Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The - PowerPoint PPT Presentation

Ana Maria Rey $ Funding $ NSF, AFOSR, ARO, ARO-DARPA-OLE, The 11th US-Japan Joint Seminar 2013 “Ultimate Quantum Systems of Light and Matter- Control and Applications”

The Sr team: KRb team: D. Jin Jun Ye M. Swallows, M. Martin, M. Bishof, S. Blatt, X. Zhang, C. Benko Theory team: B. Yan, S. Moses, J. Covey, B. Neyenhuis and B. Gadway A. Gorshkov,M. Foss-Feig, K. Hazzard, B. Zhu, S. Manmana, M. Lukin

 Fully controllable quantum systems The most precise measurements, e.g. clocks Quantum sensors  A tool for understanding quantum complexity Quantum simulation Atoms ↔ Electrons Optical lattice ↔ Ionic Crystal Richard Feynman

Possible but challenging Atoms heavier than electrons Extra low temperatures Optical lattice spacing much larger than ionic lattice spacing 10 -11 K in atomic systems ~ K in solid state systems Solutions (~ KHz) (~ Hz) Develop sophisticated cooling • Polar methods molecules Alkaline earth atoms Trapped Explore new type of systems • Ions Take advantage of • Magnetic ultra-precise tools Rydberg Atoms Atoms

Understanding quantum systems from few- to many-body with “clock” precision and control

Metastable state JILA Ultra-coherent spectroscopy: Nicholson et al ., Phys. Rev. Lett. Sr and Yb 109 (2012) 230801 3 P 0 (e) Ye’s talk this afternoon Q~10 15 , seconds coherence time 698 nm (~ 150 s) 1 S 0 (g) Magic wave length Ye, Kimble, & Katori, Science 320 , 1734 (2008). No Doppler, No Recoil No Stark shift

exp [i δτ] τ Measure # of e atoms N. Ramsey. Nobel B=2 π(ν L − ν 0 )=δ prize 1989 e 2π/τ δ: Detuning ν 0 ν L Contrast g z e-atoms e y x g What happens in the real experiment with N particles? ∑ = , , x y z S S Interactions? Non-interacting: Collective-spin S x, y, z n n

3 P 0 (e) 1 S 0 (g) Effective spin 1/2 system during clock interrogation Mode occupation is conserved. No Dominant p-wave collisions laser/interaction induced mode Both elastic and inelastic changing collisions. Decoupled motional/spin n 4 ∑ Ω x ∑ − n 3 z = − δ n S H S n n n 2 ν ~500 Hz,V~ 1 Hz n n 1 n   n + ∑ ⊥ z z z ⋅ + χ + [ J S S S S B S n n' n' n n' n' n n , n ' n , n ' n , n ' n n' n' , δ : Detun i ng Ω n : Rabi Frequency ν ~500 Hz Array of reactive Interaction parameters pancakes ( ) ( ) ⊥ = − χ = − − = − eg eg eg ee gg ee gg 2 ( ) J V U V V V B V V , ' , ' , ' , ' , ' , ' , ' , ' , ' , ' n n n n n n n n n n n n n n n n n n n n

⊥ χ , , J ⊥ ⊥ ⊥ χ → + ∆ , , , J B J J ' , ' n n n n , ' , ' , ' , ' n n n n n n n n + ∆ B B , ' n n Long range!! n’ χ + ∆ χ n constant , ' n n   ∑ ∆ 2 ⊥ = − δ − − − Ω + ⋅ + χ + ( ( 1 ) ) H N B S S J S S S H z x z , ' n n . ' n n ∑ = , , x y z S S x, y, z n n ∆ H Same Hamiltonian that two component Bose Einstein Condensate: Sorensen, Moller, Cirac, Zoller, Lewenstein, … ⊥ N J S S J=N/2 A. M. Rey, L. Jiang, M. Fleischhauer, E. Demler, and M. D. Lukin, PRA 77, 052305 (2008) .

Treat other surrounding atoms as an average = B S z cos θ (S z ) 2 → 2 ฀ H=- ฀ S z ฀ S z ฀ B=-2 ฀ ฀ S z ฀ =-N ฀ Spin precesses with a modified rate with depends on atom number z x ฀ S z ฀ θ θ controlled by first pulse 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Excitation fraction: 1/2+ ฀ S z ฀ /N M. Martin et al arXiv:1212.6291

Quantum correlations should manifest on the amplitude of the oscillations At the mean field level interactions only affect the precession rate . • • Amplitude remains constant But….. in the experiments there are many pancakes with different atom number. Due to interactions the pancakes with more atoms precess faster. Signal adds → amplitude of the oscillations decay due to dephasing or destructive interference between pancakes 1D • Atom number decay aslo leads to decay of the amplitude M. Martin et al arXiv:1212.6291

Ramsey fringe decay vs. the spin tipping angle To eliminate the effect of decay we normalize the amplitude with atom number Normalized Amplitude Shift Excitation fraction Mean filed fails to reproduce the amplitude decay at tipping angles where the density shift vanishes time M. Martin et al arXiv:1212.6291

Interplay between interactions and decoherence: complicated few many Quantum correlations induce faster decay of the amplitude Normalized Contrast We were able to solve the full master Eq for the collective model.

N Gorshkov et a l: PRL.107.115301(2011), PRA 84,033619 (2011) N “ spin ” Rotation   = − ⋅ rot 2 Rigid Rotor H BN d E i i i N=1 dipole moment | ฀ ฀ |1,0 ฀ |1,1 ฀ |1,-1 ฀ Select two ~GHz dressed levels : |0,0 ฀ Effective spin ½ system | ฀ ฀ N=0 Increasing E E=0 Related previous work Other schemes: Micheli et al , Nat. Phys. 2 341 (2006); Brennen et al , NJP 9 138 (2007); Buechler et al , Nat. Phys. 3 726 (2007); Perez-Rios, et al NJP 12 , 103007; Wall-Carr Phys. Rev. A 82, 013611 (2010)…

− θ 2 ( 1 3 cos ) = = ij ij H d d V V − dd i j dd 3 | | dd r r i j ↑ = = = 1 , 0 N M • Project d i on the two selected rotational levels ∑ ↓ = = = = σ σ ' = σ σ 0 , 0 N M ˆ d z d | ' d d σ σ σσ σ σ , ' i i i ' , ' [ ] ( ) ∑ = + + ij z z x x y y ( ) ( ) H V J d S S J d S S S S σσ ⊥ σσ ' ' dd dd z i j i j i j , i j Ising Flip-flop 𝐾 ⊥ = 2( 𝑒 ↑↓ ) 2 𝐾 𝑨 = ( 𝑒 ↑↑ − 𝑒 ↓↓ ) 2

N  Use direct dipole-dipole interaction to generate direct strong (~KHz) spin exchange interaction: 10-100 larger than super-exchange or magnetic dipoles dipole moment  Fully tunable coefficients by E field (microwaves) Gorshkov et a l: PRL.107.115301(2011), PRA 84,033619 (2011)  Long-range (1/r 3 ) and anisotropic interactions: S. R. Manmana et al PRB 87, 081106(R) (2013), A. V. Gorshkov et al arXiv:1301.5636  Spin temperature , not motional temperature matters: Relevant ratio is interaction time (~ms) to cloud lifetime (25 sec!): K. R.A. Hazzard et al PRL 110, 075301 (2013)

• Empty sites act as defects • Need to perform disorder average Dipolar interactions will be visible in the Ramsey fringe contrast even in dilute samples K. R.A. Hazzard et al PRL 110, 075301 (2013) θ = π /2 , π /10 θ = π /2 , π /10

Current experiments are carried out in a 3D lattice with a B field B: determines quantization axis Magic wavelength for their | ฀ = |N=1,M=-1 ฀ ฀ lattice ฀ B B. Neyenhuis et al Phys. Rev. Lett. 109, | ฀ = |N=0,M=0 ฀ ฀ 230403 (2012) ε φ Polarization trapping light • Non-trivial dependence on the geometry due to the anisotropic dipolar interactions. − θ 2 ( 1 3 cos ) ฀ = B ij V − 3 | | r r dd i j

𝐾 ⊥ = − ( 𝑒 ↑↓ ) 2 𝑗𝑗 𝑇 𝑦𝑗 𝑇 𝑦𝑗 + 𝑇 𝑧𝑗 𝑇 𝑧𝑗 𝐼 = 𝐾 ⊥ � 𝑊 <𝑗 , 𝑗> Cluster Expansion g=4 • Spins grouped in cluster of max size g. • Intra-cluster interactions kept • Inter-cluster interactions neglected or treated as a perturbation.

Solid lines: Cluster expansion g=10 Gaussian distribution: Filling factor: π/2 pulse 7 % 14% 21%

Learn from NMR: By applying the proper pulse sequence it is possible to eliminate dipolar interactions. 𝜌 𝑦 𝜌 𝜌 𝜌 𝜌 𝜌 𝜌 2 𝜚 2 𝑦 2 𝑧 2 −𝑦 2 −𝑦 2 𝑦 Preliminary pulse scheme for KRb 𝜐 /8 𝜐 /4 𝜐 /8 𝜐 /8 𝜐 /4 𝜐 /8 Wahuha + echo 𝜌 𝑦 𝜌 𝜌 2 𝑧 2 𝜚 echo 𝜐 /2 𝜐 /2 𝜌 𝜌 2 𝑧 2 𝜚 𝜐

• Ultra-cold polar matter offers a unique controllable laboratory for the exploration of many-body physics Strongly interacting open driven quantum systems • Manifestation of quantum magnetism observable even in a non- quantum degenerate gas • Rich physics a lot to be understood Thanks