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”

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-atoms

• 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 z y x

S S

, , n z y, 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 z n

S H δ

∑Ω

−

n x n nS

z n z n' n' z n n' n' n n' n' n

S B S S S S J

n n n n n n ' , ' , , ' ,

[ + + ⋅ +∑

⊥

χ  

( ) ( )

) ( 2

' , ' , ' , ' , ' , ' , ' , ' , ' , ' , gg n n ee n n n n gg n n ee n n eg n n n n eg n n eg n n n n

V V B V V V U V J − = − − = − =

⊥

χ

δ: Detuning Ωn: Rabi Frequency Interaction parameters Decoupled motional/spin ν~500 Hz

Long range!!

∑∆

+ + ⋅ + Ω − − − − =

⊥ ' . ' ,

) ) 1 ( (

n n n n

H S S S J S S B N H

2 z x z

χ δ  

constant

n n’

' , ' , , n n n n

J χ

⊥

' , ' , ' , ' , ' , ' ,

, , ,

n n n n n n n n n n n n

B B J J B J χ χ χ ∆ + ∆ + ∆ + →

⊥ ⊥ ⊥

J=N/2

⊥

J N

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

∑

=

n z y x

S S

, , n z y, 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=-2฀ ฀ Sz฀ =-N฀ cos 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

• scillations decay due to

dephasing or destructive interference between pancakes

• M. Martin et al arXiv:1212.6291

Ramsey fringe decay vs. the spin tipping angle

Shift Excitation fraction

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

Normalized Contrast 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

E d BN H

i i rot 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

( )

[ ]

∑

+ + =

⊥ j i y j y i x j x i z j z i z ij dd dd

S S S S d J S S d J V H

, ' '

) ( ) (

σσ σσ

3 2

| | ) cos 3 1 (

j i ij

r r V

dd

− − = θ

• Project di on the two selected rotational levels

' ' , ' ,

ˆ

i i i

d z d σ σ

σ σ σ σ

∑

=

Ising Flip-flop

' |

'

σ σ

σσ

d d =

ij dd j i dd

V d d H =

, = = = ↓ M N , 1 = = = ↑ M N

𝐾𝑨 = (𝑒↑↑ − 𝑒↓↓)2 𝐾⊥ = 2(𝑒↑↓)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

| | ) cos 3 1 (

j i ij

r r V

dd

− − = θ

𝐼 = 𝐾⊥ 𝑊

𝑗𝑗 𝑇𝑦𝑗𝑇𝑦𝑗 + 𝑇𝑧𝑗𝑇𝑧𝑗 <𝑗,𝑗>

𝐾⊥ = −(𝑒↑↓)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%

𝜐/8 𝜐/4 𝜐/8 𝜐/8 𝜐/4 𝜐/8 𝜌 2 𝑧 𝜌 2 𝜚 𝜌 2 −𝑦 𝜌 2 𝑦 𝜌 2 −𝑦 𝜌 2 𝑦 𝜌 𝑦 𝜐/2 𝜐/2 𝜌 2 𝑧 𝜌 2 𝜚 𝜌 𝑦 𝜐 𝜌 2 𝑧 𝜌 2 𝜚 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