulet (Rice Univ.)

Yong P. Chen et al., PRA 77, 233632 (2008)

From Superfluids and Superconductors to Insulators..

Insulators:•technologically important

•intellectually important to understand conductors and superconductors/superfluids

What is the essence of superfluidity and superconductivity?

understanding by (temporarily) “escaping”...

band insulator (no carriers)

Way#1: no carriers

conductor (metal)

BUT...

How to get an insulator?

Interaction and DisorderFestkorperphysik ist

Schmutzphysik!(“Solid State Physics

is Dirty Physics”)

fundamental themes incondensed matter physics

disorder+interaction?

...

(di s

o rde

r) Anderson insulator

[superfluid/superconductor]metal (interaction)

Mott insulator

Disordered Superconductor

A. Goldman and N. Markovic, Physics Today 1998

Insulator

superconductor

increasingdisorder

Example: Thin film superconductors (eg., Bi)

• “granular superconductor”:local superconductorglobal insulator

(Ec>EJ)

• “homogeneous”:any local superconductivity?

SS

S S

SS

S

•How does disorder destroys superconducting order parameter |Ψ|eiθ

• superfluidity and phase coherence • “Bose glass”?• Dissipation mechanism? intermediate

metallic phase? (“Bose metal”)•Is (dirty) boson-picture sufficient (SC)?

Superfluid/Superconductor to Insulator Transition (SIT)See also: “dirty” superfluid, random J-junction arrays etc. – “dirty bosons”

(disorder induced)

Simulate bydisordered quantum gas(both bosons & fermions)

BEC: Coherent and Superfluid(d

iso r

d er) Anderson

insulator

Coherence =Superfluidity ?

Bose glass ?..

(from W. Ketterle website)

BEC: coherent matter wave:===> atom laser

Disordered BEC:87Rb: Ingusci (Florence,2005-2006),

Aspect (Paris,2005-2006), Ertmer (Hannover, 2005)7Li: us (Rice, 2006-)

(interaction)

Mott insulator

[superfluid/BEC]M. Greiner et al., Nature (2002)

transition to insulator~loss of coherence

a nanoscience“simulator”

.

diffusive plate(rough glass,CNT film etc)

IR (1030nm)

CCD

can image both disorder potential and atoms!

How to Generate Optical Disorder: Laser Speckle

Pot

entia

l Ene

rgy

distance372 75 248 5 124 25 0 124 25 248 5 372 75

Δz

2VD

<V(r)V(r’)>:• Disorder Strength

VD tunable from0 to few kHz

• Disorder correlation length(speckle size) Δz down to~ 15 μm (limited by diff.

plate/geometry)

laser speckle is a coherent phenomenon

(incoherent lightswon’t give speckle)

•BEC radial size <~ Δz==> effective 1D disorder!

2500

2000

1500

1000

500

0

(µm

)

25002000150010005000(µm)

372 75 248 5 124 25 0 124 25 248 5 372 75

BEC

trap+disorder

How to Probe it?“sit”• in-situ imaging of cloud

-- probe ground state wavefunction

“push”• excite and collective mode ---(damping) • slow push (transport)

“fly”• free expansion (after experiencing disorder)

---probe phase coherence/fluctuation•(“restricted-fly”) evolution dynamics in disorder

--- rate of expansion /transport

µ

Typical(Interacting) BEC:[Part 1 of Talk (SIT)]

N~105-106 atomsaxial size(z)~1mmradial size ~10 µmInteracting a~200aBchemical µ~kHzT<100nK

ondisorder:off

onoptical trap:

<~1s

experimental sequence:

372 75 248 5 124 25 0 124 25 248 5 372 75

BEC

disorder

trap

Transport Experiment

trap?

initial (VD= 0)

VD~0.3µVD~ µ

dafter offset:

VD= 0d=1.4mmτoffset~1s

Transport Experiment 1: Trap offset slowly --- “Dragging BEC through disorder”

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0

200

400

600

800

1000

1200

1400

d 1400 μm 900 μm 500 μm 300 μm

Clo

ud C

ente

r (μm

)

VD / μ

d

372 75 248 5 124 25 0 124 25 248 5 372 75

d

Strong disorder pins BEC

Pinning of BEC by disorder

VD = 60Hz VD = 300HzVD = 0Hz

τevolve=75ms

200ms

300ms

500ms

600ms

800ms

950ms

Evolution of cloud following abruptly “shaking” trap (in ~5msec)

Transport Experiment 2: Trap offset abruptly --- dipole excitation

0 300 600 9000

200

400

600

-400

0

400

VD / μ

0.37 0.58 1.03

Evolution Time (ms)

(b)

VD / μ 0 0.08 0.16 0.24

Clo

ud C

ente

r (μm

)

(a)

Damping of Dipole Excitations

overdamped for VD >~0.3µ(fully pinned for VD >~µ)

dissipation/dampingsets in at very small VD

cloud moving speed~ BEC sound speed

(center)!exciting phase slips (vortices),phonons etc

372 75 248 5 124 25 0 124 25 248 5 372 75

Summary of transport properties

• We measure global transport <different from local-insulator probe such as Greiner>

Apparently 3 different regimes of transport:• High VD : inhibition of transport (global insulator)

“pinning point” (0.7-1µ) not universal value (dep on disorder realizationand measurement type) --- probably sensitive to high peaks in disorder?

• Small VD damps dipole excitation dissipation or dephasing? “metallic” regime? (cf: on lattice, DeMarco’07)dissipation mechanism --- “phase slips”, vortices ...??where does the energy go?

• Medium VD : overdamped transport what’s the transport mechanism? tunneling assisted?fate of this regime at T=0? --- “semiconductor” regime?

Time of Flight (TOF) Free Expansion

372 75 248 5 124 25 0 124 25 248 5 372 75

disorder

trap

BEC

TOF free expansion time (τ) [few ms]

Time of Flight probes phase coherence

Time of Flight (TOF) Free Expansion

disorder:

off

on

off

on

optical trap:

off

TOF free expansion time (τ) [few ms]

imaging cloud

<~1s

τTOF

0ms

1ms

2ms

3ms

6ms

8ms

0 Hz

note: color scale all relative!

VD

VD ~0.3µ

VD ~µ

0ms

1ms

2ms

3ms

6ms

8ms

increasing disorder...700 Hz

chemical potential µ~1 kHzτTOF

0ms

1ms

2ms

3ms

6ms

8ms

0 Hz

note: color scale all relative!

VD 200 Hz

(Random) interference “stripes”Yong P. Chen et al., PRA(2008)

-500 0 500

tTOF = 8 mstTOF = 0 ms (in-situ)

z (μm) z (μm)-500 0 500

VD/μ~0.3

VD/μ~0.5

VD/μ~1.0

VD/μ=0

0.00 0.25 0.50 0.75 1.000.0

0.2

0.4

0.6

0.8

1.0

1.2

8 ms TOFIn-situ

VD / μ

Con

trast

Density Fluctuations: In-situ vs TOF

Column density(phase-contrast imaging)

Random butreproducible interference fringes

Phase coherence

1400

1200

1000

800

600

400

200

0

arb

unit

5004003002001000

pixel

TOF: 4.5 ms 6 ms 9 ms 0 ms

Vd=500Hz

•not correspond to insitu disorder(though does vary with disorder realization)

•can be reproduced from shot-shot!•not sensitive to “hold time”--unlikely from random quantumfluctuation (in phase)

Features of the interference pattern

BEC phase fluctuation at t=0 ----> density fluctuation (t=τ)

n (r ) = Ψ (r ) 2 :

φ :

t=0

∂∂x

eikx( )= ikeikx

(phase ~ velocity) n (a

rb. u

nit)

25002000150010005000x (µm)

Numerics (GPE) show can be derivedand evolved from initial density fluctuation & phase coherent ground state(Clement &Sanchez-Palencia’07)

Disorder-inducedPhase fluctuation in BEC?

n(r) = Ψ(r) 2 :

φ :

t=0 t=τ

free expansion

∂∂x

eikx( )= ikeikx

(phase ~ velocity)

phase fluctuations also observed in elongated interacting BEC at finite TS.Dettmer et al., (W.Ertmer, Hanover), PRL2001

in our case: (quantum)phase fluctuation due to disorder instead of heating!

Lφ = Lφ (T ,<Vd >, B[a])

(Reproducible) Random Interference : Matterwave Speckle

llaser(coherentlightwave)

rough surface laser speckle

tBEC(coherentmatterwave)

laser speckle

atom-laser speckle

(for electrons, speckle==> universal conductance fluctuation)

Coherence

Note: in periodic potential (lattice), interference pattern (one-shot) occurs even w/o coherence

Random potential+reproducible “fluctuation” pattern=>coherence--mesoscopic physics

“interference” stripes <---coherence• reproducible• only BEC (not seen with thermal gas)• 1D modulation<--1D disorder

Reproducible TOF fringes in disordered 87Rb BEC: eg, D. Clement et al., arXiv. 0710.1984 (2007)

n (a

rb. u

nit)

25002000150010005000x (µm)

Digression: Speckle and Mescoscopic Physicsconductance through small conductors (wires, rings etc.):==>Universal Conductance Fluctuation (UCF)--- phase coherence transport

and analog of speckle for electron wavefunction

•mesoscopic: phase coherence L~ sample size•cold atoms/BEC excellent lab to study mesoscopic effects!

R.Webb’84

Strong Disorder:

VD(all 6ms TOF)

0Hz

B~720G (interacting)

8ms TOFVD/μ1

0.6

0.3

0.1

0.03

0

0ms (in-situ)

“tight binding”limit(random Josephson)[also in Rb exp]

insulator without phase coherence

[BEC/superfluid (coherent)]

disorder

lattice(Mott)

M. Greiner et al., (2002)

loss of phasecoherence

“granular” condensate/superfluid(global insulator)

each (superfluid) “grain”: number certain; (relative) phase random==> no macroscopic phase coherence

Medium Disorder: SIT and Phase Coherence

B~720G (interacting)

8ms TOFVD/μ1

0.6

0.3

0.1

0.03

0

[BEC/superfluid (coherent)]

disorder

0 ms (in-situ)

(cloud still connected)

Medium disorder:• during superfluid-insulator transition• system not yet “granular”• (global) superfluidity compromised

[losing phase rigidity]

• still has phase coherence

(not granular)

how is (global) superfluid order parameter suppressed?[mean field th broken down?/role of quantum fluctuations]

• Turn off the optical trap• Allow the condensate to evolve inside the

disorder• Turn off the disordered potential• (immediately) Image the cloud

Experimental Procedure

optical trap BEC

Exp#4: Fall/Flow in Disorder

Results• We Qualitatively compare the disordered

TOF images to a free expanding BEC

5 ms 10 ms

(no disorder)

(with disorder)[at this disorder strength strong stripes were observedin the free TOF experiment]

Localized confinement (trapping)?

• we see localized confinement few areas of the BEC

• Parts are confined for very long times (~20ms)

• Majority of the cloud “flows” away

10ms evolution in disorder

17ms evolution in disorder

[superfluid/superconductor]

disorder+interaction?

...

pinned solid(d

isor

der)

metal (interaction)

Bose glass

Quantum Coherence may be important even in insulators--- especially if you get them from a superfluid/superconductor

• “Bosonization” (eg. pair)

• Phase Coherence

• Phase Rigidity

3 steps:

And what about superfluidity &superconductivity?

φ φ φ φ φ

interaction

disorder

what’s the global phase diagramfor a disordered & interacting Bose (or Fermi) gas?(free space or trapped)

• drive quantum phase transition (cf. Q.Si and D.Natelson, NPA radio show)relevant for High Tc, heavy fermions materials, superfluid-insulator

transition, nuclear matter.....

Quantum/Phase fluctuations are interesting in Physics...

• even our fate ... :

(from http://map.gsfc.nasa.gov/)

atoms

Quantum Emulator?