Circuit QED with electrons on helium:

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1 Circuit QED with electrons on helium: What s the sound of one electron clapping? David Schuster Yale (soon to be at U. of Chicago) Yale: Andreas Fragner Rob Schoelkopf Princeton: Steve Lyon Michigan State: Mark Dykman Useful cryogenics discussions: Mike Lea / David Rees

2 Outline Circuit QED with electrons on helium Super-sensitive level meter Some preliminary measurements

3 Cavity Quantum Electrodynamics (CQED) D. Walls, G. Milburn, Quantum Optics (Spinger-Verlag, Berlin, 1994)

4 Circuit Quantum Electrodynamics elements the cavity: a superconducting 1D transmission line resonator (large E 0 ) the artificial atom: a Cooper pair box (large d) A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, PRA 69, (2004)

5 Strong coupling cavity QED!

6 Strong coupling cavity QED! r g / 2 6 GHz 2 g / 2 12 MHz / 2 / khz 2 g C 3600 Wallraff, DIS, et. al. Nature (2004)

7 Non-Resonant Qubit Read-Out A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, PRA 69, (2004)

8 Circuits make good atoms/qubits Photon number detection QND detection of photons Qubit / photon gates Non-linear optics Coupled qubits Two qubit gates Quantum algorithms Process tomography Schuster, Houck, et al., Nature, 2007 DiCarlo, Chow, et. al., Nature, 2009

9 Electrons on helium E n R 2 n 120 GHz Reduced H spectrum Potential well depth ~ R = 8 K Bohr radius 8 nm above surface Clean 2DEG (Mobility = cm 2 /Vs) Bare electron: m eff = m e, g = 2 <1 ppm 3 He nuclear spins Bulk spin coherence time > 50 ms* QC Proposal w/ vertical states: Dykman, Science 1999

An electron in an anharmonic potential 12 01 12 01 ev t 150 GHz h w 1 μm

e x 0 ~1000D DC electrodes to define trap for lateral motion Nearly

10 An electron in an anharmonic potential ev t 150 GHz h w 1 μm t 1 μm 01 ~ 10 GHz 2 ~ 100 MHz 2 x ~ 30nm 0 Big dipole moment! e x 0 ~1000D DC electrodes to define trap for lateral motion Nearly harmonic motion with transitions at ~ GHz Anharmonicity from small size of trap (~ 1mm)

Couple to other qubits through cavity bus Cavity-electron

11 An electron in a cavity E 0 V0 w Electron motion couples to cavity field Can achieve strong coupling limit of cavity QED Couple to other qubits through cavity bus Cavity-electron coupling V g ex h w 0 ~ 0 ~ 25MHz Schuster, Dykman, et. al. arxiv: (2009)

12 Accessing spin: Gradient method H m B s ~ m B ˆˆ s sb B B z x x Electricaly tunable spin-motion coupling! With no flux focusing and current geometry: 100 khz/ma

13 Decoherence Mechanisms Motional Decoherence Relaxation through bias electrodes Emission of (two) ripplons Emission of phonons dephasing relaxation Classical helium fluctuations Ripplons Phonons

14 eonhe spin memory Put many electrons on top of the resonator. Spins coupled to resonator magnetic field. g ~ 100Hz 1kHz 2 g M ~ 10kHz 100kHz 2 with ~10 4 spins Even basic ESR has never been done on eonhe 2DEG!

15 Experimental Setup Pulse-tube cooled dilution refrigerator top bottom hermetic sample holder with Indium sealing & stainless steel capillary no superfluid leaks down to 10mK

16 Superconducting Cavities as liquid He-Meters Experiment

17 Superconducting Cavities as liquid He-Meters Experiment I

18 Superconducting Cavities as liquid He-Meters Experiment I II

19 Superconducting Cavities as liquid He-Meters Experiment I II III

20 Superconducting Cavities as liquid He-Meters Experiment I II III IV

21 Superconducting Cavities as liquid He-Meters Experiment I II III IV V

22 Anatomy of an eon trap Cavity level meter Drive plate Gate plate Guard ring Sense plate

23 Detecting trapped electrons on helium Electrons No electrons

24 Detecting trapped electrons on helium Electrons No electrons

25 Making an eonhe transistor (eonfet) V gate Modulate density without losing electrons Measure density ~10 9 e/cm 2 (~few e/um 2 )

26 Making an eonhe transistor (eonfet) V gate Modulate density without losing electrons Measure density ~10 9 e/cm 2 (~few e/um 2 )

27 Making an eonhe transistor (eonfet) V gate Modulate density without losing electrons Measure density ~10 9 e/cm 2 (~few e/um 2 )

coherence, superfluid excitations, etc. We see electrons on helium!

28 Conclusions Electrons on Helium: Strong coupling limit easily reached Good coherence times for motion and spin Rich physics - single electron dynamics, motional and spin coherence, superfluid excitations, etc. We see electrons on helium!! Can trap at 10 mk without much heating (~100mK) Can hold them for hours Next up: Trapping single electrons

CIRCUIT QUANTUM ELECTRODYNAMICS WITH ELECTRONS ON HELIUM

CIRCUIT QUANTUM ELECTRODYNAMICS WITH ELECTRONS ON HELIUM David Schuster Assistant Professor University of Chicago Chicago Ge Yang Bing Li Michael Geracie Yale Andreas Fragner Rob Schoelkopf Useful cryogenics