Interfacing quantum optical and solid state qubits Cambridge, Sept 2004 Lin Tian

1. Innsbruck People : R. Blatt (experiment) P. Rabl L. Tian I. Wilson-Rae Peter Zoller In collaboration with : A. Imamoglu (ETH) I. Martin (LANL) A. Shnirman (Karlsruhe) Interfacing quantum optical and solid state qubits Cambridge, Sept 2004 Lin Tian Universität Innsbruck • Motivation: ion trap quantum computing; • future roads for exploring • Interfacing with solid-state devices: • protocols -- hybrid qubit & quantum trap; • realization -- superconducting qubit • Other approaches -- … • References: • Tian, Rabl, Blatt & Zoller, PRL (’04)

2. Ion Trap -- charged particles in electromagnetic potential • Harmonic confinement, laser manipulation Motional degree Internal degree • Generate various Hamiltonian • e.g J-C type of model • Applications • laser cooling by optical pumping • quantum state engineering • precision measurement • quantum computing • … • D. Leibfried et al, RMP (2003) red side band -- blue side band d0 : detuning h = kD x ~ 0.1, W < wn

3. Ion Trap Quantum Computing • Internal state of trapped ion as qubits • Center of mass motion as media • Swap states of spin and motion Cirac and Zoller (’95). Progress in the past 10 years : experiment: CNOT, teleportation, small algorithm, entanglement, (Innsbruck, NIST, Michigan…) theory: fast gate, quantum phase transition with ions, topological gate, scalability …

4. Scalable Ion Trap Schemes by Moving Ions Segmented trap Moving head -- Cirac, Zoller (00) -- Kielpinski, Monroe, Wineland (02) Scalable ion trap quantum computing without moving ions over long distance?

5. quantum information mesoscopic electronics quantum optical • Progress and problems of quantum optical system in quantum • information processing? • Ion trap experiments • Optical lattices • Atomic and photonic states entanglement • Efficiency and Scalability • Decoherence • Connecting with solid-state systems ?? • Advantages ?? (what do we gain ?) • Difficulties ?? (decoherence, compatibility, coupling, scalability) • Can we integrate the best of both, any limit for improving the experiments?

6. s1 s2 sj sn q1 q2 qj qn kqi qj ion trap quantum computing by connecting with solid-state devices hybrid qubit approach: • Ion trap qubit as storage • Solid-state charge qubit as processor • Capacitive coupling between the two quantum trap approach: • coupling between ion and trap mode • trap mode is quantum • effective interaction between ions • Technical Difficulties: ion trap vs charge qubit • laser of trap affects with charge qubits • ion trap at low temperature, …

7. Realization -- with superconducting devices • Coupling with the motion of trapped ions • Hybrid qubit – superconducting charge qubit, double dot qubit • Quantum trap – EM modes in superconducting cavity • Exchange information between ion qubit and charge qubit • Decoherence • Scalability

8. polarized laser pulse |0i ion interaction with charge : dipole – charge Q -- initial distance ion interaction with ion: dipole -- dipole Spin-dependent interaction induced by laser pulses -- mechanism

9. Hybrid Qubit -- Schematic Circuit of Ion, Cavity,Charge Qubit

10. Josephson junction and gauge invariance phase Charging Energy Josephson Energy Ipc Flux Qubits EJ/Ec>>1 Charge Qubits EJ/Ec<<1 | 0 > | 1> Nakamura…, Nature (1999) Mooij, Orlando…, Science (1999) Superconducting Qubits

11. Cg Cm Vg CJ EJ charge island Superconducting Charge Qubits – Quantum Two Level System EcÀ EJ Makhlin, Schön, Shnirman, RMP (2001) Decoherence time msecs; Rabi Oscillations; Ramsey; two-bit entanglemnet, Nakamura, Devoret, Esteve, Schoekopf, L

12. Inserting the Superconducting Cavity • To increase the coupling by effectively shorten the distance • between the ion and the charge qubit • To improve the compatibility by shunting the qubit from • the stray photons from the trap Cavity Cavity mode for short distance Interaction with Ion, Charge Cm: coupling, Cr: Cavity

13. Q Dipole – charge Enhanced dipole – charge Q Effective Coupling between Ion and Charge Qubit Geometry

14. Realization -- with superconducting devices • Coupling with the motion of trapped ions • Hybrid qubit – superconducting charge qubit, double dot qubit • Quantum trap – EM modes in superconducting cavity • Exchange information between ion qubit and charge qubit • Decoherence • Scalability

15. Fast Gate for Exchange Qubit States 1. Fast phase gate independent of motional state 2. Gate time much shorter than wn-1 T~20 nsec with t1,2=5nsec Pulse sequence at

16. ion trap EJa Lr Fex Vg Cg Cm Cr/2 Cr/2 CJ EJ Superconducting Switch for Coupling • Fex=F0/2, no coupling between ion and charge qubit • Fex < F0/2 e.g., nonzero coupling • 4p cos (pFex/F0)Ica/F0CaÀw02 : coupling the same as previous one • Ref: Tian,Blatt,Zoller, preprint -- • speed limited by speed of switching flux in the SQUID loop • other switches: SSET, p-junction, … • more work needed to better manipulate the coupling Makhlin, Schön, Shnirman, RMP (2001)

17. Vib Vib Vtrap Vtrap Vi Vi Quantum Trap -- Schematic Circuit of Ion Trap, Cavity, Ion Trap Allowing distant ions to communicate … ion trap ion trap superconducting cavity Note earlier work -- Heinzen,Wineland, PRA (1990).

18. Dipole – dipole Enhanced dipole – charge =L Effective Coupling between Ions Increased -- electrodes effectively shortens the distance between ions =L

19. qubit cavity reservoir = Decoherence • Noise on ion: motional state damping; • spontaneous emission… • Noise on charge qubit: charge noise • flux noise… • Noise on cavity: • no dissipation at low temperature well • below the gap; how about under laser • radiation ? • Decoherence of cavity under radiation: • Spin-oscillator-boson bath model • Calderia-Leggett approach: J0 of Rr • induces Jeff on qubit -- Jeff/w Zeff(w) • With nW scattered photons, radiates for • 100 nsec, • This is not dominate effect Grabert et al, Phys. Rep. (’88)

20. coupling laser addressing switch Scalability • small clusters of ions coupling with two charge qubits • individual addressing to select ions of operation • two bit gate via the charge qubits by selecting two ions Ref: Tian,Blatt,Zoller, preprint --

21. connecting circuitry flux flux Scalability • 2. small clusters of ions coupling with two charge qubits • electrodynamic coupling of charge qubits in different cluster • gate between ions in different cluster

22. Other aspects of connecting with solid-state systems • manipulating solid-state systems via coupling with ion --- • ion coupling with charged Carbon nanotube, • 1. quantum state engineering of mechanical motion of the nanotube • 2. preparing pure state of nanotube mode by laser cooling • 3. entanglement between two nanotubes via laser manipulation of ion: • arbitrary states y and c -- |y1,c2i +|c1,y2i Ref: L. Tian and P. Zoller, quantum-ph/0407020

23. Cooper pair box beam Gr/4 l/4 Gr/4 Gr/2 Other aspects of connecting with solid-state systems • manipulating solid-state systems with ideas in quantum optics --- • “laser cooling” of nanomechanical resonator • 1. Capacitive coupling between charge qubit and resonator • 2. Cooling of resonator to ground state via pumping of charge qubit I. Martin,Shnirman,Tian,Zoller,PRB(04)

24. Summary We studied the interfacing of the ion trap qubit with solid-state systems: 1. a hybrid qubit can be made of a trapped ion coupling with charge qubit via electrostatic interaction; 2. distant ions can couple via the quantum modes of the electrode; 3. decoherence and scalability are studied; 4. interfacing can provide manipulation of solid-state systems: mechanical modes of nanotubes, resonators