1. Novel HTS QUBIT based on anomalous current phase relation S.A. Charlebois a, T. Lindström a, A.Ya. Tzalenchuk b, Z. Ivanov a, T. Claeson a a Dep. of Microtechnology and Nanoscience - Quantum Device Physics Laboratory, Chalmers University of Technology, SE-412 96 Göteborg, Sweden b National Physical Laboratory, Teddington, Middlesex, TW11 0LW, UK

2. Outline On QUBITs –In LTS and with  -SQUIDs –Novel design in HTS with 0/45° grain boundary jonctions First steps towards realisation –Observation of a strong second harmonic component Coming work –Spectroscopy of the Josephson potential

3. Transport through a 0°-45° grain boundary in d-wave HTS In ideal cases –The current-phase relation (CPR) is  -periodic –Tunneling thru both + and – lobes lifts the degeneracy of the ±k Andreev levels In real cases –The GB is facetted and wiggling –The 2  -periodic component is not completely cancelled 200nm

4. The presence of second harmonic in the CPR of a SQUID the phase difference in junction i 1 and 2 represent the junction number I and II represent the 1 st and 2 nd harmonics The CPR of a SQUID is given by the sum of the CPR of each junction including a 2 nd harmonic For small inductance, the effective washboard potential is the cross section where the applied magnetic flux

5. Eigenstates of the washboard potential with second harmonic

6. If symmetric: silent QUBIT –The external field does not lift the state degeneracy (σ x coupling) –Unusable for quantum computing

7. Functional QUBIT for a particular asymmetry –The external field “gently” lifts the degeneracy (coupling σ z · Φ 3 ) –All single QUBIT operations realized by applying magnetic field

8. First steps towards realisation 0°-45° YBCO grain boundary junctions –250nm thick films 2µm size jonctions –I c ~ 25-60µA –R n ~ 3Ω –Non hysteretic Submicron jonctions –Width 0.3-0.6µm –I c ~ 0.5-3µA –R n ~ 50-300Ω –Hysteretic 5µm5µm The “QUBIT” is connected to perform various SQUID measurements

9. Excellent correspondence Theory Experiment Critical current : The theoretical curve (red in the right figure) fits the measurement very well SQUID response : The theoretical curve (left) fits the measurements (left) show good qualitative agreement 2µm junctions

10. Junction modulation in high field Absolute maxima not at B=0 –Characteristic of 0°-45° grain boundaries –Due to 0 and  facets Lack of ±B symmetry –Due to inductance (in large junction limit) –Due to 2 nd harmonic (in small junction limit)

11. Different behavior in submicron junctions The critical current vs. applied magnetic field for two SQUIDs with the same loop size (15×15) µm 2. SQUID A: 0.3/0.2 µm wide junctions (values multiplied by 10 for clarity). SQUID B: 2/2 µm junctions. All curves measured at 4 K. The SQUIDs with submicron junctions do not show doubling of the I c (  ) curves A small shift between the positive and negative current bias is observed: –approx. 0.1Φ o

12. Symmetric SQUID: Complex secondary maxima develop at (n+1)  for  >½ –for  >½, the potential is double well like No shift between + and – current bias Modulation is not complete even though the junctions are identical I c (  ) for various values of  Position of the minima and maxima of I c (  )

13. Asymmetric SQUID: Secondary maxima develop for  >½ –for  >½, the potential is double well like –the position is parameter dependant Shift between + and – current bias –Shift present for  <½ where the potential is not double well like I c (  ) for various values of  Position of the minima and maxima of I c (  )

14. Conclusion 2 nd harmonic in CPR has been observed –In micron size junctions with direct measurement in SQUIDs Showed obvious unconventional CPR High field modulations indicate the presence of 0 and  facets –In submicron size junctions: Presence of a small 2 nd harmonic component is observed Measurements below 1K needed to confirm The observation of unconventional CPR in 0°-45° bicrystal Josephson junctions –Confirms the “good quality” of junctions –Confirms that the fabrication process we use limits the damages to the grain boundary –Is a prerequisite to further work with the novel QUBIT design

15. Coming work Spectroscopy of the Josephson potential –Following work by Mooij –Measuring the switching current of an outer SQUID –Inductive coupling between the readout SQUID and the QUBIT –HF tuned to the level spacing modify the flux in the QUBIT –The readout SQUID measures the variation of the QUBIT flux van der Wal, 2001

16. Alexander Ya. Tzalenchuk, John Gallop and J T Janssen Alexander Zagoskin, Mohammad Amin and Alexander Blais Tobias Lindström, Serge Charlebois, Evgueni Stepantsov and Zdravko Ivanov