1. Microwave Spectroscopy of the radio- frequency Cooper Pair Transistor A. J. Ferguson, N. A. Court & R. G. Clark Centre for Quantum Computer Technology, University of New South Wales, Sydney

2. Summary 1.Engineering the properties of superconducting aluminium 2.The single cooper pair transistor (SCPT) 3.Radio frequency operation of the SCPT 4.The superconducting transport processes 5.Microwave spectroscopy

3. Aluminium Devices Y. Nakamura et al Nature 398 786 (1999) I. Chiorescu et al Science 299 1869 (2002) Superconducting Qubits Single electron (Cooper-pair) transistors

4. Aluminium Materials Science Thin films: dramatic change in superconducting properties R. Meservey and P. M. Tedrow J. Appl. Phys. 42, 51 (1971) J. Aumentado et al., PRL 92, 066802 (2004) An alternative approach to O 2 doping Tc,  Bc d (nm) 10100 1 1000 1 0.1 10 B (T) d -1 (nm -1 ) 0.3 0.1 0.01 2 3 1 Tc (K) Pauli-limited Bc: spin effects in superconducting SETs. A. J. Ferguson et al. on cond-mat soon

5. The thin-film SCPT 7 nm 30 nm  ~ 200  V  ~ 300  V  ~ 200  V ~1K of quasiparticle barrier Films evaporated onto LN 2 cooled stage at 0.1 nms -1 Electrically continuous films to 5 nm possible 7 nm 30 nm 7 nm islands used for these devices

6. Single Cooper pair transistor In a 2-band model E J /E C =0.5 E J,C 1 E J,C 2 CgCg E C =e 2 /(C 1 +C 2 +C g ) h

7. Why do it? QP poisoning Careful filtering required to avoid non-equilibrium qps These qps tunnel on and ‘poison’ supercurrent 22  1 /  2 ~exp(  2 -  1 /kT) A QP barrier reduces poisoning rate 11 The device itself becomes a qp filter 2121 2222 22 2222 J. Aumentado et al., Phys. Rev. Lett, 92, 066802 (2004)

8. rf-SET Main idea: LC circuit matches high resistance of SET towards 50 Ohms. Amplitude of reflected signal (S 11 ), related to resistance (R) of SET. R. J. Schoelkopf et al., Science 280 1238 (1998) rf (321MHz) Reflected signal either diode or mixer detected.

9. rf-SCPT I rf <I sw : R~0  I rf >I sw : R>0  Single shot: QP poisoning events J. Aumentado et al., cond-mat\0511026 Resistance is now R eff (Irf, Isw), use to find reflection coefficient in the usual way. Device I: Parameters R = 18 k  E J = 43  eV E c = 77  eV E J /E C = 0.56 Imax Imin

10. B=0T Diamonds Ec=180  eV R  =71 k  E J =11  eV E J /E C =0.06 2e supercurrent enabled by thin-island 2  1 + 2  2 = 1.05 meV 2e ‘supercurrent’ JQP DJQP Mixer out (a.u.) Device II: Parameters 0 1 Imax Imin

11. Resonant CP tunnelling D. B. Haviland et al., PRL 73, 1541 (1994) V E(n+2)-E(n)=0 E(n+2)-(E(n)-2eV)=0 Supercurrent occurs when resonance occurs for a CP on both junctions. Resonant Dissipative V 0 2 @ A 213 B 234 A DJQP resonance: QPs involved Resonant Dissipative V 0 2 @ B Resonant 0 2

12. Microwave Spectroscopy D. J. Flees et al., Phys. Rev. Lett., 78, 4817 (1997) Y. Nakamura et al., Czech. J. Phys., 46, 2301 (1996) Y. Nakamura et al., Phys. Rev. Lett., 12, 799 (1997) 40GHz -25 dBm -19 dBm Suppression of supercurrent Frequency dependent sidebands on supercurrent Frequency dependent sidebands on resonant CPT No  -waves

13. PAT + resonant CPT 0 2 00 11 22 0 2 0 2 0 2 0 2 0 2 P. K. Tien and J. P. Gordon, Phys Rev. 129, 647 (1963) 0 2

14. Frequency dependence Linear dependence of sidebands observed. Anti-crossing not observable since Ej=11  eV (2.6 GHz) 1  : 186  eV 2  : 193  eV c.f. 180  eV from transport

15. Power dependence 30 GHz 0 1 2 E C =180  eV,  =300  eV, E J =11  eV Multiple  events occur Possibly QP states excited too J. M. Hergenrother et al., Physica B 203, 327 (1994)

16. Conclusions ~100  eV of QP barrier possible with thin film Reduced QP poisoning allows 2e-periodicity rf-measurement of 2e supercurrent shown Observe individual QP poisoning events Combination of PAT and CP resonant tunneling observed

17. Future Experimental: investigate charge noise of thin film Experimental: further study individual QP poisoning events Theoretical: look at rf-supercurrent measurement as electrometer (ultimate sensitivity etc)

18. Switching current measurement Device I: Parameters R = 18 k  E J = 43  eV E c = 77  eV E J /E C = 0.56 2e-periodic Isw