ana maria rey - oist groups
TRANSCRIPT
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).
-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).
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:∑
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.
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 ∝
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