Circuit QED: Atoms and Cavities in Superconducting Microwave Circuits

1. Circuit QED: Atoms and Cavities in Superconducting Microwave Circuits Depts. of Applied Physics & Physics Yale University expt. Andreas Wallraff David Schuster Luigi Frunzio Andrew Houck Joe Schreier Hannes Majer Blake Johnson PI’s Rob Schoelkopf Steve Girvin Michel Devoret theory Alexandre Blais Jay Gambetta www.eng.yale.edu/rslab

2. Overview • Quantum optics and Cavity QED • Circuit QED: • - One-d microwave cavities and coupling to JJ qubits • Experiments showing strong coupling – splitting the photon • The beauty of being off-resonant: • - lifetime enhancement/suppression by cavity • The AC Stark shift & backaction of QND measurement – towards splitting the “atom” to see single photons • The future?: • - “bus” coupling of qubits • - other possible (microscopic?) circuit elements

3. Cavity Quantum Electrodynamics (cQED) 2g= vacuum Rabi freq. k= cavity decay rate g= “transverse” decay rate t = transit time Strong Coupling = g> k , g , 1/t Jaynes-Cummings Hamiltonian Electric dipole Interaction Quantized Field 2-level system

4. Cavity QED: Resonant Case vacuumRabioscillations # ofphotons qubit state “dressed state ladders” (e.g. Haroche et al., Les Houches notes)

5. Microwave cQED with Rydberg Atoms vacuum Rabi oscillations beam of atoms;prepare in |e> Pexcited time 3-d super-conductingcavity (50 GHz) observe dependence of atom finalstate on time spent in cavity measure atomic state, or … Review: S. Haroche et al., Rev. Mod. Phys.73 565 (2001)

6. Optical Cavity QED … measure changes in transmission of optical cavity e.g. Kimble and Mabuchi groups at Caltech

7. 2004: Year of Strong Coupling Cavity QED alkali atoms Rydberg atoms single trapped atom PRL 93, 233603(Dec. 2004) superconductor flux and charge qubits Nature (London) 431, 159 & 162(Sept. 2004) semiconductor quantum dots Nature (London) 432, 197 & 200(Nov. 2004)

8. A Circuit Implementation of Cavity QED 2g = vacuum Rabi freq. k= cavity decay rate g= “transverse” decay rate out L = l ~ 2.5 cm transmissionline “cavity” Cooper-pair box “atom” 10 mm 10 GHz in Theory: Blais et al., Phys. Rev. A69, 062320 (2004)

9. Advantages of 1d Cavity and Artificial Atom Vacuum fields:zero-point energy confined in < 10-6 cubic wavelengths Transition dipole: x 10 larger than Rydberg atom E ~ 0.2 V/m vs. ~ 1 mV/m for 3-d L = l ~ 2.5 cm Cross-sectionof mode (TEM!): B E - - + + 10 mm 10 mm

10. Implementation of Cavity on a Chip Superconducting transmission line 2 cm Si Niobium films gap = mirror 6 GHz: even when RMS voltage:

11. Qubits: Why Superconductivity? N ~ 109 total number of electrons E few electrons “forest” of states ~ 1eV superconducting gap 2D ~ 1meV SUPERCONDUCTING NANOELECTRODE ATOM

12. The Single Cooper-pair Box: an Tunable Artificial Atom “Stark shift” V “Zeeman shift” I 2D (~ 1meV) EC tunnel junctions (1 nm) N+1 EJ N

13. The Real Artificial Atom Nb Bias Gate Si Al Island containing108 or 108 +1pairs Nb Note scale Pseudo spin ½: Coulomb Energy Josephson tunneling

14. Coupling to Cavity Photons Jaynes-Cummings A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, PRA 69,062320 (2004)

15. How Big Can a Dipole Coupling Get, Anyway? for a half-wave resonator: the fine structure constantin circuit form! or g ~ 200 MHz on a 5 GHz transition “The Fine StructureLimit on Coupling”

16. Comparison of cQED with Atoms and Circuits

17. The Chip for Circuit QED Nb Si No wiresattached to qubit! Al Nb

18. Microwave Setup for cQED Experiment Transmit-side Receive-side

19. Measuring the Cavity Use microwave powers ~ 1 photon = 10-17 watts

20. Bare Resonator Transmission Spectrum

21. First Observation of Vacuum Rabi Splitting for a Single Real Atom Cs atom in an optical cavity Transmission Thompson, Rempe, & Kimble 1992

22. Bare Resonator Transmission Spectrum Qubit strongly detuned from cavity tune into resonance with cavity and repeat

23. 2g Vacuum Rabi Mode Splitting by an Artificial Atom Critical atom (N0)& photon #: (M0) Our Records So Far:

24. Spontaneous Emission into Continuum? Cg Box Power lost in resistor: Decay rate: “Atom” quality factor:

25. Spontaneous Emission into Resonator? Cg Box On resonance: Decay rate: the Purcell factorin circuit guise! “Atom” quality factor:

26. Spontaneous Emission into Resonator? Cg Box Off resonance: Dispersive limit: Decay rate: “Atom” quality factor: cavity enhancementof lifetime!

27. Off-Resonant Case: Lifetime Enhancement { “photonic part”of atom See e.g. Haroche, Les Houches 1990 Really, a way to measure non-EM part of g

28. Non-Radiative Decays of Qubit? Predicted cavity-enhancedlifetime ~ 0.001 s! Mechanism of non-radiative losses? Observed lifetimes ~ 1 -10 ms

29. dielectric changes “length” of cavity How to Measure without Dissipation? Transmission Frequency A dispersive measurement – measures susceptibility, not loss “leave no energy behind”! (c.f. “JBA amplifier,” measures mag. suscept., by Devoret et al.)

30. Dispersive Circuit QED Dispersive regime: Small “mixing” of qubit and photon, but still smallfrequency shift of cavity!

31. Dispersive QND Qubit Measurement reverse of Nogues et al., 1999 (Ecole Normale) QND of photon using atoms! A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and RS, PRA 69,062320 (2004)

32. Controlling the Qubit in the Cavity wqubit Operate at gate-insensitive“sweet spot” for long coherence - A “clock” transition for SC qubits! (after Vion et al. 2002) • Large detuning of qubit frequency from cavity • Add second microwave pulse to excite qubit

33. “Unitary” Rabi Oscillations A. Wallraff et al., PRL 95, 060501 (2005)

34. On QND Measurements is a constant of motion,measure w/out changing it a superposition is dephased Phase shift of photons transmitted measures qubit state Photons in cavity dephase qubit

35. Probe Beam at Cavity Frequency Induces ac Stark Shift of Atom Frequency Lamb shift cavity freq. shift atom ac Stark shift vacuum ac Stark shift

36. cQED Measurement and Backaction - Predictions phase shift on transmission: measurement rate: (expt. still ~ 40times worse) dephasing rate: quantumlimit?: 2x limit, since half of information wasted in reflected beam

37. AC-Stark Effect & Photon Shot Noise • g = 5.8 MHz • g2/D=0.6 MHz • shift measures n D. I. Schuster, A. Wallraff, A. Blais, …, S. Girvin, and R. J. Schoelkopf, cond-mat/0408367 (2004)

38. Explanation of Dephasing • Measurement dephasing from Stark random shifts • Gaussian lineshape is sum of Lorentzians • Coherent state has shot noise • Peaks are Poisson distributed Qubit Response Frequency,ns What if 2g2/D > g ?

39. Possibility of Observing Number States of Cavity? Simulation theoretical predictions: J. Gambetta, A. Blais, D. Schuster, A. Wallraff, L. Frunzio, J. Majer, S.M. Girvin, and R.J. Schoelkopf, cond-mat/0602322 g2/D • k = 100 kHz • g2/D = 5 MHz • n = 1 g g2/D >>g see expt. results reported later this week: D. Schuster G3.00003 Tues 9:12 AM

40. Future Prospects/Directions cavity QED = testbed system for quantum optics • nonlinear quantum optics - single atom/photon bistability • - squeezing • quantum measurements • cavity enhancement of qubit lifetime? - measuring internal dissipation of qubits • quantum bus for entanglement (cQED = “circuit quantum electrodynamics”)

41. Coupling Two Qubits via a Photon “long” range and non nearest-neighborinteractions! 2 cm ala’ Cirac-Zollerion trap gates Address with frequency-selective RF coupling pulses

42. Two Qubits in One Cavity

43. First Two Qubit Cavity Measurements Flux Gate voltage

44. Strong Cavity QED with Polar Molecules? Dispersivequbitinteraction

45. The Yale Circuit QED Team Alexandre Blais (-> Sherbrooke) Steve Girvin Andreas Wallraff(-> ETH Zurich) Dave Schuster

46. Summary • “Circuit QED”: 1-d resonators + JJ atoms for strong coupling cQEC in the microwave circuit domain • First msmt. of vacuum Rabi splitting for a solid-state qubit • Dispersive QND measurements and backaction no dissipation - don’t heat the dirt! • Control of qubit in cavity: long coherence time and high fidelity • Numerous advantages for quantum control and measurement Theory:Blais et al., Phys. Rev. A69, 062320 (2004) Vac Rabi: Wallraff et al., Nature431, 132 (2004) AC Stark: Schuster et al., PRL 94, 123602 (2005)Qubit Control:Wallraff et al., PRL 95, 060501 (2005)

47. Circuit QED Publications see: www.eng.yale.edu/rslab High visibility Rabi oscillations & coherence time measurements: A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, J. Majer, S. M. Girvin, and R. J. Schoelkopf, Phys. Rev. Lett.95, 060501 (2005) Circuit QED device fabrication: L. Frunzio, A. Wallraff, D. I. Schuster, J. Majer, and R. J. Schoelkopf, IEEE Trans. on Appl. Supercond.15, 860 (2005) AC Stark shift & measurement induced dephasing: D. I. Schuster, A. Wallraff, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Girvin, and R. J. Schoelkopf, Phys. Rev. Lett. 94,123062(2005) Strong coupling & vacuum Rabi mode splitting: A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. Girvin, and R. J. Schoelkopf, Nature (London) 431, 162(2004) Circuit QED proposal: A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, PRA 69,062320 (2004)