Ψ TThhee SSppiinnoorr BBoossee--EEiinnsstteeiinn CCoonnddeennssaattee:: AA DDiippoollaarr MMaaggnneettiicc SSuuppeerrfflluuiidd Dan Stamper-Kurn UC Berkeley, Physics Lawrence Berkeley National Laboratory, Materials Sciences Ψ Spinor gases mF = 2 Energy mF = 1 F=2 mF = 0 magnetically Optically m = -1 F trappable trapped F=2 m = -2 spinor gas F mF = -1 F=1 mF = 0 Optically mF = 1 trapped F=1 spinor gas B What do we want to know? ≈ χ χ χ ’ ≈ ρ ρ ρ ’ + + + + − +1,+1 +1,0 +1,−1 ∆ σ ,σ σ ,π σ ,σ ÷ ∆ ÷ ρ = ρ ρ ρ χ = ∆ χ + χ χ − ÷ ∆ 0,+1 0,0 0,−1 ÷ π ,σ π ,π π ,σ ∆ρ ρ ρ ÷ ∆ ÷ « −1,+1 −1,0 −1,−1 ◊ ∆χ − + χ − χ − − ÷ « σ ,σ σ ,π σ ,σ ◊ FC F = cosθ spin F m=1 coh erences y φ “orientation” x nematicity N m=2 coh erences “alignment” θ θ iφ −iφ ’ R∆e cos m =1 − e sin m = −1 ÷ « 2 2 ◊ + F′ = 2 1 1 1 12 2 2 y F =1 z x in this case small signal 2 (# photons/pixel) = + ( + + ε ) S Nγ 1 A ( 1) Fy Fy ⁄ ∝ n2D Direct imaging of Larmor precession m 0 0 3 l a n g i s t s a r t n y o F c 0.5 - ~ e s a h p 0 k a e time (50 s/frame) P Aliased sampling: 2 x 20 kHz – Observed rate = 38.097(15) kHz Spinor gas magnetometry B N atoms F F F φ Probe: t = 0 t = τ N N 0 0 N N B 0 1 N N 0 0 t = 0 t = τ > 1 ’ 1 1 Area-resolving: ∆B = ∆ ÷× = S × ∆ µ ÷ A « g B DTcoh n2 D ◊ Ttotal A Ttotal A Ψ Experimental demonstration Clarify fundamental and technical limits on precision single-particle and collective light scattering, experimental tricks unbiased phase estimation methods Measure background noise confirm areal and temporal scaling of sensitivity Measure localized magnetic field quantum-mechanical diffusion of magnetization actually measure limits to dynamic range magnetic background field with uncontrolled long-range inhomogeneities actually measure fictitious Z eeman shift from focused, off- resonance laser Ψ %F&ield“ measurements B AC Stark shift = “Fictitious” magnetic field Comparing atoms & SQUIDs Existing low freq. magnetometers actual duty cycle D ~ 0.003 (SQL) unity duty cycle D = 1 noise in backg round images —High resolution magnetometry with a spinor BEC,“ arXiv:cond-mat/0612685 Ψ B5ose-Einstein condensates with spin mF = 2 Energy mF = 1 F=2 mF = 0 magnetically trappable, Optically mF = -1 trapped F=2 mixtures decay m = -2 87 spinor gas F Long lived in Rb (Cornell group) mF = -1 F=1 mF = 0 Optically mF = 1 trapped F=1 spinor gas B Quantum fluids are described by vector order parameter (somewhat similar to 3He) FFC Ψ(x) Ψ(x) so what? Symmetries of order parameter broken symmetries + excitations, phase transitions, topologies Symmetries in interactions F=1 e.g. F=1 spinor, low B F=1 Ftot = 0 Ftot = 1 Ftot = 2 ultracold gas a0 no interactions a2 (s-wave) leads to spin waves single spatial mode a not allowed a (e.g. BEC) 0 2 Energy Scales in a Spinor Condensate Ψ (circa 2006) • Spin dependent interaction energy FC 2 = E spin c2 n F 8 Hz, or 400 picokelvin! ∝ ∆a Klausen, Bohn, Greene, PRA 64, 053602 (2001) • Non-linear (quadratic) Zeeman shift E = q F 2 quad z -1 + +1 0 + 0 q = (72 Hz / G 2 )h × B 2 isotropic anisotropic interaction energy dominates quadratic term dominates 2 0 = q (∝ B ) q 2 c2 n Q)uenching across a symmetry-breaking transition James Higbie, Sabrina Leslie, Lorraine Sadler, Mukund Vengalattore FC 2 = − + 2 E c F q Fz gradual (2nd order) transition = unmagnetized gas Fz 0 Tc (for BEC) ) T ( e unmagnetized, scalar state r u t a r e ferromagnetic state p m e T BEC q = 2 c quadratic Zeeman shift (q) Quench dynamics; phase-ordering kinetics z B Thold = 30 ms Thold = 90 ms = + ∝ iφ 0.4 nF T n(Fx iFy ) Ae 0.2 C × Asin(ωt +φ)] Signal 0.0 x ∝ Fy -0.2 -0.4 probe -y 0 5 10 15 20 Point number Thold = 150 ms Thold = 210 ms m 0 3 3 Spontaneously formed = φ ferromagnetism A n FT • inhomogeneously broken symmetry • ferromagnetic domains, large and small • unmagnetized domain walls marking rapid reorientation φ A / AMAX Thold = 30 60 90 120 150 180 210 ms Spontaneously formed = φ ferromagnetism A n FT • inhomogeneously broken symmetry • ferromagnetic domains, large and small Continuous spin texture • unmagnetized domain walls marking rapid ~50 micron pitch reorientation φ Alternating spin domains and domain walls A / AMAX 10 ms 60 90 120 150 180 210 Thold = 30 60 90 120 150 180 210 ms Ψ Ferromagnetism via spinodal decomposition m = 0 + m = ±1 m =1 + m = −1 Polar (Na) Separate Mix MIT Ferro (Rb) Mix Separate G-Tech = + mx 1 = mz 0 + = = − mx 1 Exponential timescale τ = > / ∆E =13.7(3)ms S = − = + mx 1 mx 1 Unmagnetized domain boundary of size πξ = 8.3µm ≅ ξ = µ Ferromagnetic domain of size S b S 2.6 m Timmermans, PRL 81 5718 (1998); Saito and Ueda, PRA 72, 023610 (2005) Ψ Spectrum of stable and unstable modes Bogoliubov spectrum = Gapless phonon (m=0 phase/density excitation) mz 0 Spin excitations Energies E 2 = (k 2 + q)(k 2 + q − 2) S scaled by c2n 3 qq = =q - =210. 501 2 E2 1 0 -1 0.0 0.5 1.0 1.5 2.0 k q>2: spin excitations are gapped by q(q − 2) 1>q>2: broad, —white“ instability 0>q>1: broad, —colored“ instability q<0: sharp instability at specific q0 * F T ,L (r +δ r)n(r +δ r) F T ,L (r)n(r) spin-spin …ƒ Ÿ G (δ r) = Re r correlation T ,L … +δ Ÿ … ƒ n(r r)n(r) Ÿ function r ⁄ rise time = 15(4) ms – compare to 13.7(3) ms measure of area of domain walls GT (x, z) phase separation occurs/symmetry broken spontaneously in disconnected radial bands Ψ Topological defect formation across a symmetry- breaking phase transition Kibble (1976), Zurek (1985) 5π φ = “causal horizon” 3 φ = 0 4π φ = 3 φ = 0 2π φ = 3 “Cosmology in the laboratory” Liquid crystals [Chuang et al, Science 251, 1336 (1991)] Superfluid helium [Hendry et al., Nature 368, 315 (1994)] Spontaneously formed spin vortices F T candidates: Mermin-Ho vortex (meron) mz=0 core F L “Polar core” spin vortex Thold = 150 ms Nature 443, 312 (2006) Spontaneously formed spin vortices candidates: × ’ FFC a(r) 1 Ψ = ∆ × −iφ ÷ ∆b(r) e ÷ ∆ −2iφ ÷ «c(r) × e ◊ Mermin-Ho vortex (meron) mz=0 core ≈a(r) × eiφ ’ FFC ∆ ÷ Ψ = ∆b(r) × 1 ÷ ∆ −iφ ÷ «c(r) × e ◊ “Polar core” spin vortex Broken chiral symmetry; Saito, Kawaguchi, Ueda, PRL 96 065302 (2006) Ferromagnetic spin textures generate helical spin pattern (uniform spin current) using inhomogeneous field Evolve dB /dz 0 z t n e i d a r g o / w t n e i d a r g h t i w Ψ Ferromagnetic spin textures clean starting point for studying dynamics energy budget: spin-dependent contact interaction: FC 2 − c2 n F ~ - 0.5 nK, minimized quadratic Zeeman shift: 2 q qF = excess ~ 30 pK; N = 60 Om z 2 spin current kinetic energy N ≥ 50 Om ν ≤ 1 Hz φ Ψ Dissolving spin textures A / AMAX 10 60 90 120 150 180 30 60 90 1 20 1 50 180 ms initial texture = uniform initial texture = wound up Dipolar interactions: magnetism in a quantum fluid @ 4 1014 cm-3 M ≈ µ = (µ µ ) self-field: B 0M 0 gF B n 23 G = µ 2 µ 2 energy per particle: E ( 0 gF B )n kB x 0.8 nK Comparison to other energy scales: total interaction energy: O ~ kB x 200 nK 52 Pfau, Santos, Lewenstein, others: Cr (6 OB), polar molecules (>137 OB) spin-dependent interaction energy: O ~ kB x 0.8 nK Yi and Pu, PRL 97, 020401 (2006); Kawaguchi, Saito, Ueda PRL 97, 130404 (2006) ferromagnetic spin texture: K.E. < kB x 30 pK Ψ PCresent/future directions/speculation Equilibrium phase diagram of spinor BEC vs. q, T, … effects of long-range, anisotropic interactions effects of dimensionality Phase transitions, quantum and thermal ascertain role of quantum vs thermal fluctuations: 2 temperatures quantum atom optics: is it still a BEC? critical exponents Phenomenology of spinor BEC dynamics domain walls, various spin vortices, interactions b/w them Spinor gas magnetometry surpass atomic shot noise; spatially resolved spin squeezing applications to …? Ψ Daniel Brooks, Jennie Guzman, Sabrina Leslie, Kevin Moore, Kater Murch, Tom Purdy, Lorraine Sadler, Ed Marti, Ryan Olf, Subhadeep Gupta, Mukund Vengalattore Looking for great students and postdocs http://physics.berkeley.edu/research/ultracold AFOSR .