1. 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) 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)

2. Ion Trap -- charged particles in electromagnetic potential Harmonic confinement, laser manipulation red side band -- blue side band  0 : detuning  = k  x   <  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) Motional degree Internal degree

3. Ion Trap Quantum Computing Cirac and Zoller (’95). Internal state of trapped ion as qubits Center of mass motion as media Swap states of spin and motion 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 -- Kielpinski, Monroe, Wineland (02) Segmented trap Moving head -- Cirac, Zoller (00) Scalable ion trap quantum computing without moving ions over long distance?

5. 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? quantum information mesoscopic electronics quantum optical

6. 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 snsn sjsj s2s2 s1s1 qnqn qjqj q2q2 q1q1  q i q j Technical Difficulties: ion trap vs charge qubit laser of trap affects with charge qubits ion trap at low temperature, … quantum trap approach:  coupling between ion and trap mode  trap mode is quantum  effective interaction between ions

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

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

10. Superconducting Qubits Charging EnergyJosephson Energy Charge Qubits E J /E c <<1 Nakamura…, Nature (1999) Flux Qubits E J /E c >>1 Mooij, Orlando…, Science (1999) I pc | 0 >| 1> Josephson junction and gauge invariance phase

11. Makhlin, Schön, Shnirman, RMP (2001) VgVg C J E J CgCg CmCm charge island E c À E J Decoherence time  secs; Rabi Oscillations; Ramsey; two-bit entanglemnet, Nakamura, Devoret, Esteve, Schoekopf,  Superconducting Charge Qubits – Quantum Two Level System

12. Inserting the Superconducting Cavity 1.To increase the coupling by effectively shorten the distance between the ion and the charge qubit 2.To improve the compatibility by shunting the qubit from the stray photons from the trap Interaction with Ion, Charge Cavity Cavity mode for short distance C m : coupling, C r : Cavity

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

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  -1 T~20 nsec with t 1,2 =5nsec Pulse sequence at

16. Superconducting Switch for Coupling C r /2 LrLr VgVg CmCm C J E J CgCg E Ja  ex C r /2 ion trap  ex =  0 /2, no coupling between ion and charge qubit  ex <  0 /2 e.g., nonzero coupling 4  cos (  ex /  0 )I ca /  0 C a À  0 2 :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,  -junction, … more work needed to better manipulate the coupling Makhlin, Schön, Shnirman, RMP (2001)

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

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

19. Decoherence Decoherence of cavity under radiation: Spin-oscillator-boson bath model Calderia-Leggett approach: J 0 of R r induces J eff on qubit -- J eff /  Z eff (  ) With nW scattered photons, radiates for 100 nsec, This is not dominate effect = Grabert et al, Phys. Rep. (’88) 1.Noise on ion: motional state damping; spontaneous emission… 2.Noise on charge qubit: charge noise flux noise… 3.Noise on cavity: no dissipation at low temperature well below the gap; how about under laser radiation ? qubitcavityreservoir

20. Scalability 1.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 -- switch coupling laser addressing

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

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  and  -- |  1,  2 i +|  1,  2 i Ref: L. Tian and P. Zoller, quantum-ph/0407020

23. 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 Other aspects of connecting with solid-state systems beam Cooper pair box I. Martin,Shnirman,Tian,Zoller,PRB(04)  r /4 44  r /2  r /4

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