AUSTRIAN ACADEMY OF SCIENCES UNIVERSITY OF INNSBRUCK Quantum Computing with Polar Molecules: quantum optics - solid state interfaces SFB Coherent 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–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 atom cavity 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–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=3/2 J=5/2 "S" "D" "S 1/2 " "P 3/2 " "D 5/2 " "D 3/2 " "P 1/2 " H = B N 2 H = B N 2 +  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/R 3 angular dependence strong! (temperature requirements) repulsion attraction

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-type strong 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 ensemble optical 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-scale electrode structure 0.1  m 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. Scholekopf M. Lukin et 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 XXYY ZZ xx zz Duocot, Feigelman, Ioffe et al. Kitaev 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/R 3 repulsion – for R > R 0 ) Coulomb: WC for low density (ions) dipole-dipole: crystal for high density 2D triangular lattice (Abrikosov lattice) mean distance WC Tonks gas / BEC (liquid / gas) ~ 100 nm 1st order phase transition H.P. Büchler V. Steixner G. Pupillo M. Lukin … quantum statistics g(R) R solid liquid

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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 d 1 d 2 /R 3 Applications:

Quantum Optical / Solid State Interfaces

Cooper Pair Box (qubit) as nonlinearity superconducting (1D) microwave transmission line cavity (photon bus) molecular ensemble optical 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 ) 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 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 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 ensemble qubits 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

microwave spin-rotation coupling dipole-dipole: anisotropic + long range effective spin-spin coupling Basic idea of engineering spin-spin interactions

Adiabatic potentials for two (unpolarized) polar molecules Spin Rotation ( here:  /B = 1/10 ) Induced effective interactions: 0 g + :+ S 1 · S 2 { 2 S 1 c S 2 c 0 g { :+ S 1 · S 2 { 2 S 1 p S 2 p 1 g :+ S 1 · S 2 { 2 S 1 b S 2 b 1 u : { S 1 · S 2 2 g :+ S 1 b S 2 b 0 u :0 2 u :0 for e body = e x and e pol = e z 0 g + :+XX {YY+ZZ 0 g { :+XX+YY {ZZ 1 g : {XX+YY+ZZ 1 u : {XX{YY{ZZ 2 g :+XX S 1/2 + S 1/2  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