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”

Theory team: B. Yan, S. Moses, J. Covey, B. Neyenhuis and B. Gadway

D. Jin Jun Ye

KRb team:

A. Gorshkov,M. Foss-Feig, K. Hazzard, B. Zhu, S. Manmana, M. Lukin

The Sr team:

M. Swallows, M. Martin, M. Bishof, S. Blatt, X. Zhang, C. Benko

Fully controllable quantum systems

The most precise measurements, e.g. clocks Quantum sensors A tool for understanding quantum complexity

Richard Feynman

Quantum simulation

Atoms ↔ Electrons

Optical lattice ↔ Ionic Crystal

Possible but challenging

Optical lattice spacing much larger than ionic lattice spacing

Atoms heavier than electrons

Extra low temperatures

10-11 K in atomic systems ~ K in solid state systems

• Develop sophisticated cooling methods

• Explore new type of systems • Take advantage of

ultra-precise tools

Solutions

Trapped Ions

Magnetic Atoms

Polar molecules

Rydberg Atoms

Alkaline earth atoms

(~ KHz) (~ Hz)

Understanding quantum systems from few- to many-body

with “clock” precision and control

No Doppler, No Recoil No Stark shift

Metastable state

1S0 (g)

3P0(e)

698 nm (~ 150 s)

Sr and Yb

Ye, Kimble, & Katori, Science 320, 1734 (2008). Magic wave length

JILA Ultra-coherent spectroscopy: Nicholson et al., Phys. Rev. Lett. 109 (2012) 230801

Q~1015, seconds coherence time Ye’s talk this afternoon

ν0 g

e

τ

νL

exp [iδτ]

Measure # of e atoms

2π/τ

e-a

tom

s

N. Ramsey. Nobel prize 1989

What happens in the real experiment with N particles?

B=2π(νL− ν0 )=δ

e

g

δ: Detuning

z

x y

Contrast

Non-interacting: Collective-spin S ∑=n

zyxSS ,,nzy,x, Interactions?

Effective spin 1/2 system during clock interrogation

Array of pancakes reactive

Mode occupation is conserved. No laser/interaction induced mode changing collisions.

1S0 (g)

3P0 (e)

Dominant p-wave collisions

Both elastic and inelastic

n ν~500 Hz,V~ 1 Hz n1

n2 n3 n4 ∑−=

n

znSH δ ∑Ω−

n

xnnS

zn

zn'

znn'n

n'nSBSSSSJ nnnnnn ',',

,',[ ++⋅+ ∑ ⊥ χ

( ) ( ) )(2 ',',',',',',',',',',ggnn

eennnn

ggnn

eenn

egnnnn

egnn

egnnnn VVBVVVUVJ −=−−=−=⊥ χ

δ: Detuning

Ωn: Rabi Frequency

Interaction parameters

Decoupled motional/spin

ν~500 Hz

Long range!!

∑∆++⋅+Ω−−−−= ⊥

'.',))1((

nnnnHSSSJSSBNH 2

zxz χδ

constant n n’

',', , nnnnJ χ⊥

',

',

',',',', ,,,

nn

nn

nnnnnnnn

BB

JJBJ

χχ

χ

∆+

∆+

∆+→ ⊥⊥⊥

J=N/2

⊥JN

H∆ Same Hamiltonian that two component Bose Einstein Condensate: Sorensen, Moller, Cirac, Zoller, Lewenstein, …

∑=n

zyxSS ,,nzy,x,

S S A. M. Rey, L. Jiang, M. Fleischhauer, E. Demler, and M. D. Lukin, PRA 77, 052305 (2008) .

Treat other surrounding atoms as an average

H=- (Sz )2→2 Sz Sz= B Sz

x

z

Sz

Spin precesses with a modified rate with depends on atom number

θ

θ controlled by first pulse

B=-2Sz=-Ncos θ

Excitation fraction: 1/2+Sz/N

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

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.

1D

• Atom number decay aslo leads to decay of the amplitude

Signal adds → amplitude of the oscillations decay due to dephasing or destructive interference between pancakes

M. Martin et al arXiv:1212.6291

Ramsey fringe decay vs. the spin tipping angle

Shif

t

Excitation fraction

To eliminate the effect of decay we normalize the amplitude with atom number

N

orm

alize

d Am

plitu

de

time

Mean filed fails to reproduce the amplitude decay at tipping angles where the density shift vanishes

M. Martin et al arXiv:1212.6291

Interplay between interactions and decoherence: complicated

few many

We were able to solve the full master Eq for the collective model.

Nor

mal

ized

Cont

rast

Quantum correlations induce faster decay of the amplitude

dipole moment

“spin” N

Rotation

Select two dressed levels : Effective spin ½ system

Rigid Rotor

N=0

EdBNH iirot

i

⋅−= 2

~GHz

N=1

E=0 |

|

Increasing E

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)…

Gorshkov et al: PRL.107.115301(2011), PRA 84,033619 (2011)

|1,-1

|1,0

|1,1

|0,0

N

( )[ ]∑ ++= ⊥ji

yj

yi

xj

xi

zj

ziz

ijdddd SSSSdJSSdJVH

,'' )()( σσσσ

3

2

||)cos31(

ji

ij

rrV

dd −−

=θ

• Project di on the two selected rotational levels '

', ',ˆ iii dzd σσσσ σσ∑=

Ising Flip-flop

'|' σσσσ dd =

ijddjidd VddH =

0,0 ===↓ MN

0,1 ===↑ MN

𝐽𝑧 = (𝑑↑↑ − 𝑑↓↓)2

𝐽⊥ = 2(𝑑↑↓)2

Use direct dipole-dipole interaction to generate direct strong (~KHz) spin exchange interaction: 10-100 larger than super-exchange or magnetic dipoles Fully tunable coefficients by E field (microwaves) Gorshkov et al: PRL.107.115301(2011), PRA 84,033619 (2011) Long-range (1/r3) and anisotropic interactions: S. R. Manmana et al PRB 87, 081106(R) (2013), A. V. Gorshkov et al arXiv:1301.5636

dipole moment

N

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

θ=π/2, π/10

K. R.A. Hazzard et al PRL 110, 075301 (2013)

θ=π/2, π/10

Current experiments are carried out in a 3D lattice with a B field B: determines quantization axis |= |N=1,M=-1

|= |N=0,M=0

Magic wavelength for their lattice

B. Neyenhuis et al Phys. Rev. Lett. 109, 230403 (2012)

B

ε φ Polarization

trapping light

• Non-trivial dependence on the geometry due to the anisotropic dipolar interactions.

B 3

2

||)cos31(

ji

ij

rrV

dd −−

=θ

𝐻 = 𝐽⊥ 𝑉𝑖𝑖 𝑆𝑥𝑖𝑆𝑥𝑖 + 𝑆𝑦𝑖𝑆𝑦𝑖<𝑖,𝑖>

𝐽⊥ = −(𝑑↑↓)2

Cluster Expansion

• Spins grouped in cluster of max size g.

• Intra-cluster interactions kept • Inter-cluster interactions

neglected or treated as a perturbation.

g=4

Solid lines: Cluster expansion g=10 Gaussian distribution:

π/2 pulse Filling factor: 7 % 14% 21%

𝜏/8 𝜏/4 𝜏/8 𝜏/8 𝜏/4 𝜏/8

𝜋2 𝑦

𝜋2 𝜙

𝜋2 −𝑥

𝜋2 𝑥

𝜋2 −𝑥

𝜋2 𝑥

𝜋 𝑥

𝜏/2 𝜏/2

𝜋2 𝑦

𝜋2 𝜙

𝜋 𝑥

𝜏

𝜋2 𝑦

𝜋2 𝜙

Wahuha + echo

echo

Learn from NMR: By applying the proper pulse sequence it is possible to eliminate dipolar interactions.

Preliminary pulse scheme for KRb

• 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