INT International Conference, Frontiers in Quantum Simulation with Cold Atoms, March 30 April 2, 2015

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1 Ana Maria Rey INT International Conference, Frontiers in Quantum Simulation with Cold Atoms, March 30 April 2, 2015

2 The JILA Sr team: Jun Ye A. Koller Theory: S. Li X. Zhang M. Bishof S. Bromley M. Martin (Caltech) N. Cooper A. Gorshkov, P. Julienne, C. Kraus, P. Zoller

3 Unique atomic properties Atomic clock experiments JILA,NIST, Paris, Tokyo, PTB, NICT, NPL, NIM, NRC

4 Metastable states 3 P 0 (e) Linewidth Dn 0 ~ mhz n 0 =5x10 14 Hz 1 S 0 (g) lifetime ~ 10 2 sec JILA state-of-the-art laser: Q>10 15, seconds coherence time Quality factor: n 0 /Dn 0 >10 17 Once set, it swings during the entire age of the universe Nicholson et al, PRL (2012) Same trapping potential for both states Ye, Kimble, & Katori, Science 320, 1734 (2008). 3 P 0 (e) 1 S 0 (g) No Doppler No recoil No stark shifts Tight confinement No Doppler, No Recoil No Stark shift

5 Fractional Frequency Uncertainty Bloom et al., Nature 506, 71 (2014) Cs Beam / Cs Fountain Ion Clock Sr Optical Lattice Clock Yb Optical Lattice Clock Sr: lowest uncertainty in atomic clocks: 6.4 x Achieving this 100x faster than other clocks Now: 2.1 x Year Nicholson et al.,arxiv:

6 energy energy Atomic Clock Exquisite Control Ultra-precise Long probing times Many-body Physics Quantum Magnetism, many-body physics Clock precision = quantum numbers quantum numbers

7 S Large collective spin: Good better signal to noise No interactions All the spins precess collectively V ab : p-wave int U ab : s-wave int Interactions: Degrade signal: even in identical fermionic atoms. In 2008 gave rise to the second largest uncertainty to the 10 T~ 30mK -16 error budget JILA:G. Campbell 9 2 et al Science 324, 360 (09) NIST: N. Lemke et al PRL 103, (09) Clock V ab : p-wave int U ab : s-wave int p-wave s-wave

8 JILA? Observation of SU(N) symmetry and characterization of scattering parameters: Science, 345,1467 (2014). Confirmation of Elastic/Inelastic p-wave interactions: manybody spin system in an optical lattice clock: Science 341, 632 (2013) & 331, 1043 (2011). Theoretical prediction: SU(N) symmetry & chiral spin liquid phases: Nature Physics (2010), PRL (2009). Observation of frequency dependent density shifts in polarized fermionic clocks: Science 324,360(2009).

9 SU(N=2I+1) symmetry: I independent scattering parameters V ± ± αβ ~ b 3 αβ U αβ ~a αβ J=0 Nuclear spin symmetric Nuclear spin Anti-symmetric

10 Ramsey Spectroscopy t Phase 2p/t Ramsey fringe: A(t) cos[ (d+b eff ) t] Contrast Phase Contrast Spin precesses with a modified rate which depends on atom number: N. B eff = N C cos θ χ c and C: P-wave Interaction parameters d C = (V ee -V gg )/2 χ = (V ee -2V eg + V gg )/2

11 q B eff ~N C χ cos θ q 1 controlled by first pulse Excitation fraction: (1-cos θ 1 )/2 M. Martin et al, Science 341, 632 (2013)

12 N I Interrogated Statistical mixture B-field Clock N S : Spectators 9 2 SU(N): density shift only depends on the total number of spectators not on its distribution Δν = Δν I + Δν S Spectators density shift Δν S = ΛN S Both s and p-wave contributions Slope depends only on p-wave Independent of distribution or temperature at the 3% level

13 Use: Relation between p and s-wave through Van-der-Waals coefficient Channel S-wave(ao) P-wave(ao) Determination [S-wave] Two-photon photoassociative gg 96.2(1) 74(2) [P-wave] Analytic relation [S-wave] Analytic relation eg + 169(8) -169(23) [P-wave] Density shift in a polarized sample [S-wave] Density shift in a spin eg - 68(22) mixture at different temperatures [P-wave] Analytic relation ee (elastic) ee (inelastic) 176(11) -119(18) a ee = 46(19) b ee = 125(15) [S-wave] [P-wave] Analytic relation Density shift in a polarized sample Two-body loss measurement

14 JILA? Topological pumping & transport. Engineering & controlling spin-orbit coupling. Observation of SU(N) symmetry and characterization of scattering parameters: Science, 345,1467 (2014). Confirmation of Elastic/Inelastic p-wave interactions: manybody spin system in an optical lattice clock: Science 341, 632 (2013) & 331, 1043 (2011). Theoretical prediction: SU(N) symmetry & chiral spin liquid phases: Nature Physics (2010), PRL (2009). Observation of frequency dependent density shifts in polarized fermionic clocks: Science 324,360(2009).

15 Rabi frequency W W f W W f d: Laser detuning 3 P 0 (e) n 0 =5x10 14 Hz 1 S 0 (g) a W f W f ka=f=p 1.17 A. Celi et al PRL 112, (2014) Synthetic Gauge Fields in Synthetic Dimensions

16 Hofstadter model: D. Hügel& B. Paredes PRA 89,023619(2014 Lattice integer quantum Hall Topologically non-trivial bands, chiral edge states Eigenstates of 2-leg ladder with rational flux 2p/3 are edge states of 2D model! Away from this flux: adiabatically connected chiral states. W W d Non-trivial topology W d > W d crit Je iφ/2 W Je iφ/2

17 I. Bloch: Nature physics 10,( 2014) Array of coupled doubled wells in a synthetic gauge-field: f=p/2 Bose-Einstein condensate of Rb atoms~10-50 nk Probing tools: Time of flight Projection to isolate double-wells

18 J e n Thermal transverse modes j-1 j j+1 Optical lattice magic wavelength : ka=f=p 1.17 a g V r = [V 0 + V lat cos 2 (zπ/a )]e 2r2 /w P 0 (e) 1 S 0 (g) Thermal T~1-5 mk : Thermal axial modes lowest band but J«T: Infinite temperature Axial and radial directions coupled: Gaussian potential Current probing tools: Rabi and Ramsey spectroscopy Exquisite clock sensitivity

19 Collisions of two optically dressed BEC lead to effective higher partial wave scattering Identical spin coupled fermions can collide via effective p-wave Majorana modes: C. Zhang, et al, PRL, 101, (2008). L. Jiang et al., PRL. 106, (2011) Science, ( 2012): Fractional Hall phases M. Lewenstein Nat. Com. 4, 2046 (2013)

20 Simple picture: j-1 j j+1 n j W 2 j n j σ j n j = cos jφ, sin jφ, 0 g g [cos Wt 2 g j + ie iφj sin Wt 2 e j cos Wt 2 g j+1 + ie iφ(j+1) sin Wt 2 e j+1 A triplets + B sin( φ/2) singlet Tunneling: preserves spin p-wave interactions s-wave interactions

21 Observations: spin-orbit induced density shift proportional to s-wave interactions in polarized fermions B eff = B 0 eff N (Jτ) 2 ξ cos θ 1 sin 2 φ 2 ξ : s-wave contribution: U+ eg ξ = V eg U + eg /6

22 H qn = B eff (q) σ B eff q = 1 2 {Ω n q, 0, ΔE n q δ E gn = 2J n cos qa E n q ΔE n q = [E en E gn E en = 2J n cos qa + φ n: harmonic oscillator e g qa Non-zero chirality; C = qa σ z ψ qn = cos(θ qn/2) sin(θ qn /2) tan θ qn = Ω n q, ΔE n q δ θ qn chiral current J C = σ z H q q

23 Normalized excitation Information about f and J for W<J Ideal separable Thermal Rabi shape V r = [ 0 V lat cos 2 (zπ/a ) e 2r2 /w 0 2 n transverse Hz W/J=0.1 p W/J= 4 (p-pulse) W/J= 4 (5p-pulse) d /J width = 8J Sin[φ/2

24 E(q)/J 1. Selectively apply a p pulse for q 0 ± sin q 0 ± = δ/(4j sin(φ/2)) Use detuning and small W 2. Quench W to desired value and let the system Rabi oscillate under H q = B q σ q 0 + qa/π q 0 σ z q0 = cos 2 θ q0 cos(2t B q0 )sin 2 (θ q0 ) σ z q cos 2 θ q cos(2t B q )sin 2 (θ q ) 3. Repeat 2 but without 1 Record Signal Subtract σ z q cos 2 θ q cos(2t B q ))sin 2 (θ nq ) Record Signal

25 Issue: For a given d, the selected q 0 ± depends on J. In reality J depends on transverse mode n n transverse Hz n transverse Hz q q0 n transverse Hz Clock sensitivity opens the door for the investigation of spinorbit coupled ladders W=J, d=-2j Ideal T=0.1,1,3 mk q 0 /ap

26 Non-trivial topological bands D. Hügel& B. Paredes PRA 89,023619(2014 H q = H q Ω d cos(qa) σ x H q = B σ W d eff Closing the gap: effective magnetic field vanishes at some q eff B z =0 by controlling d B x eff =0 by dressing e with higher bands Including p-wave interactions H p E R V nz q,q,k,σσ b σσ a 3 = a e, 0 + e, 1 1 a 2 = g, 0 (cos q cos q cos k) c σ,q +k c σ c,q k σ,q c σ,q Mean-field : cos(qa) σ x q B qq σ x

27 Use synthetic direction in a more versatile way N. R. Cooper, A. M. Rey: arxiv: L. Wang, M. Troyer, and X. Dai, PRL. 111, (2013). F. Mei et al., PRA 90, (2014). R. Wei and E. J. Mueller, arxiv:

28 Transfer charge/particles in a quantized fashion: closely related to the quantized Hall transport in the quantum Hall effect. 1D system: Transport quantized according to a Chern number C, defined over [D. J. Thouless(1983)]: 1D Brillouin zone (1D lattice) + Time-dependent periodic parameter in a cycle (synthetic dimension) c(t) g, e, e, g, j-1 j j+1 Ω j s,s+1 = Ωe i jφ χ 4 Also with Raman: M. Mancini et al., arxiv: , B. K. Stuhl et al., arxiv:

29 H Ω,j s Ω j s s + 1 Ω j s + 1 s E j = 2 Ω cos χ τ 4 jφ + k s Preparation ground state τ i(jφ χ Ω j = Ωe 4 ) k s = 1 2 s e isk s s k s 0 π 2, π 3π 2 } 1. Initially s=0,s=0, 2. Slowly increase W and decrease d H δ δ s s s s For example: f=p/2 k 0 k 1 k 2 k 3 The ground state has alternating dressed states j j+1 j+2 j+4

30 c At t=0 a k s =0 particle is at j=0 and c=0 Turn on tunneling: J Particle frozen because next site is off resonance. Adiabatically increase c. Slowly than J/h At c=p tunneling resonance appears Particle is adiabatically pumped to j=1 at c=2p

31 At t=0 a k s =p/2 particle is at j=0 and c=0 Transport will be in the other direction when varying c

32 J DV= Fa At c=p ΔV/2 J J ΔV/2 j D a Protocol: j+1 1. Suddenly turn off J=0 ψ + = [cos Θ 2 k s = 0 j + sin Θ 2 k s = 0 j+1 sin 2 Θ 2 ~ ΔV 2J + 2. Reverse c to 0 3. k s = 0 j+1 is now excited state Population of k s = 0 j+1 proportional to Δ 4. Slowly turn off W and on d 5. Measure s 1 population

33 For the case U J,W J J At c=p State ~ equal superposition of U Turn off J will lead to Ramsey oscillations with frequency U measureable spectroscopically In a double well superlattice the same procedure to measure D can be applied to measure U If the interactions are not SU(4) k s 0,p/2 will be populated For the case U J,W Transport will be blocked

34 Bloch waves of Harper Eq. with f=2pp/q characterize by:{k x,k s +c/4} Topological bands with C 0: Chern Number when k x vary (-p/q,p/q) and c from (0, 2p) For an insulating state C: # particles than move under adiabatic: c =0 2p One filled band, p/q=1/4 C= 1 Preparation: Band Insulator at W=0 W>0 at c p Non-trivial topological insulator How can be adiabatically connected?? Ok, since 1D k s is discrete

35 Force: F x Synthetic current I s = H Ω χ NaF x Σ I s 0 2π Σdχ = C quantized S: Average Berry curvature Local picture: I s = - an ΩΔV 4 2J Σ = Ω 4 2J

36 W Nuclear spin polarized W c Two levels k s = 0, π = g ± e 2 H Ω,j = 2Ω cos χ jφ σ x φ π

37 Protocol: 1. Prepare local dressed levels J=0 2. Adjust c and turn on J fast 3. Wait for tunneling 4. Ramp up lattice and vary c 5. Solwly turn off W and on d 6. Measure e

38 D Population c c=p Should be spatially solvable with a B-field gradient site 5 100

39 Clock sensitivity can allow for probing spin orbital physics and quantum magnetism at µk temperature. Spin-orbit experiment under preparation in the JILA clock Many-body localization in the clock? H Ω,j = 2Ω cos χ jφ σ x φ π Synthetic gauge fields + SU(N): route for a stabilize chiral spin liquid? arxiv: ,synthetic gauge fields stabilize a chiral spin liquid phase, G. Chen, K.R.A. Hazzard, A.M. Rey & M. Hermele

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