AUSTRIANACADEMY OF

SCIENCES

UNIVERSITY OF INNSBRUCK

Quantum Computing with Polar Molecules: quantum optics - solid state interfaces

SFBCoherent Control of Quantum Systems

€U networks

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)

Cold polar molecules

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

• Interface AMO – CMP

– example:

F–

exp: DeMille, Doyle, Mejer, Rempe, Ye, …

molecular ensembles / single molecules

superconducting circuits

compatible setups & parameters

strength / weakness complement each other

electric dipole moments

Quantum Optics with Atoms & Ions

• trapped ions / crystals of …

• CQED

atomcavity

laser

• cold atoms in optical lattices

laser

• atomic ensembles

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– dephasing

dipole moment

rotation

Polar molecules

• basic properties

1a. Single Polar Molecule: rigid rotor

• single heteronuclear molecule

dipole d~10 Debye

rotation B~10 GHz (anharmonic )

(essentially) no spontaneous emission (i.e. excited states useable)

N=0

N=1

N=2

"S"

"P"

"D"

F–

…

d

rigid rotor

d

• Strong coupling to microwave fields / cavities; in particular also strip line cavities

"P"

1b. Identifying Qubits

• rigid rotor • adding spin-rotation coupling (S=1/2)

N=0

N=1

N=2

N=0

N=1

N=2

J=1/2

J=1/2

J=3/2

J=3/2

J=5/2

"S"

"D"

"S1/2"

"P3/2"

"D5/2"

"D3/2"

"P1/2"

H = B N2 H = B N2 + N·S

• How to encode qubits? ``looks like an Alkali atom on GHz scale´´(we adopt this below as our model molecule)

spin qubit(decoherence)

charge qubit

spin-rotation splitting

2. Two Polar Molecules: dipole – dipole interaction

• interaction of two molecules

features of dipole-dipole interaction

long range ~1/R3

angular dependence

strong! (temperature requirements)

repulsion

attractionVdd d1d2 3 d1eb ebd2

R3

What can we do with Polar Molecules?

• a few examples & ideas

Cooper Pair Box (qubit)

superconducting (1D) microwave transmission line

cavity(photon bus)

1. Hybrid Device: solid state processor & molecular memory + optical interface

Yale-typestrong coupling CQED

R. Schoelkopf, S. Girvin et al.

see talk by A. Blais on Tuesday

Cooper Pair Box (qubit)

as nonlinearity

superconducting (1D) microwave transmission line

cavity(photon bus)

molecular ensembleoptical

cavity

laser

optical (flying) qubit

1. Hybrid Device: solid state processor & molecular memory + optical interface

polar molecular ensemble 1:quantum memory

(qubit or continuous variable)[Rem.: cooling / trapping]

polar molecular ensemble 2:quantum memory

(qubit or continuous variable)

strong coupling CQED

P. Rabl, R. Schoelkopf, D. DeMille, M. Lukin …

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

• 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 (?)– Interaction with surface

e.g. van der Waals interaction

micron-scaleelectrode structure

0.1m

Electrostatic Z trap (EZ trap)

• DC voltage: same trap potential for N=1,2 states at ~10 kV/cm• AC voltages: same trap potential for

N=0,1 states at “magic” detuning

Andre Axel, R. ScholekopfM. Lukin et al.

@ h~0.1 and t> 10 MHz shifts levels by less than 1%

|2>

|1>

Sideband cooling with stripline resonator (“g cooling”)

• “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

engineered dissipation + analogy to laser cooling

2. Realization of Lattice Spin Models

• polar molecules on optical lattices provide a complete toolbox to realize general lattice spin models in a natural way

• Motivation: virtual quantum materials towards topological quantum computing

XX YY

ZZ

xx

zz

Duocot, Feigelman, Ioffe et al. Kitaev

HspinI

i 1 1

j 1 1 J i,jz i,j 1

z cos i,jx i 1,jx Hspin

II J x links

jx kx J y links

jy ky

Jz z links

jz kz

#

# protected quantum memory:

degenerate ground states as qubits

A. Micheli, G. Brennen, PZ, preprint Dec 2005

Examples:

3. (Wigner-) Crystals with Polar Molecules

• “Wigner crystals“ in 1D and 2D (1/R3 repulsion – for R > R0)

Coulomb: WC for low density (ions)

dipole-dipole: crystal for high density

2D triangular lattice(Abrikosov lattice)

mean distance

WCTonks gas / BEC

(liquid / gas)

~ 100 nm

e2/R

2/2MR2~R

1st order phase transition

H.P. BüchlerV. SteixnerG. PupilloM. Lukin…

quantum statistics

g(R)

R

solid

liquid

potential energy

kinetic energy d2/R3

2/2MR2~ 1R

n1/3

• Ion trap like quantum computing with phonons as a bus.

• Exchange gates based on „quantum melting“ of crystal– Lindemann criterion x ~ 0.1 mean distance– [Note: no melting in ion trap]

• Ensemble memory: dephasing / avoiding collision dephasing in a 1D and 2D WC– ensemble qubit in 2D configuration– [there is an instability: qubit -> spin waves]

x

phonons

(breathing mode indep of # molecules)

ion trap like qc, however:

d variable

spin dependent d

qu melting / quantum statistics

compare: ionic Coulomb crystal

d1 d2 /R3

Applications:

Quantum Optical / Solid State Interfaces

Cooper Pair Box (qubit)

as nonlinearity

superconducting (1D) microwave transmission line

cavity(photon bus)

molecular ensembleoptical

cavity

laser

optical (flying) qubit

Hybrid Device: solid state processor & molecular memory + optical interface

polar molecular ensemble 1:quantum memory

(qubit or continuous variable)[Rem.: cooling / trapping]

polar molecular ensemble 2:quantum memory

(qubit or continuous variable)

strong coupling CQED

with P. Rabl, R. Schoelkopf, D. DeMille, M. Lukin

1. strong CQED with superconducting circuits

• Cavity QED

• [... similar results expected for coupling to quantum dots (Delft)]

• [compare with CQED with atoms in optical and microwave regime]

R. Schoelkopf, M. Devoret, S. Girvin (Yale)

SC qubit

strong coupling!(mode volume V/ 3 ¼ 10-5 )

good cavity

“not so great” qubits

Jaynes-Cummings

• rotational excitation of polar molecule(s)

• superconducting transmission line cavities

• hyperfine excitation of BEC / atomic ensemble

atoms /molecules

SC qubit

hyperfine structure

» 10 GHz

rotational excitations

» 10 GHz

N=1

N=0

… with Yale/Harvard

ensemble

2. ... coupling atoms or molecules

• 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…

3. Atomic / molecular ensembles:collective excitations as Qubits

• ground state

• one excitation (Fock state)

• two excitations ... eliminate?– in AMO: dipole blockade, measurements ...

etc.

microwave

|g|q

|r

microwave

nonlinearity due to Cooper Pair Box.

harmonic oscillator

• also: ensembles as continuous variable quantum memory (Polzik, ...)

• collisional dephasing (?)

molecules:qubit 1

SC qubit

molecules:qubit 2

solid state system swap molecule - cavity

ensemblequbits

4. Hybrid Device: solid state processor & molec memory

time independent

+ dissipation (master equation)

5. Examples of Quantum Info Protocols

• SWAP

• Single qubit rotations via SC qubit

• Universal 2-Qubit Gates via SC qubit

• measurement via ensemble / optical readout or SC qubit / SET

Cooper Pair

cavity (bus)

molec ensemble

Atomic ensembles complemented by deterministic entanglement operations

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

A. Micheli, G. Brennen & PZ, preprint Dec 2005

Duocot, Feigelman, Ioffe et al. Kitaev

HspinI

i 1 1

j 1 1 J i,jz i,j 1

z cos i,jx i 1,jx Hspin

II J x links

jx kx J y links

jy ky

Jz z links

jz kz

#

#

microwave microwavespin-rotation

couplingspin-rotation

coupling

dipole-dipole: anisotropic + long range

effective spin-spin coupling

Basic idea of engineeringspin-spin interactions

Adiabatic potentials for two (unpolarized) polar molecules

• Spin Rotation ( here: /B = 1/10 )

Induced effective interactions:

0g+ : + S1 · S2 { 2 S1

c S2c

0g{ : + S1 · S2 { 2 S1

p S2p

1g : + S1 · S2 { 2 S1b S2

b 1u : { S1 · S2

2g : + S1b S2

b

0u : 02u : 0

for ebody = ex and epol = ez

0g+ : +XX{YY+ZZ

0g{ : +XX+YY{ZZ

1g : {XX+YY+ZZ1u : {XX{YY{ZZ2g : +XX

S1/2 + S1/2

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 …

Feature 2. We can choose the range of the interaction for a given spin texture

Rem.: for a multifrequency field we can add the corresponding spin textures.

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