1 / 22

Meet the transmon and his friends

Departments of Physics and Applied Physics, Yale University. Chalmers University of Technology, Feb. 2009. Meet the transmon and his friends. Jens Koch. Outline. Bullwinkle. Transmon qubit ► from the CPB to the transmon ► advantages of the transmon

nedaa
Download Presentation

Meet the transmon and his friends

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Departments of Physics and Applied Physics, Yale University Chalmers University of Technology,Feb. 2009 Meet the transmonand his friends Jens Koch

  2. Outline Bullwinkle Transmon qubit ► from the CPB to the transmon ► advantages of the transmon ► theoretical predictions vs. experimental data Circuit QED with the transmon – examples

  3. Review: Cooper pair box 3 parameters: offset charge (tunable by gate) Josephson energy (tunable by flux in split CPB) charging energy (fixed by geometry) charge basis: numerical diagonalization phase basis: exact solution with Mathieu functions

  4. CPB as a charge qubit Charge limit:

  5. CPB as a charge qubit Charge limit: big small perturbation

  6. Noise from the environment • Noise can lead to energy relaxation ( )dephasing ( ) • Persistent problem with superconducting qubits: short Superconducting qubits are affected by charge noise flux noise critical current noise bad for qubit! Reduce noise itself Reduce sensitivity to noise ► materials science approach► eliminate two-level fluctuators J. Martinis et al., PRL 95, 210503 (2005) ► design improved quantum circuits ► find smart ways to beat the noise! Paradigmatic example: sweet spot for the Cooper Pair Box

  7. Outsmarting noise: CPB sweet spot energy ◄ charge fluctuations sweet spot only sensitive to 2nd order fluctuations in gate charge! energy ng (gate charge) Vion et al., Science 296, 886 (2002) ng

  8. CPB sweet spot: the good and the bad Linear noise Sweet spot T2 ~ 1 nanosecond (e.g. Nakamura) T2 > 0.5 microsecond (e.g. Saclay, Yale) disadvantages: ► need feedback ► still no good long-term stability ► does not help with “violent” charge fluctuations How to make a sweeter spot?

  9. Towards the transmon: increasing EJ/EC ► charge dispersion becomes flat (peak to peak) ► anharmonicity decreases sweet spot everywhere!

  10. Harmonic oscillator approximation • Consequences of► strong “gravitational pull”► small angles dominate quantum rotor(charged, in constant magnetic field ) expand ignore periodic boundary conditions eliminate vector potential by “gauge” transformation

  11. Harmonic oscillator approximation • resulting Schrödinger equation: ► harmonic spectrum ► no charge dispersion

  12. Anharmonic oscillator • Anharmonic oscillator approximation expand like before perturbation Perturbation theory in quartic term • anharmonic spectrum • still no charge dispersion

  13. Charge dispersion ► full 2p rotation, Aharonov-Bohm type phase ► quantum tunneling with periodic boundary conditions - WKB with periodic b.c.- instantons- asymptotics of Mathieu characteristic values

  14. Coherence and operation times chargeregime T2 from 1/f charge noise at sweet spot Top due to anharmonicity transmonregime the “anharmonicity barrier” at EJ/EC = 9

  15. Increase EJ/EC Increase the ratio by decreasing Island volume ~1000 times biggerthan conventional CPB island

  16. Experimental characterization of the transmon Reduction of charge dispersion: Improved coherence times theory Strong coupling 2g ~ 350 MHz vacuum Rabi splitting THEORY: J. Koch et al., PRA 76, 042319 (2007), EXPERIMENT: J. A. Schreier et al., Phys. Rev. B 77, 180502(R) (2008)

  17. Cavity & circuit quantum electrodynamics ►coupling an atom to discrete mode of EM field cavity QED Haroche (ENS), Kimble (Caltech) J.M. Raimond, M. Brun, S. Haroche, Rev. Mod. Phys. 73, 565 (2001) circuit QED A. Blais et al., Phys. Rev. A 69, 062320 (2004) A. Wallraff et al., Nature 431,162 (2004) R. J. Schoelkopf, S.M. Girvin, Nature 451, 664 (2008) k= cavity decay rate 2g = vacuum Rabi freq. g= “transverse” decay rate Jaynes-Cummings Hamiltonian resonator mode coupling atom/qubit

  18. Circuit QED atom artificial atom: SC qubit cavity 2D transmission line resonator integrated on microchip paradigm for study of open quantum systems ► coherent control ►quantum information processing ►conditional quantum evolution ► quantum feedback ► decoherence

  19. Coupling transmon - resonator qubit resonator mode Cooper pair box / transmon: coupling to resonator:

  20. Control and QND readout: the dispersive limit • Control and readout of the qubit: (detune qubit from resonator) dispersive limit : detuning canonical transformation dynamical Stark shift Hamiltonian dispersive shift:

  21. Circuit QED with transmons 2006/7 Realization of a two-qubit gate ► two transmons coupled via exchange ofvirtual photons Probing photon states via the numbersplitting effect ►transmon as a detector for photon states J. Gambetta et al., PRA 74, 042318 (2006); D. Schuster et al., Nature 445, 515 (2007) 2007 J. Majer et al., Nature 449, 443 (2007) 2008 Observing the √n nonlinearity of the JC ladder A. Wallraff et al. (ETH Zurich) L. S. Bishop et al. (Yale)

  22. Rob Schoelkopf Steve Girvin Michel Devoret

More Related