Quantum Computing with Polar Molecules quantum optics solid

Quantum Computing with Polar Molecules: quantum optics - solid state interfaces UNIVERSITY OF INNSBRUCK Peter Zoller A. Micheli (Ph. D student) P. Rabl (Ph. D student) H. P. Buechler (postdoc) G. Brennen (postdoc) Harvard / Yale collaborations: Misha Lukin (Harvard) John Doyle (Harvard) Rob Schoellkopf (Yale) Andre Axel (Yale) David De. Mille (Yale) AUSTRIAN ACADEMY OF SCIENCES SFB Coherent Control of Quantum Systems €U networks

Cold polar molecules exp: De. Mille, Doyle, Mejer, Rempe, Ye, … What‘s next in AMO physics? • Cold polar molecules in electronic & vibrational ground states – control & very little decoherence – F 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 ü compatible setups & parameters ü 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

1 a. Single Polar Molecule: rigid rotor • single heteronuclear molecule – … N=2 "D" N=1 "P" N=0 "S" rigid rotor • F d d üdipole d~10 Debye ürotation B~10 GHz (anharmonic ) ü(essentially) no spontaneous emission (i. e. excited states useable) Strong coupling to microwave fields / cavities; in particular also strip line cavities

1 b. Identifying Qubits • • rigid rotor adding spin-rotation coupling (S=1/2) H = B N 2 + N·S H = B N 2 "D 5/2" "D" J=5/2 N=2 "D 3/2" N=2 "P" N=1 "P 1/2" "S" charge qubit • "P 3/2" N=1 N=0 How to encode qubits? J=3/2 N=0 J=3/2 J=1/2 "S 1/2" 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 ü long range ~1/R 3 ü angular dependence repulsion attraction ü 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 (1 D) microwave transmission line cavity (photon bus) Yale-type strong coupling CQED Cooper Pair Box (qubit)

P. Rabl, R. Schoelkopf, D. De. Mille, M. Lukin … 1. Hybrid Device: solid state processor & molecular memory + optical interface optical cavity molecular ensemble optical (flying) qubit laser superconducting (1 D) 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 k. V/cm 0. 1 mm • • • 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”) • “ 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 |2> |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 protected quantum memory: degenerate ground states as qubits • Motivation: virtual quantum materials towards topological quantum computing

3. (Wigner-) Crystals with Polar Molecules • “Wigner crystals“ in 1 D and 2 D (1/R 3 repulsion – for R > R 0) H. P. Büchler V. Steixner G. Pupillo M. Lukin … dipole-dipole: crystal for high density Coulomb: WC for low density (ions) 2 D triangular lattice (Abrikosov lattice) g(R) 1 st 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. d 1 d 2 /R 3 ion trap like qc, however: x phonons • • ü d variable ü spin dependent d ü 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 1 D and 2 D WC – ensemble qubit in 2 D configuration – [there is an instability: qubit -> spin waves]

Quantum Optical / Solid State Interfaces

with P. Rabl, R. Schoelkopf, D. De. Mille, M. Lukin Hybrid Device: solid state processor & molecular memory + optical interface optical cavity molecular ensemble optical (flying) qubit laser superconducting (1 D) 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

3. Atomic / molecular ensembles: collective excitations as Qubits • 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. Kitaev

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

Adiabatic potentials for two (unpolarized) polar molecules • Spin Rotation ( here: /B = 1/10 ) Induced effective interactions: 0 g+ : 0 g{ : 1 g : 1 u : 2 g : 0 u : 2 u : S 1/2 + S 1 · S 2 { 2 S 1 c S 2 c + S 1 · S 2 { 2 S 1 p S 2 p + S 1 · S 2 { 2 S 1 b S 2 b { S 1 · S 2 + S 1 b S 2 b 0 0 for ebody = ex and epol = ez 0 g+ : 0 g{ : 1 g : 1 u : 2 g : +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 • •