New Physics with Interacting Cold Atomic Gases California Condensed Matter Theory Meeting UC Riverside November 2, 2008 Ryan Barnett Caltech Collaborators: H.P. Buchler, E. Chen, E. Demler, J. Moore, S. Mukerjee, D. Podolsky, M. Porter, G. Refael, A. Turner, A. Vishwanath
Outline for talk 1. Intro To Field Sample of Experiments 2. Rotating Mixtures of condensates 3. Spinor Condensates
Bose Einstein Condensation
New Era in Cold Atoms Research Systems with strong interactions Optical lattices Feshbach resonances Rotating condensates One dimensional systems Multicomponent tsystems (e.g. long range dipolar interactions, mixtures, or spinor condensates)
Atoms in optical lattices Theory: Jaksch et al. PRL (1998) Experiment: Kasevich et al., Science (2001); Greiner et al., Nature (2001); Phillips et al., J. Physics B (2002) Esslinger et al., PRL (2004);
Superfluid to insulator transition Greiner et al., Nature 415 (2002) μ U Mott insulator Superfluid n 1 J/U
Current Efforts in Optical Lattices Dynamics Collapseand and Revival Boson Fermion Mixtures Low Temperature Fermions
Spinor Condensates: Spin structure from hyperfine interaction I=nuclear spin=3/2 S=electron spin=1/2 F=total spin=1 or 2 I S Alkalis H HF = I S = 1 2 (F 2 I 2 S 2 ) ~7 GHz F z = 2 F = 1 F = 0 = 1 = 2 z z F z F z F=2 87 Rb F1 F=1 Fz = 1 F = 0 = 1 z F z
Spinor Condensates: Order Parameter Order Parameter: ψ ψ a for a = F...F Scattering Interaction: V (r 1 r 2 )=δ(r 1 r 2 )(g 0 P 0 + g 2 P 2 +...g 2F P 2F ) Example: Spin one Ferromagnetic g 0 <g 2 ψ 1 0 0 Polar g 0 >g 2 ψ 0 1 0
Spinor Condensates: Stern Gerlach Experiments B m=1 m=0 m= 1 87 Rb Schmaljohan et al (2002) (Sengstock group)
Experiments on spinor condensates Quantum quenching experiments: Polar > Ferromagnetic F z = 1 F z = 0 F z =1 Sadler et al (2006) (Stamper Kurn group)
Experiments on vortex lattices Energy in rotating frame Irrotational v = θ v =0 Feynman Relation (for vortex density) Ketterle Group
Vortices in Optical Lattice Potential Optical Mask Feynman Relation (for vortex density) rotate at Ω m density of holes ρ m Resonance : Ω m = ρ m hπ m E. Cornell Group 2006
Modification of System: Mixtures Two BECs having different masses m1 > m2 No interaction: will have Ω (1) = Ω d = Ω (2) With interaction, will have attraction between vortices: Species 1 Species 2 Ω (1) < Ω d < Ω (2)
Vortices in Mixtures Locked Ω (1) < Ω d < Ω (2) Magnus Force: Critical Radius: Barnett, Refael, Porter, Buchler (NJP) 2008
Vortices in Mixtures: Numerical Confirmation μψ 1 = 1 2 2 ψ 1 + V trap ψ 1 + g 1 ψ 1 2 ψ 1 + g 12 ψ 2 2 ψ 1 Ω d ϕ ψ 1 μψ 2 = 1 2 2 ψ 2 + V trap ψ 2 + g 2 ψ 2 2 ψ 2 + g 12 ψ 1 2 ψ 2 Ω d ϕ ψ 2 Split Operator Method: evolve in imaginary time τ V ψ(τ + τ) e 2 e T τ τ V e 2 ψ(τ) ; H = T + V Chen, Barnett, Refael 2008
Vortices in Mixtures: Numerical Confirmation Preliminary Results Chen, Barnett, Refael 2008
Spinor Condensates: Symmetry description Two Body interaction: V (r 1 r 2 )=δ(r 1 r 2 )(g 0 P 0 + g 2 P 2 +...g 2F P 2F ) Interaction Hamiltonian: H int = 1 2 P S,m g Sψ aψ b hab SmihSm a0 b 0 iψ a 0ψ b 0. Classification of MF states Break down into spin 1/2s Example: Spin one Ferromagnetic g 0 <g 2 Polar g 0 >g 2 ψ 1 0 0 ψ 0 1 0 Barnett, Turner, Demler (PRL) 2006 x 2
Symmetry of F=2 condensates H int = 1 2 P S,m g Sψ aψ b hab SmihSm a0 b 0 iψ a 0ψ b 0. T ψ ~ (1,0,0,0,0) ψ ~ (sin( η) / 2,0, cos( η),0,sin( η) / T 2) Ferromagnetic Nematic ψ ~ ( 1/ 3,0,0, T 2 / 3,0) Cyclic
F=2 spinor condensates Parameters (a 0,a 2, a 4 ) Barnett, Turner, Demler (2006) Ciobanu, Yip, Ho (2002)
Parameters (a 0,a 2, a 4, a 6 ) F=3 spinor condensates See also Santos, Pfau, PRL 96:190404 (2006); Diener, Ho, PRL 96:190405 (2006) Barnett, Turner, Demler (PRA) 2007
Nematic states of F=2 spinor condensates Degeneracy of nematic states at the mean-field level Square nematic Biaxial nematic Uniaxial nematic But.not a symmetry of the hamiltonian x 2 x 2
Order by disorder (From Ashvin s talk ) E η
Nematic states: breaking the degeneracy by quantum fluctuations Need to compute excitations: each will have the Bogoliubov form: E nk = 2 ε k + 2gnn0ε k 3 spin modes, one density mode, and one eta mode. F = T n, k log( 2sinh(2β Compute contribution to free energy: E nk ))
Revised phase diagram : nematic order by disorder Quantum/Thermal Fluctuations Turner, Barnett, Demler, Vishwanath (PRL) 2007 Song, Semenoff, Zhou (PRL) 2007
Vortices in spinor condensates Can have vortices in both spin and charge degrees of freedom (different from U(1)) Example: cyclic state tt w/ B field O(3) spin symmetry Low energy states parameterized by: ψ e iθ e if zα χ 0 E = K c R d 2 r( θ) 2 + K s R d 2 r( α) 2 Vortices Given by CHARGE Charge Stiffness SpinStiffness Stiffness & SPIN winding (n,m) 1 <K s /K c 1/4 <K s /K c < 1 0 <K s /K c < 1/4 (1/3,2/3) (2/3,1/3) (1,0) (1/3, 1/3) 1/3) Barnett, Mukerjee, Moore (PRL) 2008 (1/3, 1/3) (1/3, 1/3)
Sequence of vortex lattices (determined from Ewald summation)????
Hydrodynamics of spinor condensates Write ψ a = ψχ a L = 1 1 2 iψ a t ψ a ψ 2 a ψ a gρ E s. 2 = iψ t ψ + ρa t 1 2 ( i a)ψ 2 1 2 ρυ 1 2 gρ2 E s Vector potential a t hχ t χi ; a ihχ χi χi CPN model Υ h α χ α χi hχ α χih α χ χi. Superfluid velocity v = θ a. For states with < F >= 0, a =0 For ferromagnetic state v = 1 4 ε αβγn α ( n β n γ ) (Mermin Ho relation) Barnett, Podolsky, Refael 2008
Hydrodynamics of ferromagnetic condensate Incompressible, 2d Lamacraft (PRA) 2008 Skyrmion Configuration Skyrmion Texture Barnett, Podolsky, Refael 2008
Conclusions Cold atoms offer variety of interesting systems from a condensed matter perspective Vortex lattices ltti in condensate mixtures it Spinor condensates have order parameters with symmetries like points on sphere F=2 condensates exhibit order by disorder Spin and charge combine to give a variety of vortices and vortex lattices Hydrodynamical description in terms of symmetry variables Thank you. Thanks to collaborators: H.P. Buchler, E. Chen, E. Demler, J. Moore, S. Mukerjee, D. Podolsky, M. Porter, G. Refael, A. Turner, A. Vishwanath