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

1. 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) AUSTRIAN ACADEMY OF SCIENCES SFBCoherent Control of Quantum Systems €U networks Harvard / Yale collaborations:Misha Lukin (Harvard) John Doyle (Harvard)Rob Schoellkopf (Yale)Andre Axel (Yale) David DeMille (Yale)

2. F– 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 • Interface AMO – CMP • example: electric dipole moments molecular ensembles / single molecules superconducting circuits • compatible setups & parameters • strength / weakness complement each other

3. trapped ions / crystals of … CQED Polar Molecules Quantum Optics with Atoms & Ions • cold atoms in optical lattices laser rotation dipole moment • 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 cavity atom laser • atomic ensembles

4. Polar molecules • basic properties

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

6. rigid rotor adding spin-rotation coupling (S=1/2) 1b. Identifying Qubits H = B N2 H = B N2 + N·S "D5/2" "D" J=5/2 N=2 "D3/2" J=3/2 N=2 "P" "P3/2" N=1 J=3/2 N=1 "P1/2" J=1/2 spin-rotation splitting "S" "S1/2" N=0 N=0 J=1/2 charge qubit spin qubit(decoherence) • How to encode qubits? ``looks like an Alkali atom on GHz scale´´(we adopt this below as our model molecule)

7. 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 attraction

8. What can we do with Polar Molecules? • a few examples & ideas

9. 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-typestrong coupling CQED Cooper Pair Box (qubit)

10. molecular ensemble optical cavity laser polar molecular ensemble 1:quantum memory(qubit or continuous variable)[Rem.: cooling / trapping] polar molecular ensemble 2:quantum memory(qubit or continuous variable) P. Rabl, R. Schoelkopf, D. DeMille, M. Lukin … 1. Hybrid Device: solid state processor & molecular memory + optical interface optical (flying) qubit superconducting (1D) microwave transmission line cavity(photon bus) strong coupling CQED Cooper Pair Box (qubit) as nonlinearity

11. 0.1mm Andre Axel, R. ScholekopfM. Lukin et al. 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 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 micron-scale electrode structure @ h~0.1 and nt> 10 MHz shifts levels by less than 1%

12. |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

13. A. Micheli, G. Brennen, PZ, preprint Dec 2005 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 Examples: Kitaev Duocot, Feigelman, Ioffe et al. xx zz ZZ XX YY protected quantum memory:degenerate ground states as qubits

14. H.P. BüchlerV. SteixnerG. PupilloM. Lukin… 3. (Wigner-) Crystals with Polar Molecules • “Wigner crystals“ in 1D and 2D (1/R3 repulsion – for R > R0) dipole-dipole: crystal for high density Coulomb: WC for low density (ions) 2D triangular lattice(Abrikosov lattice) 1st order phase transition g(R) solid liquid Tonks gas / BEC (liquid / gas) WC mean distance R quantum statistics ~ 100 nm

15. Applications: compare: ionic Coulomb crystal • 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] d1 d2 /R3 ion trap like qc, however: • d variable • spin dependent d • qu melting / quantum statistics x phonons (breathing mode indep of # molecules)

16. Quantum Optical / Solid State Interfaces

17. molecular ensemble optical cavity laser polar molecular ensemble 1:quantum memory(qubit or continuous variable)[Rem.: cooling / trapping] polar molecular ensemble 2:quantum memory(qubit or continuous variable) with P. Rabl, R. Schoelkopf, D. DeMille, M. Lukin Hybrid Device: solid state processor & molecular memory + optical interface optical (flying) qubit superconducting (1D) microwave transmission line cavity(photon bus) strong coupling CQED Cooper Pair Box (qubit) as nonlinearity

18. R. Schoelkopf, M. Devoret, S. Girvin (Yale) 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] SC qubit Jaynes-Cummings good cavity strong coupling!(mode volume V/ 3¼ 10-5 ) “not so great” qubits

19. hyperfine structure » 10 GHz … with Yale/Harvard 2. ... coupling atoms or molecules • hyperfine excitation of BEC / atomic ensemble • superconducting transmission line cavities atoms /molecules SC qubit • rotational excitation of polar molecule(s) • 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… N=1 rotational excitations » 10 GHz N=0 ensemble 

20. 3. Atomic / molecular ensembles:collective excitations as Qubits • ground state • one excitation (Fock state) • two excitations ... eliminate? • in AMO: dipole blockade, measurements ... microwave microwave harmonic oscillator nonlinearity due to Cooper Pair Box. etc. • also: ensembles as continuous variable quantum memory (Polzik, ...) • collisional dephasing (?)

21. 4. Hybrid Device: solid state processor & molec memory molecules:qubit 1 SC qubit time independent molecules:qubit 2 solid state system ensemblequbits swap molecule - cavity + dissipation (master equation)

22. 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

23. Spin Models with Optical Lattices A. Micheli, G. Brennen & PZ, preprint Dec 2005 • 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

24. Duocot, Feigelman, Ioffe et al. Kitaev

25. Basic idea of engineeringspin-spin interactions dipole-dipole: anisotropic + long range spin-rotationcoupling spin-rotationcoupling microwave microwave effective spin-spin coupling

26. Spin Rotation Adiabatic potentials for two (unpolarized) polar molecules ( here: /B = 1/10 ) Induced effective interactions: 0g+ : + S1·S2{ 2 S1c S2c 0g{ : + S1·S2{ 2 S1p S2p 1g : + S1·S2{ 2 S1b S2b 1u : {S1·S2 2g : + S1b S2b 0u : 0 2u : 0 for ebody = ex and epol = ez 0g+ : +XX{YY+ZZ 0g{ : +XX+YY{ZZ 1g : {XX+YY+ZZ 1u : {XX{YY{ZZ 2g : +XX  S1/2 + S1/2 Feature 1. By tuning close to a resonance we can select a specific spin texture

27. 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

28. 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