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 discussions: Mike Lea / David Rees Princeton Steve Lyon Michigan State Mark Dykman Looking for students/postdocs! (schusterlab.uchicago.edu)
Outline Electrons on helium Circuit QED with electrons on helium Decoherence mechanisms and technical challenges Ge and Andy to follow up with experimental progress
An electron dimple Low energy electrons get stuck on the surface Force from positive electrode causes a dimple M.W. Cole. Rev. Mod. Phys. 46, 3 1974
An electron on helium See Jackson 4.4 He Electron bound at < 8K + V 1 Re En 2 4e nz 0 2 Levitates 8nm above surface (in vacuum) Clean 2DEG : Mobility = 10 10 cm 2 /Vs R/ h157ghz Bare electron: m eff = 1.005 m e, g = 2 <1 ppm 3 He nuclear spins e = 1.057 a 0 = 7.6 nm QC Proposal w/ vertical states: Dykman, Science 1999
Electrons on helium vs. traditional 2DEGs Filament 2DEG 2DEG He Electrodes Top gate GaAs Back gate Ohmic contact Dopant layer Semiconductor Liquid/Superfluid interface No ohmic contacts (DC transport) Mobility = 10 10 cm 2 /Vs Bulk spin coherence time > 50 ms* Effective mass = 0.99 m e g-factor = 2 Classical 2DEG / Wigner crystal Filament > 1 cm # of electrons well defined He3 nuclear spins < 1ppm Crystalline interface Ohmic contacts (DC transport) Mobility = 3 x 10 7 cm 2 /Vs Single spin coherence time ~100 ms Effective mass = 0.067 m e g-factor = -0.44 Quantum 2DEG / QHE Dopants < 100 nm Chemical potential well defined 100% Nuclear spins
An electron in an anharmonic potential DC electrodes to define trap for lateral motion Nearly harmonic motion with transitions at a few GHz Anharmonicity from small size of trap (w ~ d ~ 1mm)
CCD s for electrons on helium Massive CCD of electrons on helium Control many electrons with just a control inputs Courtesy Lyon group Needed: to load/detect exactly 1 electron/pixel Needed: way to entangle pairs of pixels together
Detection of single electrons on helium Electrons transferred 1 at a time from a resevoir into a 10 micron size trap Charge is quantized but no detection of coherent motion or spin Rousseau, et. al. PRB 79 045406 (2009)
Cavity QED with circuits and floating electrons 2g = vacuum Rabi freq. k = cavity decay rate g = transverse decay rate Strong coupling: 2g > k, g out transmission line cavity 10 mm 10 GHz in Trapped electron Theory: Blais, Huang, et al., Phys. Rev. A 69, 062320 (2004)
What can you do with cavity QED? Quantum Optics Measure individual photon # states Produce single photon states Tomography of arbitrary quantum states DIS *, Houck*, et. al., Nature, (2007) Bishop, Chow, et. al., Nature Physics, (2009) Quantum Computing Two qubit gates Quantum algorithms Process tomography Fundamental Cavity QED Measurement of field quantization Create large photon # states DiCarlo, Chow, et. al., Nature, (2009)
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 Predicted decay rate <10 khz Schuster, Dykman, et. al. Phys. Rev. Lett. 105, 040503 (2010)
Measuring without absorption A. Blais, R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, PRA 69, 062320 (2004)
Accessing spin: Artificial spin-orbit coupling Electricaly tunable spin-motion coupling! With no flux focusing and current geometry: 100 khz/ma
Decoherence due to electrodes Noise on gate electrode: Assume worst case scenario of SET (w 1fF capacitance) charge noise as voltage noise. S V ~10 10 V/Hz 9 7 1/ 2 7 10GHz 10 V ~ 2.5kHz 400mV Johnson noise is even smaller. Odd mode noise should be similar but potential is first order insensitive to odd fields, so should also be smaller. Linearly sensitive to voltage noise, should be similar to flux bias lines, and those seem ok at the microsecond level.
Interactions with Helium Electron motion can couple to waves in helium. To cause relaxation, must match Energy and Momentum p h / x 0 Relaxation rate: k p 1 2 h / x k k 0 1 2 p h / x ~ k ~ k 0 k k k x y 2 2 2 x y z small 400 Hz 400 Hz Dephasing rate: small 50 Hz?? 1/ 2
Interactions with Helium 2 What about classical vibrations? Channel is filled by capillary action. Tilting container could change level? We re pretty sensitive to He level ~ 10 MHz/nm Superfluid to the rescue! 1cm t 28nm h 2 / 7 Would need 9mm change in reservoir to get Dt=1nm!
Electron Debye Waller Factor Electron-ripplon sideband transitions e g No ripplon transition Phonon + ripplon transition N-1 N N+1 Ripplon While Rabi flopping possible to emit ripplon. Ripplon spectrum has no gap: 3/ 2 k Gives error while driving (not while qubit resting). Solutions: so present at any Rabi frequency. Error may be as bad as 15%... Reduce coupling to ripplons Develop ripplon resistant pulses
Motional Decoherence Mechanisms Relaxation through bias electrodes Dephasing from level fluctuations Emission of (two) ripplons Emission of phonons dephasing relaxation
Experimental path towards realizing this dream Build an apparatus compatible with both SC resonators/qubits and electrons on helium Good microwave performance (and thermalized down to 20mK) Hermetic to superfluid / low vibrations Create stable superfluid filled trap for electrons Build resonators with capillary channels Develop sensitive helium level meter Characterize fluctuations Trap and detect many (and eventually single electrons) Need electron source (filament, photocathode, field emitter,) Need many electron trap Need to load single electron trap Need to detect and manipulate single electrons
State of electrons on helium experiments Helium+Dil-fridge+microwaves Trapping and DC detection of electrons Cavity-Helium coupling (Yang) Cavity-based trapping/detection (Fragner)
Conclusions Circuit QED with electrons on helium Rich physics - single electron dynamics, motional and spin coherence, superfluid excitations, etc. Strong coupling limit should be easily reached Good coherence times for motion and spin Making rapid experimental progress Sensitive detection of helium using superconducting cavities Trapping of many electrons Much more to accomplish Next up: Experimental progress!