Quantum Computing with Polar Molecules:
quantum optics - solid state interfaces
UNIVERSITY OF
INNSBRUCK
Peter Zoller
A. Micheli (PhD student)
P. Rabl (PhD student)
H.P. Buechler (postdoc)
G. Brennen (postdoc)
Harvard / Yale collaborations:
Misha Lukin (Harvard)
John Doyle (Harvard)
Rob Schoellkopf (Yale)
Andre Axel (Yale)
David DeMille (Yale)
AUSTRIAN
ACADEMY OF
SCIENCES
SFB
Coherent Control of
Quantum Systems
€U networks
Cold polar molecules
exp: DeMille, Doyle,
Mejer, Rempe, Ye, …
What‘s next in AMO physics?
• Cold polar molecules in electronic & vibrational ground states
– control & very little decoherence
What new can we do?
• AMO physics:
– new scenarios in quantum computing & cold gases
•
electric dipole
moments
Interface AMO – CMP
– example:
superconducting
circuits
molecular ensembles /
single molecules
 compatible setups & parameters
 strength / weakness complement each other
Quantum Optics
with Atoms & Ions
•
Polar Molecules
cold atoms in optical lattices
laser
rotation
dipole moment
•
•
trapped ions / crystals of …
•
•
•
CQED
cavity
atom
•
laser
•
atomic ensembles
single molecules / molecular ensembles
coupling to optical & microwave fields
– trapping / cooling
– CQED (strong coupling)
– spontaneous emission / engineered
dissipation
interfacing solid state / AMO & microwave
/ optical
– strong coupling / dissipation
collisional interactions
– quantum deg gases / Wigner (?) crystals
– dephasing
Polar molecules
•
basic properties
1a. Single Polar Molecule: rigid rotor
•
single heteronuclear molecule
…
N=2
"D"
d
N=1
N=0
"P"
"S"
rigid rotor
•
d
dipole d~10 Debye
rotation B~10 GHz (anharmonic )
(essentially) no spontaneous emission 
(i.e. excited states useable)
Strong coupling to microwave fields / cavities; in particular also strip
line cavities
1b. Identifying Qubits
•
•
rigid rotor
adding spin-rotation coupling (S=1/2)
H = B N2 +  N·S
H = B N2
"D5/2"
"D"
J=5/2
N=2
"D3/2"
N=2
"P"
N=1
"P3/2"
N=1
"P1/2"
"S"
N=0
charge qubit
•
How to encode qubits?
J=3/2
J=3/2
J=1/2
"S1/2"
N=0
spin-rotation
splitting
J=1/2
spin qubit
(decoherence)
``looks like an Alkali atom on GHz scale´´
(we adopt this below as our model molecule)
2. Two Polar Molecules: dipole – dipole interaction
•
interaction of two molecules
features of dipole-dipole interaction
 long range ~1/R3
 angular dependence
repulsion
V dd 

d 1 
d 2 3 
d 1 
eb
R3

eb 
d2
attraction
 strong! (temperature requirements)
What can we do with Polar Molecules?
•
a few examples & ideas
1. Hybrid Device:
solid state processor
& molecular memory
+ optical interface
R. Schoelkopf, S. Girvin et al.
see talk by A. Blais on Tuesday
superconducting (1D)
microwave transmission line
cavity
(photon bus)
Yale-type
strong coupling CQED
Cooper Pair Box
(qubit)
P. Rabl, R. Schoelkopf, D. DeMille, M. Lukin …
1. Hybrid Device:
solid state processor
& molecular memory
+ optical interface
optical
cavity
molecular
ensemble
optical
(flying) qubit
laser
superconducting (1D)
microwave transmission line
cavity
(photon bus)
polar molecular ensemble 1:
quantum memory
(qubit or continuous variable)
[Rem.: cooling / trapping]
strong coupling CQED
Cooper Pair Box
(qubit)
as nonlinearity
polar molecular ensemble 2:
quantum memory
(qubit or continuous variable)
Trapping single molecules above a strip line
•
Three approaches:
– magnetic trapping (similar to neutral atoms)
– electrostatic trap: d.E interaction DC
– microwave dipole trap: d.E interaction AC
Andre Axel,
R. Scholekopf
M. Lukin et al.
Electrostatic Z trap (EZ trap)
• DC voltage: same trap potential
for N=1,2 states at ~10 kV/cm
0.1mm
•
•
• AC voltages: same trap potential for
N=0,1 states at “magic” detuning
micron-scale
electrode structure
Goals
– Trapping of relevant states h~0.1 mm from surface
– High trap frequencies ( > 1-10 MHz)
– large trap depths …
Challenges:
– Loading – no laser cooling (?)
@ h~0.1 and t> 10 MHz
– Interaction with surface
shifts levels by less than 1%
e.g. van der Waals interaction
Sideband cooling with stripline resonator (“g cooling”)

|2>


•
“g” cooling: position
dependence of coupling g(r) to
cavity gives rise to force
•
“” cooling: spatially uniform g
but different traps in upper/lower
states → gives rise to force
|1>
engineered dissipation +
analogy to laser cooling
2. Realization of Lattice Spin Models
•
A. Micheli, G. Brennen, PZ,
preprint Dec 2005
polar molecules on optical lattices provide a complete toolbox to realize
general lattice spin models in a natural way
Examples:
Duocot, Feigelman, Ioffe et al.
Kitaev
xx
zz
ZZ
XX YY
1
1
I
H
zi,jzi,j1 cos xi,jxi1,j
spin   i1  j1 J
protected quantum memory:
degenerate ground states as qubits
•
II
y y
x x
H
J



J

#




spin
j k
j
k
xlinks
J z

ylinks
zj zk
zlinks
Motivation: virtual quantum materials towards topological quantum
computing
#
3. (Wigner-) Crystals with Polar Molecules
•
“Wigner crystals“ in 1D and 2D (1/R3 repulsion – for R > R0)

potential energy
kinetic energy

d 2 /R 3
2 /2MR 2
H.P. Büchler
V. Steixner
G. Pupillo
M. Lukin
…
~ R1  n 1/3
dipole-dipole: crystal for high density

2 /2MR 2
~R
Coulomb: WC for low density (ions)
2D triangular lattice
(Abrikosov lattice)
g(R)
e 2 /R
1st order phase
transition
solid
liquid
R
Tonks gas / BEC
WC
(liquid / gas)
mean
distance
quantum
~ 100 nm
statistics
Applications:
•
compare: ionic Coulomb crystal
Ion trap like quantum computing with phonons as a bus.
d1 d2 /R3
ion trap like qc, however:
x
phonons
•
•
 d variable
 spin dependent d
 qu melting / quantum
statistics
Exchange gates based on „quantum melting“ of crystal
– Lindemann criterion x ~ 0.1 mean distance
– [Note: no melting in ion trap]
(breathing mode indep of # molecules)
Ensemble memory: dephasing / avoiding collision dephasing in a 1D
and 2D WC
– ensemble qubit in 2D configuration
– [there is an instability: qubit -> spin waves]
Quantum Optical / Solid State Interfaces
with P. Rabl, R. Schoelkopf, D. DeMille, M. Lukin
Hybrid Device:
solid state processor
& molecular memory
+ optical interface
optical
cavity
molecular
ensemble
optical
(flying) qubit
laser
superconducting (1D)
microwave transmission line
cavity
(photon bus)
polar molecular ensemble 1:
quantum memory
(qubit or continuous variable)
[Rem.: cooling / trapping]
strong coupling CQED
Cooper Pair Box
(qubit)
as nonlinearity
polar molecular ensemble 2:
quantum memory
(qubit or continuous variable)
R. Schoelkopf, M. Devoret,
S. Girvin (Yale)
1. strong CQED with superconducting circuits
•
Cavity QED
SC qubit
Jaynes-Cummings
good cavity
strong coupling!
(mode volume V/ 3 ¼ 10-5 )
•
•
“not so great” qubits
[... similar results expected for coupling to quantum dots (Delft)]
[compare with CQED with atoms in optical and microwave regime]
… with Yale/Harvard
2. ... coupling atoms or molecules
•
superconducting transmission
line cavities
atoms /
•
hyperfine excitation of BEC /
atomic ensemble
molecules
hyperfine structure
» 10 GHz
SC qubit
•
•
Remarks:
– time scales compatible
– laser light + SC is a problem: we
must move atoms / molecules to
interact with light (?)
– traps / surface ~ 10 µm scale
– low temperature: SC, black body…
rotational excitation of polar
molecule(s)
N=1
rotational excitations
» 10 GHz
N=0
ensemble

|r
3. Atomic / molecular ensembles:
collective excitations as Qubits
|q
|g
•
ground state
microwave
•
one excitation (Fock state)
microwave
harmonic
oscillator
•
•
•
two excitations ... eliminate?
– in AMO: dipole blockade, measurements ...
nonlinearity due to
Cooper Pair Box.
etc.
also: ensembles as continuous variable quantum memory (Polzik, ...)
collisional dephasing (?)
4. Hybrid Device: solid state processor & molec memory
molecules:
qubit 1
SC qubit
time independent
molecules:
qubit 2
ensemble
qubits
solid state system
+ dissipation (master equation)
swap molecule cavity
5. Examples of Quantum Info Protocols
•
SWAP
Cooper Pair
cavity (bus)
molec ensemble
•
Single qubit rotations via SC qubit
•
Universal 2-Qubit Gates via SC qubit
•
measurement via ensemble / optical readout or SC qubit / SET
Atomic ensembles complemented by deterministic entanglement operations
A. Micheli, G. Brennen & PZ,
preprint Dec 2005
Spin Models with Optical Lattices
•
•
we work in detail through one example
quantum info relevance:
– polar molecule realization of models for protected quantum
memory (Ioffe, Feigelman et al.)
– Kitaev model: towards topological quantum computing
Duocot, Feigelman, Ioffe et al.
1
1
I
H
zi,jzi,j1 cos xi,jxi1,j
spin   i1  j1 J
Kitaev
II
y y
x x
H
J



J

#




spin
j k
j
k
xlinks
J z

zlinks
ylinks
zj zk
#
Basic idea of engineering
spin-spin interactions
dipole-dipole:
anisotropic + long range
microwave
spin-rotation
coupling
spin-rotation
coupling
effective spin-spin coupling
microwave
Adiabatic potentials for two (unpolarized) polar molecules
•
Spin Rotation ( here: /B = 1/10 )
Induced effective interactions:
0g+ :
0g{ :
1g :
1u :
2g :
0u :
2u :

S1/2 + S1/2
+ S1 · S2 { 2 S1c S2c
+ S1 · S2 { 2 S1p S2p
+ S1 · S2 { 2 S1b S2b
{ S1 · S2
+ S1b S2b
0
0
for ebody = ex and epol = ez
0g+ :
0g{ :
1g :
1u :
2g :
+XX{YY+ZZ
+XX+YY{ZZ
{XX+YY+ZZ
{XX{YY{ZZ
+XX
Feature 1. By tuning close to a resonance we can select a specific spin texture
Example: "The Ioffe et al. Model"
•
Model is simple in terms of long-range resonances …
Rem.: for a multifrequency field we
can add the corresponding spin
textures.
Feature 2. We can choose the range of the interaction for a given spin texture
Feature 3. for a multifrequency field spin textures are additive: toolbox
Summary: QIPC & Quantum Optics with Polar Molecules
•
•
•
•
single molecules / molecular ensembles
coupling to optical & microwave fields
– trapping / cooling
– CQED (strong coupling)
– spontaneous emission / engineered dissipation
interfacing solid state / AMO & microwave / optical
– strong coupling / dissipation
collisional interactions
– quantum deg gases / Wigner crystals (ion trap like qc)
– WC / dephasing