1. Two Level Systems in Phase Qubits: Tunnel Barriers & Wiring Dielectrics Jeff Kline March 6, 2008

2. Josephson Junctions  : complex pair wavefunction  : phase of Cooper pairs  =  1 -  2 is the phase difference across the junction Josephson Inductance The phase  changes according to the potential U The motion of  has an exact correspondence with the motion of a particle moving in the potential U It is easier to visualize the particle’s motion, so we speak in terms of the fictitious “particle” in the washboard potential “Flux quantum” Tilted Washboard Potential Josephson Relations S1S1 S2S2 I

3. Phase Qubits Nonlinearity Unlike other qubits, the phase qubit must be current-biased with I bias ~I o and  ~  /2 This is necessary to obtain a large nonlinearity in the Josephson inductance This nonlinearity is what produces the unequal energy level spacing required for unique level addressability I bias JJ A phase qubit is simply a current biased JJ in parallel with its “self capacitance” For I bias ~I o &  ~  /2 It is a cubic potential (i.e.,  3 ), so QM energy levels have unequal spacing Avg. Slope of U(  ) is  –I/Io For I<I o, U(  ) has relative minima, and particle can be trapped When particle is trapped, JJ is in zero-voltage state When particle escapes from well, JJ makes transition to non-zero voltage state (a.k.a. running state) CJCJ “self-capacitance” Trapped stateRunning state QM Energy levels

4. I bias ~ I o U(  ) |0> |1> ħ  10 Qubit Spectroscopy-Theory I bias JJ

5. Qubit Spectroscopy-Theory I bias ’ > I bias U(  ) |0> |1> |0’> |1’> ħ  10 ’ ħ  10  10 (GHz) I bias (a.u.) I bias JJ

6. Qubit Spectroscopy-Experiment “Splittings”

7. Spurious Two Level Systems Displacement Transverse Bond direction Rotational SiO 2 U ħħ 1 2 11  2 2  d (displacement) Isolated Harmonic Potentials ħħ

8. U EoEo E1E1 tunneling Spurious Two Level Systems Displacement Transverse Bond direction Rotational SiO 2 00 11 d Dipole moment + - - + Overlapped Harmonic Potentials 

9. Spurious TLS coupled to qubit S S I + - + - Microwave + TLS || TLS  TLS II –Can align with electric field –Lowers energy state TLS  –Cannot align –No preferred orientation TLS fluctuates with microwave field –Resonant effect, only when TLS energy matches microwave energy –Dissipates microwave power Resonant interaction between TLS and qubit –Only occurs when TLS and qubit energies match S S I - + + - ~ Microwave - TLS || TLS  V ac +++ --- --- +++ ~

10. Raw data-multiple valued “Splittings”

11. Smoothed data-single valued Flux bias (mV) Frequency (GHz)

12. Sizes of splittings

13. Integrated splittings N/GHz (.01 GHz < S < S’) Splitting size S’ (GHz) Integrate splittings and display on semi- log graph Normalize to 1 GHz bandwidth Density of splittings S: Integrate w.r.t S: A: junction area  : materials constant related to defect density Slope =  Maximum splitting size S max N tot

14. Integrated splittings-material comparisons epi-Al 2 O 3 epi-MgO amorph-AlO x  = 20  = 60

15. Min-SiO 2 Re/MgO/Al Qubit Splitting density –Similar to AlO x T 1 = 80 ns –Worse than Al 2 O 3 & AlO x –Phonon loss? P1 (%) t (ns) P1 (%) T 1 = 80 ns t (ns) Flux bias (mV) Freq (GHz) Spectroscopy Rabi Osc.

16. Spurious TLS in wiring dielectrics S S I + - + - Microwave + TLS || TLS  TLS II –Can align with electric field –Lowers energy state TLS  –Cannot align –No preferred orientation TLS fluctuates with microwave field –Resonant effect, only when TLS energy matches microwave energy –Dissipates microwave power Resonant interaction between TLS and qubit –Only occurs when TLS and qubit energies match +++ --- ~ V ac Insulator thickness Tunnel barrierWiring Dielectric 2 nm200nm Dielectric loss decreases at high T or high power Schickfus 1977

17. Future Directions Re/Al 2 O 3 /Al qubit with Re wiring –Avoid trap states in native oxide of Al wiring Try atomic oxygen for Al 2 O 3 barrier growth –Fix pinhole problem? Try annealing finished chip in hydrogen –Passivate surface states? Try rf-sputt MgO and AlO x t-barrier –Could be pinhole free Try Nb/Al 2 O 3 /Al JJ –University of Illinois failed, but could be tool-specific Try ALD of dielectrics –Conformal coverage  can decrease thickness!