Rob Schoelkopf , Applied Physics, Yale University

1. Quantum Optics in Circuit QED: From Single Photons to Schrodinger Cats…. Rob Schoelkopf, Applied Physics, Yale University PI’s: RS Michel Devoret Luigi Frunzio Steven Girvin Leonid Glazman Postdocs & grad students wanted!

2. Thanks to cQED Team Thru the Years! Steve Girvin, Michel Devoret, Luigi Frunzio, Leonid Glazman Theory Experiment (present) • AlexandreBlais • Lev Bishop • Jay Gambetta • Jens Koch • EranGinossar • Nunnenkamp • G. Catelani • Lars Tornberg • Terri Yu • Simon Nigg • Dong Zhou • MazyarMirrahimi • ZakiLeghtas Experiment (past) Hanhee Paik Luyan Sun Gerhard Kirchmair Matt Reed Adam Sears Brian Vlastakis Eric Holland Matt Reagor Andy Fragner Andrei Petrenko Jacob Blumhoff Teresa Brecht Andreas Wallraff Dave Schuster Andrew Houck Leo DiCarlo Johannes Majer Blake Johnson Jerry Chow Joe Schreier

3. Outline Cavity QED vs. Circuit QED How coherent is a Josephson junction? Scaling the 3D architecture A bit of nonlinear quantum optics Deterministic Schrödinger cat creation

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

5. 2012: Year of Quantum Measurement "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems" Serge Haroche (ENS/Paris) Dave Wineland (NIST-Boulder) Quantum jumps w/ trapped ions Cavity QED w/ Rydberg atoms

6. Qubits Coupled with a Quantum Bus use microwave photons guided on wires! “Circuit QED” transmissionline “cavity” out Josephson-junctionqubits 7 GHz in Thy:Blaiset al., Phys. Rev. A (2004)

7. Superconducting Qubits Transmon Superconductor Lj Insulating barrier 1 nm Cj C Energy Superconductor (Al) nonlinearity from Josephson junction (dissipationless) electromagnetic oscillator • Engineerablespectrum • Lithographically produced features • Each qubit is an “individual” • Decoherence mechanisms? See reviews: Devoret and Martinis, 2004; Wilhelm and Clarke, 2008

8. Advantages of 1d Cavity and Artificial Atom Vacuum fields: mode volume zero-point energy density enhanced by Transition dipole: x 10 larger than Rydberg atom L = l ~ 2.5 cm Supports a TEM mode like a coax: coaxial cable 5 mm

9. Advantages of 1d Cavity and Artificial Atom Vacuum fields: mode volume zero-point energy density enhanced by Transition dipole: x 10 larger than Rydberg atom compare Rydberg atom or optical cQED: Circuit QED much easier to reach strong interaction regimes!

10. The Chip for Circuit QED Nb Qubittrappingeasy: it’s“soldered”down! Si Al Nb Expt:Wallraff et al., Nature (2004)

11. Cavity QED: Resonant Case vacuumRabioscillations # ofphotons “phobit” qubit state “quton” “dressed state ladders” (see e.g. “Exploring the Quantum…,” S. Haroche & J.-M. Raimond)

12. Strong Resonant Coupling: Vacuum Rabi Splitting g >> [k, g] 2g ~ 350 MHz Can achieve “Fine-Structure Limit” Cooperativity: 6.75 6.85 6.95 7.05 Review: RS and S.M. Girvin, Nature451, 664 (2008). Nonlinear behavior: Bishop et al., Nature Physics (2009).

13. But does it “compute”? Algorithms: DiCarlo et al., Nature460, 240 (2009).

14. A Two-Qubit Processor 1 ns resolution DC - 2 GHz T = 10 mK cavity: “entanglement bus,” driver, & detector transmon qubits

15. General Features of a Quantum Algorithm Qubit register M Working qubits measure encode function in a unitary process create superposition initialize will involve entanglement between qubits Maintain quantum coherence 1) Start in superposition: all values at once! 2) Build complex transformation out of one-qubit and two-qubit “gates” 3) Somehow* make the answer we want result in a definite state at end! *use interference: the magic of the properly designed algorithm

16. Grover Algorithm Step-by-Step The correct answer is found >80% of the time! Coherence time ~ 1 ms Total pulse sequence:104 nanoseconds Previously implemented in NMR: Chuang et al., 1998 Ion traps: Brickman et al., 2003 Linear optics: Kwiat et al., 2000

17. Will it ever scale? or, “Come on, how coherent could this squalid-state thing ever really get?” (H. Paik et al., PRL, 2011)

18. Schoelkopf’s Law:Coherence increases 10x every 3 years! Progress in Superconducting Charge Qubits Similar plots can probably be made for phase, flux qubits

19. Materials: Dirt Happens! Dolan Bridge Technique PMMA/MAA bilayer Al/AlOx/Al Qubit: two 200 x 300 nm junctions Rn~ 3.5 kOhms Ic ~ 40 nA Current Density ~ 30- 40 A/cm2

20. E d - - + + a-Al2O3 Why Surfaces Matter… Nb 5 mm “participation ratio” = fraction of energy stored in material even a thin (few nanometer) surface layer will store ~ 1/1000 of the energy If surface loss tangent is poor ( tand ~ 10-2) would limit Q ~ 105 Increase spacings decreases energy on surfaces increases Q as shown in: Gao et al. 2008 (Caltech) O’Connell et al. 2008 (UCSB) Wang et al. 2009 (UCSB)

21. One Way to Be Insensitive to Surfaces… 3-D waveguide cavitymachined from aluminum(6061-T6, Tc ~ 1.2 K) TE101 fundamental mode 50 mm Increased mode volumedecreases surface effects! Observed Q’s to 5 M

22. TransmonQubit in 3D Cavity Vacuum capacitor ~ mm g 100 MHz 50 mm Smaller fields compensated by larger dipole Still has same net coupling!

23. Coherence Dramatically Improved T1 = 60 ms Dt p T2 = 14 ms Dtp/2/2 Dtp/2/2 p p/2 p/2 Dtp/2 Techo = 25 ms p/2 p/2 meas.

24. Ramsey Experiment/Hahn Echo T2echo = 145 ms

25. Remarkable Frequency Stability f01 = 6 808 737 605 (608) Hz Overall precision after 12 hours: ~ 19 Hz or 3 ppb No change in Hamiltonian parameters > 80 ppb in 12 hours!?

26. Charge Qubit Coherence, Revised QEC limit? Schoelkopf’s law 10x every 3 years!

27. Milliseconds and Beyond? 0.6 Billion Ringdown of TE011 Fit (Black): τ = 3.7ms QL=ωτ=265M best qubits E Now this is a Quantum Memory for qubits!! M. Reagor et. al. to be published

28. Building Blocks for Scaling Many Atoms Many Cavities One Atom One Cavity Two Atoms One Cavity One Atom Two Cavities

29. Two-Cavity Design 45mm 900μm Al2O3 500nm 1.2mm

30. Strong dispersive limit: QND measurement of single photons Algorithms: DiCarlo et al., Nature460, 240 (2009).

31. Dispersive Limit of cQED “phobit” DiagonalizingJ-C Hamilt.: qubit cavity “quton” Dispersive (D>>g):

32. Photon Numbersplitting Strong Dispersive Hamiltonian: “doubly-QND” interaction n=2 n=2 n=1 qubit absorption n=1 n=0 n=0 Qubit Frequency (GHz)

33. QND Measurement of Photon Number Quantum “go-fish” “Got any ‘s? “Click!” cavity g e 2) then measure qubitstate using second cavity g qubit 1) perform n-dependent flip of qubit Repeated QND of n=0 or n=1:B. Johnson, Nature Phys., 2010

34. Coherent Displacements create

35. Coherent Displacements

36. Using a cavity as a memory:Schrodinger cats on demand experimenttheoryG. Kirchmair M. Mirrahimi B. Vlastakis Z. Leghtas “No, no mini-Me, we don’t freeze our kitty!”

37. Driving a Quantum Harmonic Oscillator Giving a classical ‘drive’ to a quantum system: Phase-space portrait of oscillator state: Where: with Our state is described by two continuous variables, an amplitude and phase. A ‘coherent’ state.

38. What’s a Coherent State? E x x Glauber (coherent) state

39. What’s a Coherent State? E x x Glauber (coherent) state

40. What’s a Coherent State? E x x Glauber (coherent) state

41. Measured Q functions of a Coherent State g e g

42. Deterministic Cat Creation cavity qubit

43. Deterministic Cat Creation cavity qubit

44. Deterministic Cat Creation cavity transmission w 5ns pulse cavity qubit

45. Deterministic Cat Creation cavity qubit

46. Deterministic Cat Creation cavity qubit

47. Deterministic Cat Creation cavity qubit

48. Deterministic Cat Creation cavity qubit

49. Deterministic Cat Creation cavity qubit

50. So, What’s a Cat State? E x x Schrödinger cat state Superposition with distinguishability, D