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Ming-Shien Chang Institute of Atomic and Molecular Sciences Academia Sinica Dynamics of Spin-1 Bose-Einstein Condensates

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Outline Introduction to spinor condensates Dynamics of spin-1 condensates Temporal dynamics: coherent spin mixing Spatial dynamics: miscibility and spin domain formation Progress report: BEC experiments at the IAMS Summary

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Quantum Gases Exquisitely clean experimental system Widely variable parameters: l Different atomic species l Bosons, fermions l Internal d.o.f. Spin systems l Tunable interactions Feshbach resonances l Molecular quantum gases l Lattice systems Benefits from 80+ yrs of theoretical many-body research l Stimulating much new research Tests of mean-field theories l ground state properties Interactions: repulsive, attractive, ideal gas l Excitations Free expansion, vortices, surface modes l Multi component mixtures Beyond mean field theories l Strongly correlated systems Mott-insulator states, BCS l Entanglement and squeezing

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BEC Physics BEC JILA, 1995 Order parameter χ(r) ~ N 1/2 ψ s (r) Coherent Matter Wave Mean-field theory works

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Phase space density BEC occurs when: interparticle spacing, n 0 1/3 ~ de Broglie wavelength Phase space density Ambient conditions10 -15 Laser cooling10 -6 Nobel Prize, 1997 BEC 1 Nobel Prize, 2001 Phase space density De Broglie wavelength

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Bose-Einstein Condensate: Mean-field theory (1961, nonlinear Schrodinger eqn) Gross-Pitaevskii equation s-wave scattering length

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Quest for BEC W. Ketterle (1995) BEC, 1995 Nobel Prize, 2001 A. Cornell C. Wieman Standard recipe M. Chapman (2001) All-optical approach

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All-Optical BEC Gallery Cross trap 1-D lattice Single focus ~ spherical disk cigar 30,000 atoms 300,000 atoms Common features: 87 Rb CO 2 trapping laser Simple MOT < 2 s evaporation time

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F=1 Spinor BEC Stern-Gerlach absorption image of a BEC created in an optical trap (GaTech, 2001) m F = -1 m F = 0 m F = 1 F = 1

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Studies of F=1 Spinor BEC in an optical trap A multi-component (magnetic) quantum gas

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Spinor Condensates A multi-component magnetic quantum gas Spinor system Spin mixing Spin domains, spin tunneling (Anti-) Ferromagnetism Rotating spinors Spin textures Skyrmion vortices Quantum Magnetism Spin squeezing, entanglement Spinors in an optical lattice Spin chains QPT, quantum quench

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Interacting Spin-1 BEC a 0 (Bohr) a 2 (Bohr) c 0 (x10 -12 Hz·cm 3 ) c 2 (x10 -12 Hz·cm 3 ) 87 Rb101.8100.47.793-0.0361 23 Na50.055.015.5870.4871 anti-ferromagnetic ferromagnetic Intuitive picture: F = 0, 1, 2 Atomic Parameters c 2 << c 0 Ho, 98

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Hamiltonian for Spin-1 BEC Ho, PRL (98) Machida, JPS (98) Spin changing collisions 2 nd Quantized Form

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Coupled Gross-Pitaevskii Eqn. for Spin-1 Condensates Cross-phase modulation Modulational instability, domain formation Coherent spin (4-wave) mixing Condensate wave function Bigelow, 98-00 Meystre, 98-99 …….

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When c 2 = 0 … 3 Zeeman components are decoupled. First BEC in 1995 Nobel Prize in 2001 Condensate wave function

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Spinors In B fields 72 Hz/G 2 One can study spinor condensates in mG ~ G regime. When linear Zeeman effects are canceled, quadratic Zeeman effect favors m 0. m=+1 m=0 m=-1

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Single mode approximation (SMA) Spin-dependent interaction strength Quadratic Zeeman energy Condensate magnetization Hamiltonian reduces to just two variables to describe internal spin : Simplification on spinor dynamics if all spin components have same spatial wave function (SMA): Population of ±1 components follows:

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Spinor energy contourszero field

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Spinor energy contoursfinite field

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Spin Mixing in spin-1 condensates 2 sec For no interactions, m 0 is lowest energy (2 nd order Zeeman shift) m F = 1 0 -1 t = 0 s

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Ferromagnetic behavior Ferromagnetic spinor Anti-ferromagnetic spinor Chapman, 04 You, 03 Sengstock, 04

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Deterministically initiate spin mixing At t=0: (ρ 1, ρ 0, ρ -1 ) = (0, 0.75, 0.25)

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Coherent Spin Mixing Chapman, 05 Josephson dynamics driven only by spin-dependent interactions

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Coherent Spin Mixing Oscillation Frequency: Bigelow, 99 Direct measurement of c (c 2 )

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Direct measurement of c 2 (or a F=2 - a F=0 ) a F=2 - a F=0 = -1.4(3) a B (this work) a F=2 - a F=0 = -1.40(22) a B (spect. + theory) from oscillation frequency from condensate expansion

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Spin mixing is a nonlinear internal AC Josephson effect You, 05 de Passos, 04

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AC Josephson Oscillations For high fields where d >> c, the system exhibits small oscillations analogous to AC- Josephson oscillations: Compare with weakly linked superconductors:

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Controlling spinor dynamics Quadratic Zeeman energy θ (rad) when Pulse on a magnetic field

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Controlling spinor dynamics Change trajectories by applying phase shifts via the quadratic zeeman effect θ (rad) Ferromagnetic ground state

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Search for ferromagnetic spinor ground state

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Coherence of the ferromagnetic ground state Restarting the coherent spin mixing by phase-shifting out of the ground state at a later time Spin coherence time = condensate lifetime

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Beyond the Single-Mode Approx. (SMA) Formation of spin domains Miscibilities of spin components Formation of spin waves Atomic four-wave mixing

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Healing length Healing length: smoothes the boundary layer and determines the size of vortices. Using shortest distance ξ over which the wavefunction can change

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Beyond SMA: formation of spin domains Spin healing length: Condensate size: (2r c,2z c ) ~ (7, 70) m condensate is unstable along the z direction. Single-Mode Approx. (SMA): weak B gradient during TOF z

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Miscibility of spin-1 (3-component) superfluid 1-fluid M-F 2-fluid M-F 3-fluid M-F Goal: minimize the total mean-field energy MIT, 98-99

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Miscibility of two-component superfluids Total Energy of two-component superfluid If they are spatially overlapped with equal mixture: If they are phase separated: The condensates will phase –separated if

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Miscibility of spin-1 (3-component) superfluid 2-fluid M-F 3-fluid M-F 1-fluid M-F

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Miscibility of two-component superfluid <1 miscible >1 immiscible 23 Na >1 immiscible <1 miscible 87 Rb Ferromagneti c: Stern-Gerlach Exp. During TOF

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Invalidity of the Single-Mode Approx.

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Spin waves induced by coherent spin mixing mFmF 1 0 - Validate coupled GP eqn. - Theoretical explanation of spin waves. - Atomic 4-wave mixing - Evidence of dynamical instability ( 1, 0, -1 ) = (0, 0.75, 0.25)

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mFmF 1 0 ( 1, 0, -1 ) = (0, 0.5, 0.5) ( 1, 0, -1 ) = (0, 0.83, 0.17) total Domain formation induced by dynamical instability

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Miscibility of ferromagnetic spin-1 superfluid -3 components in the ferromagnetic ground state appear to be miscible -Energy for spin waves (external) is derived from internal spinor energy mFmF 1 0

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Return to the SMA m F = -1 m F = 0 m F = 1 Single focus trap Cross trap

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Validity of the SMA Spin healing length: (2 c,2z c ) ~ (7, 70) m Condensate should be physically smaller than spin healing length Cross trap 1-D lattice Single focus ~ spherical disk cigar (2 c,2z c ) ~ (1, 10) m Condensate size (2 c,2z c ) ~ (7, 7) m

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Improving the SMA Single-focus trap result

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Improving the SMA Cross trap result

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Improving the SMA

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SMA vs. spin waves (domains) Single-focused trap R z = 70 μm ξ s = 15 μm Cross trap R z = 7 μm ξ s = 11 μm mFmF 1 0

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Research projects with ultracold atoms at the IAMS Optical dipole trap (ODT) for cold-atom experiments Optical lattice for quantum simulation / quantum information experiment ODT for Single atom trapping All-optical BEC of Potassium / Rubidium Spinor condensates studies of Potassium / Rubidium Determination of the spin nature of potassium complex ground state, SSS spin mixing of only two atoms (entangled pair after mixing) Mixture of bosonic and fermionic spinors Rydberg atom quantum information

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Quest for all-Optical BEC at the IAMS

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Optical Trap Far off-resonant lasers work as static field Focused laser beam form a 3D trap: l gaussian beam: radial l focus: longitudinal Importance of optical trap l State-Independent Potential l Trapping of Multiple Spin States l Evaporative Cooling of Fermions +-+-

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All-Optical BEC Gallery Cross trap 1-D lattice Single focus ~ spherical disk cigar 30,000 atoms 300,000 atoms

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III. BEC in a Single-Focused Trap weak focus large trap volume low density Initial loading: tight focus small trap volume high density Compression and evaporation: Scaling for Optical Trap Scaling for adiabatic compression Density Elastic collision rate Effective Trap Volume Trap frequency

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Dynamical Trap Compression Time 00.6 s 2.5 mm P = 70 w w0w0 30 μm 70

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Gallery of optical lattices In-situ imaging CO 2 lattice constant: 5.3 μ m Time-of-flight(TOF) imaging CO 2 lattice constant: 0.43 μ m Bookjen, PhD thesis I. Bloch (01) Weiss(07) Greiner (09)

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CO 2 laser vs. Nd:YAG laser CO2 laserNd:YAG (μm)10.61.06 P (W)1000 30 (single frequency) Scattering rate (same trap parameters) 12200 Rayleigh range (same beam waist) 110 OpticsZnSe / GeUsual glass Spatial modeUsually better Lattice constant of an optical lattice(μm) 5.3 (easier to resolve)0.53 (lattice physics)

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Aspect ratio: CO 2 vs. Nd:YAG

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Trap frequency: CO 2 vs. Nd:YAG

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Trap Loading: single-focus beam Vapor cell MOT Dipole trap

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Trap Loading: cross beams Hold time (1 sec)

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Free evaporation kBTkBT hot atoms escape

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Free Evaporation # of atomsN1.0x10 5 trap frequencyf2,120Hz trap frequencyω13,300rad/s temperatureT50 μKμK peak densityn0n0 4.57147E+131/c.c. phase space densityΛ8.5x10 -4

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Force evaporation # of atomsN3000 trap frequencyf530Hz trap frequencyω3300rad/s temperatureT6 μKμK peak densityn0n0 3.4x10 11 1/c.c. phase space densityΛ2.3x10 -4

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Spinor condensates with potassium atoms Spinor condensates of potassium in an optical trap Spin mixing Determine nature of the spinors Determine spin-dependent scattering lengths Spinor condensates in an optical lattice Simulation of quantum magnets Mixture of Bosonic and Fermionic spinors

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Zeeman slower for potassium experiment

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Summary Formation of spinor condensates in all-optical traps Observation of coherent spinor dynamics Observation of spatial-temporal spinor dynamics Current progress of the BEC experiments at the IAMS Preliminary data of Rb force evaporation Zeeman slowing of K

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Acknowledgement

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