Brookhaven National Laboratory May 23, 2008 Expanding Atomic Quantum Gases with tunable interaction and disorder ---emulating dynamics and fluctuations in superfluids and nuclear matter? Yong P. Chen Quantum Matter and Devices Lab Department of Physics and School of Electrical and Computer Engineering and Birck Nanotechnology Center Purdue University <yongchen@purdue.edu> Nuclear Physics & RIKEN Theory Seminar
My question 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) 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! 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 transition evolution of quantum and density fluctuations Please stop me for questions!
Bose-Einstein Condensate [ 7 Li] ~1μK 50nK [ 7 Li] [ 6 Li]
7 Li -- boson (3p +, 4n) + 3e - Meet Our Atom: Lithium-7 Bose-Einstein Condensation 6 Li -- fermion (3p +, 3n) + 3e - E 2 2 S 1/2 F=2 F=1 (m F =2) (1) (0) (-1) (-2) (-1) (0) (1) (continuum) r Tunable Interaction (Feshbach Resonance) of 7 Li in (1,1) state mean field interaction a 0 repulsive attractive
Experimental Creation of BEC Zeeman Slowing --------------> MOT ------> optical pumping ---> U (2,2) laser cooling: (671nm) ω F=-kυ υ ω N~few 10 10 T~1mK (1,1) B Magnetic trap (2,2) state [a<0] ~700K rf evaporation N~few 10 6 T~10 μk 80nK N~10 5-10 6 BEC! 300 nk 1 μk (1, 1) state go to high B <---------------optical evaporation<----------------- optical trap (1030nm) z U
How to Experimentally Probe an Atomic Gas sit in-situ imaging of cloud -- probe ground state wavefunction fly free expansion: momentum space translates into real space ---probe phase coherence/fluctuation ( restricted-fly ) evolution dynamics in selective potentials Just watch it! kick excite and collective mode
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 Inter. BEC (bosonic molecules) B BCS (cooper pairs) (from Ketterle 05) k F a > 1 Feshbach Resonance
atoms in optical lattices (eg., BEC/superfluid-Mott insulator) [2002-] M. Greiner et al., (2002) (Mott insulator) atoms in optical disorder potential [2005-] (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
Magnetic Field (G) (a) Scattering Length (a B ) 200 150 100 50 0-50 Li-7 in (1,1) state (b) B=717G (c) B=551G (d) B=544G -100 400 600 800 1000
551G: a<~1a B TOF images 544G: a<0 TOF images 0.005ms 0.5ms 0.3ms 1ms 1ms 3ms 3ms 6ms 6ms 9ms 9ms 11ms 11ms
Dipolar Interaction and Dipolar Collapse at a>0 Cr-52 BEC: a dipolar BEC (Pfau 05)
Disordered BEC, fluctuations Yong P. Chen et al., PRA 77, 233632 (2008) Collaborators: James Hitchcock, Dan Dries, Mark Junker, Chris Welford and Randy Hulet (Rice Univ.)
From Superfluids and Superconductors to Insulators.. What is the essence of superfluidity and superconductivity? understanding by (temporarily) escaping... technologically important Insulators: intellectually important to understand conductors and superconductors/superfluids How to get an insulator? Way#1: no carriers band insulator (no carriers) conductor (metal) BUT...
Interaction and Disorder Festkorperphysik ist Schmutzphysik! ( Solid State Physics is Dirty Physics ) fundamental themes in condensed matter physics (disorder) Anderson insulator disorder+interaction?... metal [superfluid/superconductor] Mott insulator (interaction)
(disorder induced) Superfluid/Superconductor to Insulator Transition (SIT) See also: dirty superfluid, random J-junction arrays etc. dirty bosons Disordered Superconductor Example: Thin film superconductors (eg., Bi) A. Goldman and N. Markovic, Physics Today 1998 Insulator increasing disorder granular superconductor : local superconductor global insulator (E c >E J ) homogeneous : any local superconductivity? superconductor How does disorder destroys superconducting order parameter Ψ e iθ superfluidity and phase coherence Bose glass? Dissipation mechanism? intermediate metallic phase? ( Bose metal ) Is (dirty) boson-picture sufficient (SC)? S S S S S S S Simulate by disordered quantum gas (both bosons & fermions)
BEC: Coherent and Superfluid BEC: coherent matter wave: ===> atom laser (disorder) Anderson insulator (from W. Ketterle website) Bose glass?.. a nanoscience simulator Coherence = Superfluidity? Disordered BEC: 87 Rb: Ingusci (Florence,2005-2006), Aspect (Paris,2005-2006), Ertmer (Hannover, 2005) 7 Li: us (Rice, 2006-) [superfluid/bec] Mott insulator (interaction) transition to insulator ~loss of coherence M. Greiner et al., Nature (2002)
How to Generate Optical Disorder: Laser Speckle diffusive plate (rough glass, CNT film etc) IR (1030nm) 2500 2000 CCD can image both disorder potential and atoms! 1500 (µm) 1000 laser speckle is a coherent phenomenon (incoherent lights won t give speckle) 500 0 0 500 1000 (µm) 1500 Potential Energy 2000 2500 Δz. 2V D <V(r)V(r )>: Disorder Strength V D tunable from 0 to few khz Disorder correlation length (speckle size) Δz down to ~ 15 μm (limited by diff. plate/geometry) 372 75 248 5 124 25 0 124 25 248 5 372 75 distance BEC radial size <~ Δz ==> effective 1D disorder!
372 75 248 5 124 25 0 124 25 248 5 372 75 How to Probe it? sit in-situ imaging of cloud -- probe ground state wavefunction push excite and collective mode ---(damping) slow push (transport) experimental sequence: disorder: off optical trap: on µ on <~1s fly free expansion (after experiencing disorder) ---probe phase coherence/fluctuation ( restricted-fly ) evolution dynamics in disorder --- rate of expansion /transport BEC Typical (Interacting) BEC: [Part 1 of Talk (SIT)] N~10 5-10 6 atoms axial size(z)~1mm radial size ~10 µm Interacting a~200a B chemical µ~khz T<100nK trap + disorder
Transport Experiment 372 75 248 5 124 25 0 124 25 248 5 372 75? BEC trap trap disorder Transport Experiment 1: Trap offset slowly --- Dragging BEC through disorder d=1.4mm τ offset ~1s d after offset: V D = 0 initial (V D = 0) V D ~0.3µ V D ~ µ
Pinning of BEC by disorder 372 75 248 5 124 25 0 124 25 248 5 372 75 Cloud Center (μm) 1400 1200 1000 800 600 400 200 0 d d Strong disorder pins BEC d 1400 μm 900 μm 500 μm 300 μm 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 V D / μ
Transport Experiment 2: Trap offset abruptly --- dipole excitation Evolution of cloud following abruptly shaking trap (in ~5msec) V D = 0Hz V D = 60Hz V D = 300Hz τ evolve =75ms 200ms 300ms 500ms 600ms 800ms 950ms
Damping of Dipole Excitations 372 75 248 5 124 25 0 124 25 248 5 372 75 Cloud Center (μm) 400 0-400 600 400 200 0 0 300 600 900 Evolution Time (ms) (a) (b) V D / μ V D / μ dissipation/damping sets in at very small V D 0 0.08 0.16 0.24 0.37 0.58 1.03 cloud moving speed ~ BEC sound speed (center)! exciting phase slips (vortices),phonons etc overdamped for V D >~0.3µ (fully pinned for V D >~µ)
Summary of transport properties We measure global transport <different from local-insulator probe such as Greiner> Apparently 3 different regimes of transport: High V D : inhibition of transport (global insulator) pinning point (0.7-1µ) not universal value (dep on disorder realization and measurement type) --- probably sensitive to high peaks in disorder? Small V D damps dipole excitation dissipation or dephasing? metallic regime? (cf: on lattice, DeMarco 07) dissipation mechanism --- phase slips, vortices...?? where does the energy go? Medium V D : overdamped transport what s the transport mechanism? tunneling assisted? fate of this regime at T=0? --- semiconductor regime?
Time of Flight (TOF) Free Expansion BEC trap disorder 372 75 248 5 124 25 0 124 25 248 5 372 75 TOF free expansion time (τ) [few ms] Time of Flight probes phase coherence
TOF free expansion time (τ) [few ms] Time of Flight (TOF) Free Expansion disorder: off on imaging cloud off optical trap: on <~1s off
V D 0 Hz 0ms 1ms 2ms 3ms 6ms note: color scale all relative! 8ms τ TOF
V D ~0.3µ
V D ~µ 0ms 1ms 2ms 3ms 6ms 8ms
increasing disorder... V D 0 Hz 200 Hz 700 Hz 0ms 1ms 2ms 3ms 6ms note: color scale all relative! 8ms τ TOF (Random) interference stripes Yong P. Chen et al., PRA(2008) chemical potential µ~1 khz
Density Fluctuations: In-situ vs TOF t TOF = 0 ms (in-situ) Column density (phase-contrast imaging) V D /μ=0 V D /μ~0.3 V D /μ~0.5 t TOF = 8 ms -500 0 500 z (μm) V D /μ~1.0-500 0 500 z (μm) 1.2 Contrast 1.0 0.8 0.6 0.4 Random but reproducible interference fringes Phase coherence 0.2 0.0 8 ms TOF In-situ 0.00 0.25 0.50 0.75 1.00 V D / μ
Features of the interference pattern arb unit 1400 1200 1000 800 600 Vd=500Hz TOF: 4.5 ms 6 ms 9 ms 0 ms 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 quantum fluctuation (in phase) 400 200 0 0 100 200 300 400 500 Numerics (GPE) show can be derived and evolved from initial density fluctuation & phase coherent ground state (Clement &Sanchez-Palencia 07) φ : n(r ) = Ψ(r ) 2 : t=0 pixel BEC phase fluctuation at t=0 ----> density fluctuation (t=τ) ( )= ike ikx x eikx (phase ~ velocity) n (arb. unit) 0 500 1000 1500 2000 2500
φ : Disorder-induced Phase fluctuation in BEC? t=0 t=τ ( )= ike ikx x eikx (phase ~ velocity) n(r) =Ψ(r) 2 : free expansion phase fluctuations also observed in elongated interacting BEC at finite T S.Dettmer et al., (W.Ertmer, Hanover), PRL2001 in our case: (quantum) phase fluctuation due to disorder instead of heating! L φ = L φ (T,< V d >, B[a])
Note: in periodic potential (lattice), interference pattern (one-shot) occurs even w/o coherence (Reproducible) Random Interference : Matterwave Speckle laser (coherent lightwave) rough surface l laser speckle Coherence interference stripes <---coherence reproducible only BEC (not seen with thermal gas) 1D modulation<--1d disorder laser speckle Reproducible TOF fringes in disordered 87 Rb BEC: eg, D. Clement et al., arxiv. 0710.1984 (2007) BEC (coherent matterwave) t atom-laser speckle n (arb. unit) 0 500 1000 1500 x (µm) 2000 2500 (for electrons, speckle==> universal conductance fluctuation) Random potential+reproducible fluctuation pattern=>coherence--mesoscopic physics
Digression: Speckle and Mescoscopic Physics conductance 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: disorder V D /μ 1 0.6 0.3 0.1 B~720G (interacting) insulator without phase coherence 8ms TOF (all 6ms TOF) 0ms (in-situ) V D tight binding limit (random Josephson) [also in Rb exp] granular condensate/superfluid (global insulator) 0.03 0 [BEC/superfluid (coherent)] each (superfluid) grain : number certain; (relative) phase random ==> no macroscopic phase coherence lattice (Mott) M. Greiner et al., (2002) 0Hz loss of phase coherence
disorder V D /μ 1 0.6 0.3 0.1 Medium Disorder: SIT and Phase Coherence B~720G (interacting) 8ms TOF Medium disorder: during superfluid-insulator transition system not yet granular (global) superfluidity compromised [losing phase rigidity] still has phase coherence 0 ms (in-situ) 0.03 (cloud still connected) (not granular) 0 [BEC/superfluid (coherent)] how is (global) superfluid order parameter suppressed? [mean field th broken down?/role of quantum fluctuations]
Exp#4: Fall/Flow in Disorder Experimental Procedure optical trap BEC Turn off the optical trap Allow the condensate to evolve inside the disorder Turn off the disordered potential (immediately) Image the cloud
Results We Qualitatively compare the disordered TOF images to a free expanding BEC (no disorder) 5 ms 10 ms (with disorder) [at this disorder strength strong stripes were observed in 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
Quantum Coherence may be important even in insulators --- especially if you get them from a superfluid/superconductor (disorder) disorder+interaction? pinned solid... Bose glass And what about superfluidity & superconductivity? 3 steps: Bosonization (eg. pair) Phase Coherence metal [superfluid/superconductor] (interaction) Phase Rigidity φ φ φ φ φ
disorder what s the global phase diagram for a disordered & interacting Bose (or Fermi) gas? (free space or trapped) interaction
Quantum/Phase fluctuations are interesting in Physics... 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... even our fate... : Quantum Emulator? atoms (from http://map.gsfc.nasa.gov/)