Ana Maria Rey

Okinawa School in Physics 2016: Coherent Quantum Dynamics

Okinawa, Japan, Oct 4-5, 2016

• Quantum simulations

• Production and control of KRb molecules

• Exploring quantum magnetisms with ultra-cold molecules

Digital: Quantum Computer

A machine that can perform computations using quantum mechanical elements.

“Simulating Physics with computers” IJTP, 21,467 1982

Analog: Quantum Simulation

Use a controllable quantum system to simulate another quantum system

The Nobel Prize in Physics 1965

AMO• Fully controllable, no

defects, no vibrations

• Lattice spacing micrometers

• Atoms mass ~ 10-100 amu

• Low-Temperature : 0.01 nK

CM• Very complex condensed

matter environment

• Lattice spacing Angstroms

• Electron mass 1/1900 amu

• Low –Temperature : T~ 1 K

Atoms ↔ Electrons

Optical lattice ↔ Solid Crystal

At the moment temperature is a strong limitation

TN

U/J

Paramagnetic Mott

Metal

Anti-ferromagnetic Mott

Current experiments

UcJN JeT /~

UJTN /~ 2Harvard:2016

• Develop sophisticated cooling methods• Explore new type of systems• Take advantage of ultra-precise tools

Solutions

Magnetic AtomsRydberg atoms

Polar molecules Alkaline‐earth atoms Trapped ions

• Strong dipolar interactions: Long range and anisotropic• Rich internal structure:

Rotation, vibration, hyperfine.• Chemistry• Quantum Information

JIL: A quantum dipolar gas in a lattice

Why polar molecules??

Many to come: MIT, Innsbruck, JQI, Columbia, Amsterdam, Hong‐Kong… 

Atom vs. molecule

T = 100 nK

N = 106 atomsn = 1013 cm-3

Bose-Einstein Condensation1995

Molecules (pre-2008): T = 100 mK, n = 106 cm-3

Molecules are complex!

0.1 K 38 μK6000 K

10 orders of magnitude

1010 108 105 102 1

200 nK

vibration

bindingenergy

rotation hyperfine translation

1 μK

trap depth

100 K

KRb, LiCs, RbCs, NaK, LiNa,LiRb, RbSr, RbYb and LiYb

Two paths to ultra-cold molecules

• Stark deceleration• Buffer‐gas cooling

• Laser cooling?• Polarization cooling?• Sympathetic cooling?• Evaporative cooling?

SrF

YO

BrO

CH

NO

OH

CH3F

KRb molecules(Dipole ~0.5 Debye)

K. Ni et al., Science 322, 231 (2008).

Nature Phys. 4, 622 (2008) Science 322, 231 (2008)

40K Fermions 87Rb Bosons

K. Ni et al., Science 322, 231 (2008).

KRb moleculesRo‐vibrational ground stateT/TF ~ 1 Density ~1012/cm3

(Dipole ~0.5 Debye)

105 times colder, 106 times more dense than other results for polar molecules!

Light provides the answer

Photons carry away the energy!

Start with ultracold atoms.40K 87Rb

K-Rb Feshbach resonance

Make large, floppy molecules

Convert a pair of atoms into a molecule

Control the interactions.

Coherent two-photon transfer

12

3

1

3

1

Inter-nuclear distance R

Ener

gy

v = 0, N = 0, J = 0

6000

K

ℓ → ℓ ℓ ℓ

Pauli Exclusion principle

(2) Angular momentum is quantized: Ultra cold atoms collide via the lowest partial waves

(3) Quantum statistics matter

Identical fermions anti-symmetric spatial wave function p-wave

(1) Particles behave like waves (T → 0)

s-wave , l=0,Spatially symmetric

p-wave , l=1Spatially anti-symmetric

R

Cen

trifu

gal b

arrie

r → 0

KRb+ KRb K2+Rb2 +

Ultracold chemistry

At low T, the quantum statistics of fermionic molecules suppresses chemical reaction rate!

Ener

gy

distance between the molecules

Ospelkaus et al.,Science 327, 853 (2010).

Temp. (K)

β (p-wave) ∝ T

β (s-wave)

2/)1(~ rll

24K

-1.5 kV

+1.5 kV

E = 0 (no induced dipoles) p-wave suppression

Dipolar interaction “turns on” collisions- anisotopic, long range

K.-K. Ni et al., Nature 464, 1324 (2010).

Collisions in 3D space average over different channels.

p-wave barrier

0.01 0.1

1

10

(B)

Dipole moment (Debye)

/ T

(10-5

cm3 s-1

K-1)

~ d6

(Attractive dipole dipole interaction)

miliseconds lifetime

Possibility of  observing quantum magnetism even at current conditions: PRL 110, 075301 (2013)

3D   Trap 

LifetimeTrapping 

miliseconds

Low density: filling 0.1

PRL 108, 080405 (2012)

Pancakes: 2D seconds

Nature Phys. 7, 502 (2011)

3D lattice  Up to 25 s

Tubes: 1D seconds

PRL.107.115301(2011), PRA 84,033619 (2011)

Use direct dipole‐dipole interaction to generate direct strong spin‐spin interactions: 

Spin temperature, not motional temperature matters: 

Decoupling between motional and spin degrees of  freedom

Long range spin‐spin interactions even in frozen molecules

• Empty sites act as defects• Need to  perform disorder average

Dipolar interactions should  be visible in the Ramsey fringe contrast even in dilute samples, PRL 110, 075301 (2013)

Diluteness: doesn’t slow!

Rigid Rotor EdBNH iirot

i

2

E

N=0

~GHz

N=1|1,-1�|1,0�|1,1�

|0,0�

Electric field mixes rotational states

|↓�

|↑�

d↑≠0, d↓≠0

↓|d|↑��d↑↓≠0↑|d|↑��d↑↓|d|↓��d↓

d↑=d↓=0E=0

Rigid Rotor EdBNH iirot

i

2

E

N=0

~GHz

N=1|1,-1�|1,0�|1,1�

|0,0�

Electric field mixes rotational states

|↓�

|↑�

d↑≠0, d↓≠0

↓|d|↑��d↑↓≠0↑|d|↑��d↑↓|d|↓��d↓

Hyperfine:Split degeneracy

d↑=d↓=0E=0

|↓�

|↑�

Control of populated levels with B field

~100 kHz

One excited level: Exchange

Two excited level: Chirons

Three excited level: Weyl

Dipolar physics is complex strongly depend on the accessible levels

Υ

=0

Attract

=

Repel

Virtual exchange of photons

Project d operators in N=0,N=1 manifolds

∓

√

Υ ∝

Long range and anisotropic

R

E

plane

ji

zj

zizjiji

ij

ijdd SSJSSSSJ

RH

2)cos31(

3

2

Project on the two selected rotational levels

~ GHz

N=1|1,-1�

|1,0�

|1,1�

N=0 |0,0�

|↑�

|↓�

∝

2)( ddJz

22 dJ

|1,-1

|1, 0|1, 1

|0, 0

|1,-1

|1, 0|1, 1

|0, 0

Project on the two selected rotational levels

~ GHz

N=1 |1,-1� |1,0�

|1,1�

N=0 |0,0�

|↓�

∝|↑�~

Reduced by a factor of two!! Time average: |1,1� rotating

ji

zj

zizjiji

ij

ijdd SSJSSSSJ

RH ~

4)cos31(

3

2

|1,-1|1, 0 |1, 1

|0, 0

|1,-1 |1, 0 |1, 1

|0, 0

2/2/~ 22~ ddJ

2~ )(~

ddJz

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

V0j

Nature 501, 521 (2013).

Current experiments are carried out in a 3D lattice with a B field

∑

• Use rotational state choice to control interaction strength

V: p-wave intU: s-wave int

xy

z

V: p-wave intU: s-wave int

Prepare all down and then apply a microwave pulse

PreccesionNo interactions Interactions introduce correlations?

# of  ↑

Measure

Measure # of e particles

e-at

oms

B=2L

Detuning ContrastRamsey spectroscopy: a quench

Prepare

EvolveT Measure

Phase

Ramsey fringe:   C(T) cos )T]

Contrast Phase

Phase: 

controlled by first pulse

Depolarization of the transverse spin, quantum effect ∝ sin

Spin precesses with a modified rate which  depends on molecule number.

No mean field dynamics at 

cos

x y

z

Contrast ∶

Beff

j

(1) Observed  oscillation  frequency  consistent with   / = 52 Hz 

(2) contrast decay time ∼ /

Contrast  ≡

Nature 501, 521 (2013).

/8 /4 /8 /8 /4 /8

2 22 2 2 2

/2 /2

2 2

2 2

Wahuha + echo

echo

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

Pulse scheme for KRb

Non-magic trap

∑

Need to compare to theory, but looks impossible• Strongly interacting and non‐equilibrium disordered system• Long‐range interactions, 3D [ 104 particles talking to each other]• Mean field prediction: nothing happens!

We came up with a way: Improved cluster expansionK. Hazzard et al, PRL  113 195302 (2014) 

Used before

• Spins  grouped in cluster of max size g.

• Intra‐cluster interactions kept and solved exactly

• Inter‐cluster interactions neglected.

g=4

Ours: MACE   “Moving Average Cluster Expansion”

• For each spin i select an optimal cluster of size g

• Solve the dynamics for that cluster: :

• Total dynamics: Sum over clusters:∑

Contrast

Exact solution

XX oscillates more

With only one fitting parameter to determine the density we are able to reproduce the experiment

Theory (MACE) Experiment

K. Hazzard et al, PRL  113 195302 (2014) 

TheoryImproves

ExperimentImproves

Quantum simulation

S. V. Syzranov, et al “Spin–orbital dynamics in a system of polar molecules”, Nature Communications, 5391, 2014.

Two excited level: Chirons

Conservation of total angular momentum:                              Coupling spin and motional degrees of freedom

Einstein De‐Hass effect

Various proposals to see the effect in bosonic magnetic atoms.• Vortex formation: Santos, Ueda                           

Not seen yet.• Demagnetization: Laburte‐Tolra, Pfau

Exchange Spin-orbit

|1,-1�

|1,0�

|1,1�

|0,0�

|1,-1�

|1,0�

|1,1�

|0,0�i j

Vacuum|1,1�|1,-1�

Excitation can propagate even for pinned particles in a lattice while flipping their spin

x

y

zE

ij

Diagonal in quasi-momentum k and spin

00

Diagonal in k but causes spin-flips⇆ :

00

,

Exchange Spin-orbit

↑ ↓ ↑ ↑

,

Mimic Bilayer graphene

, =|1, 0,0|

~ ⋅

2 , 2 , 0

2

/

fast

slow

Non trivial:             Berry phase 2

Dispersion: Two‐branches

Bilayer graphene

Unconventional Hall Effect

C. Neto et al RMP 81, 00346861 (2009)

Generalized Ramsey scheme: Can be used to detect chirality and Berry phase

# ofMeasure

Non-collective pulses

|0,0�→

2 Berry phase:d-wave geometry

Pinned case

The Berry phase will be still visible in dilute samples

10% filling

Just reduced signal: The peak magnitude is reduced by a factor of 20 compared to unit filling.

Non-trivial spatial oscillations in the density

|0,0�→ |↑�

Measure ↓

Total density

Vortex

Weyl fermions are fundamental massless particles with a definite handedness that were first predicted by Hermann Weyl back in 1929, but they have never been observed  in high‐energy experiments.  

Recently found in solid materials                                                                   (TaAs ‐‐Princeton & Beijing‐‐, Photonic crystals –MIT‐‐)

Weyl excitations naturally emerge in dipolar particles 

Ingredients: J=0 to J=1 structure

• Polar molecules

• Alkaline earth atoms

~ ⋅

,

Excitation propagates for pinned particles in a lattice while flipping their spin

, =|Ji=1, 1,0 Ji=0,0|

Project into J=0, J=1 manifoldsAn excitation

Υ ∝

Υ ∝

Υ ∝

~ ⋅ Chirality

B

pz=0px=0

q

q

Population 

+ +

LPolar molecules 

Science (2015)

PRL, (2016)

arXiv:1608.03854

Rich internal structure

Dipolar interactions

Second generation

Dipolar exchange

Nature (2013) PRL (2014)

Stable orbitals

Zeno effect PRL (2014)

Synthetic gauge fields

Nat. Com (2014)Nat. Com (2016)

Low entropy lattice gas

Science(2015)

KRb second  generation• All electrodes in the vacuum chamber

• Very stable DC fields and controllable gradients: Cooling, Dipole control

• Submicron imaging resolution and optical access for lattices

Science cellQuadrupole trap

LPolar molecules 

Science (2015)

PRL, (2016)

arXiv:1608.03854

Frustrated magnetism Many-body

localization

Rich internal structure

Dipolar interactions

Second generation

Dipolar exchange

Nature (2013) PRL (2014)

Stable orbitals

Zeno effect PRL (2014)

Synthetic gauge fields

Nat. Com (2014)Nat. Com (2016)

Low entropy lattice gas

Science(2015)

Fractional ChernInsulatorsDebbie Jin

Theory: 

Jun Ye 

KRb team:D. Jin

M. Wall

B. Zhu

M. Foss‐Feig, K. Hazzard A. Gorshkov

S. Syzranov

S. Manmana, M. Lukin, P. Julienne

Review Material

• G. Quéméner and P. S. Julienne, Ultracold molecules under control, Chemical Reviews. 112(9), 4949–5011, (2012).

• M. L. Wall, K. R. A. Hazzard, A. M. Rey Quantum magnetism with ultracold molecules, arXiv:1406.4758.

• L. D. Carr, D. Demille, R. V. Krems, and J. Ye, Cold and ultracold molecules: Science, technology, and applications, New J. Phys. 11, 055049, (2009).

• Jacob P. Covey, Steven A. Moses, Jun Ye, Deborah S. JinControlling a quantum gas of polar molecules in an optical lattice,arXiv:1609.07671