Presentation on theme: "Dynamics of Spin-1 Bose-Einstein Condensates"— Presentation transcript:
1 Dynamics of Spin-1 Bose-Einstein Condensates Ming-Shien ChangInstitute of Atomic and Molecular SciencesAcademia Sinica
2 OutlineIntroduction 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
3 Quantum Gases Tests of mean-field theories ground state properties Exquisitely clean experimental systemWidely variable parameters:Different atomic speciesBosons, fermionsInternal d.o.f.Spin systemsTunable interactionsFeshbach resonancesMolecular quantum gasesLattice systemsBenefits from 80+ yrs of theoretical many-body researchStimulating much new researchTests of mean-field theoriesground state propertiesInteractions: repulsive, attractive, ideal gasExcitationsFree expansion, vortices, surface modesMulti component mixturesBeyond mean field theoriesStrongly correlated systemsMott-insulator states, BCSEntanglement and squeezing
4 BEC Physics BEC Order parameter χ(r) ~ N1/2 ψs(r) Coherent Matter Wave JILA, 1995Order parameterχ(r) ~ N1/2 ψs(r)Coherent Matter WaveMean-field theory works
5 Phase space densityPhase space densityDe Broglie wavelengthBEC occurs when: interparticle spacing, n01/3 ~ de Broglie wavelengthPhase space densityAmbient conditionsLaser cooling Nobel Prize, 1997BEC Nobel Prize, 2001
7 Quest for BEC BEC, 1995 Nobel Prize, 2001 All-optical approach A. CornellC. WiemanNobel Prize, 2001All-optical approachStandard recipeHess, Kleppner, Greytak et al. (1986/7), Pritchard et al. (1989), Ketterle et al. (1993/4), Cornell et al. (1994)slow (60 s)—requires exceptional vacuum not everything can be magnetically trapped magnetic fields difficult to generateM. Chapman (2001)W. Ketterle (1995)
15 When c2 = 0… 3 Zeeman components are decoupled. First BEC in 1995 Condensate wave functionFirst BEC in 1995Nobel Prize in 20013 Zeeman components are decoupled.
16 Spinors In B fields 72 Hz/G2 m= m= m=-1When linear Zeeman effects are canceled, quadratic Zeeman effect favors m0.m= m= m=-172 Hz/G2One can study spinor condensates in mG ~ G regime.
17 Single mode approximation (SMA) Simplification on spinor dynamics if all spin components have same spatial wave function (SMA):Hamiltonian reduces to just two variables to describe internal spin :Condensate magnetizationSpin-dependent interaction strengthQuadratic Zeeman energyPopulation of ±1 components follows:
31 Coherence of the ferromagnetic ground state Restarting the coherent spin mixing by phase-shifting out of the ground state at a later timeSpin coherence time = condensate lifetime
32 Beyond the Single-Mode Approx. (SMA) Formation of spin domainsMiscibilities of spin componentsFormation of spin wavesAtomic four-wave mixing
33 Healing lengthshortest distance ξ over which the wavefunction can changeUsingHealing length: smoothes the boundary layer and determines the size of vortices.
34 Beyond SMA: formation of spin domains weak B gradient during TOFzSingle-Mode Approx. (SMA):Spin healing length:Condensate size: (2rc,2zc) ~ (7, 70) mcondensate is unstable along the z direction.
35 Miscibility of spin-1 (3-component) superfluid Goal: minimize the total mean-field energy1-fluid M-F2-fluid M-F3-fluid M-FMIT, 98-99
36 Miscibility of two-component superfluids Total Energy of two-component superfluidIf they are spatially overlapped with equal mixture:If they are phase separated:The condensates will phase –separated if
37 Miscibility of spin-1 (3-component) superfluid 2-fluid M-F3-fluid M-F1-fluid M-F
38 Miscibility of two-component superfluid Stern-Gerlach Exp. During TOF<1miscible>1immiscible23Na87RbFerromagnetic:
49 Research projects with ultracold atoms at the IAMSOptical dipole trap (ODT) for cold-atom experimentsOptical lattice for quantum simulation / quantum information experimentODT for Single atom trappingAll-optical BEC of Potassium / RubidiumSpinor condensates studies of Potassium / RubidiumDetermination of the spin nature of potassiumcomplex ground state, SSSspin mixing of only two atoms (entangled pair after mixing)Mixture of bosonic and fermionic spinorsRydberg atom quantum information
51 Optical Trap - + Far off-resonant lasers work as static field Focused laser beam form a 3D trap:gaussian beam: radialfocus: longitudinalImportance of optical trapState-Independent PotentialTrapping of Multiple Spin StatesEvaporative Cooling of Fermions
53 III. BEC in a Single-Focused Trap Initial loading:Scaling for Optical TrapEffective Trap Volumeweak focuslarge trap volumelow densityTrap frequencyScaling for adiabatic compressionCompression and evaporation:DensityElastic collision ratetight focussmall trap volumehigh density
54 Dynamical Trap Compression P = 70 ww07030 μm2.5 mmTime0.6 s
62 Free Evaporation 𝟖 𝑾→𝟖 𝑾 𝒊𝒏 𝟏 𝒔𝒆𝒄 # of atoms N 1.0x105 trap frequency 2,120Hzω13,300rad/stemperatureT50μKpeak densityn0E+131/c.c.phase space densityΛ8.5x10-4
63 Force evaporation 𝟖 𝑾→𝟎.𝟓 𝑾 𝒊𝒏 𝟏.𝟕 𝒔𝒆𝒄 # of atoms N 3000 trap frequencyf530Hzω3300rad/stemperatureT6μKpeak densityn03.4x10111/c.c.phase space densityΛ2.3x10-4
64 Spinor condensates with potassium atoms Spinor condensates of potassium in an optical trapSpin mixingDetermine nature of the spinorsDetermine spin-dependent scattering lengthsSpinor condensates in an optical latticeSimulation of quantum magnetsMixture of Bosonic and Fermionic spinors
68 Summary Formation of spinor condensates in all-optical traps Observation of coherent spinor dynamicsObservation of spatial-temporal spinor dynamicsCurrent progress of the BEC experiments at the IAMSPreliminary data of Rb force evaporationZeeman slowing of K