1. Metastability and self-oscillations in superconducting microwave resonators integrated with a dc-SQUID Eran Segev Quantum Engineering Laboratory, Technion, Israel

3. Indirect measurements approach:

4. Resonance Readout - The quantum device is coupled to a superconducting resonator.

5. The state of the device modifies the resonance frequencies.

6. Readout is done by probing these resonance frequencies.Quantum Device Input Probe Output Signal Resonance Curve S12 Input Probe Output Signal Freq

8. Heat transfer to a coolant

9. Heat production:A. VI. Gurevich and R. G. Mints, Rev. Mod. Phys. 59, 941 (1987)

13. Self-Modulation - Time Domain II Time Domain @ -27.85[dBm] Pump Power Time Domain 40 20 |B|2 0 -20 0 2 4 6 8 10 Time [  Sec] Frequency domain ~ Frequency Domain -40 Power [dBm] -60 -80 -50 0 50 Frequency [MHz] Spectrum Oscillo- scope Analyzer

14. Self-Modulation - Time Domain III Time Domain ~ Frequency Domain Spectrum Oscillo- scope Analyzer Time Domain @ -27.72[dBm] Pump Power 40 20 |B|2 0 -20 0 200 400 600 800 1000 Time [nSec] Frequency domain -30 -40 Power [dBm] -50 -60 -70 -50 0 50 Frequency [MHz]

15. Self-Modulation - Time Domain IV Time Domain ~ Frequency Domain Spectrum Oscillo- scope Analyzer Time Domain @ -21.81[dBm] Pump Power 40 20 |B|2 0 -20 0 100 200 300 400 500 Time [nSec] Frequency domain -40 Power [dBm] -60 -80 -50 0 50 Frequency [MHz]

16. Self-Modulation - Time Domain V Time Domain @ -19.35[dBm] Pump Power Time Domain 40 20 |B|2 0 -20 0 100 200 300 400 500 Time [nSec] Frequency domain ~ Frequency Domain -40 Power [dBm] -60 -80 -50 0 50 Frequency [MHz] Spectrum Oscillo- scope Analyzer

17. Self-Modulation – Power Dependence ~ Spectrum Oscillo- scope Analyzer

20. Theory vs. Experiment – Time Domain mono-stable (N) bistable bistable Un-s  mono-stable (S) working point  Theoretical Results Experimental Results 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.2 0.2 (iii) (vii) 0 0 -0.2 [a.u.] -0.2 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.4 0.4 (ii) (vi) ref 0.2 P 0.2 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 t [ m Sec]

21. Theory vs. Experiment – Threshold phenomenon mono-stable (N) bistable bistable un-stable mono-stable (S) working point Theoretical Results Experimental Results Noise is added to simulation Noise is added to simulation  

26. Self-Oscillations.

27. Strong non-linear amplification and detection

32. Thermal balance EOMExperiment Simulation

33. Physical model of DC-SQUID Squid Potential: Sine Term Quadric Term Source Internal variable Control parameters Parameters_______________________

34. DC-SQUID Potential – Roll of Hysteresis Parameter Sine Term Quadric Term Source Hysteretic parameter that control the degree of metastability.

35. DC-SQUID Potential – Roll of control parameters Tilt by Current Control parameters Tilt by magnetic Flux

37. CJ – JJ capacitance.

38. L – Self-inductance.Control parameters Kirchhoff Equations Internal variable DC-SQUID EOM Parameters JJ Current Coupling

39. Stability boundaries – Phase space Hessian Local Stable Zones Local Extremum Points Stability Diagram in the plane of Stability Diagram in the plane of Local stability zones

40. Stability boundaries – Alternating excitation 6 2 1 4 0 -1 2 -2 0 F / 0 x F -2 -4 -6 -1 0 1 I /I x c $ $ $ $ Stability Diagram in the plane of Stability Diagram in the plane of $ $ $ $ $ $ $ $ $ $ $ $ $ Periodic dissipative zone – Static stability zones were dissipation of energy occurs under periodic excitation.

41. Numerical results Periodic dissipative static zones

42. Periodic dissipative static zone 2 1 0 F / 0 x F -1 -2 0.96 0.97 0.98 0.99 1 I /I x C Periodic non-dissipative static zone Free running zone Periodic dissipative static zone Periodic dissipative static zone E38 Parameters:

44. Double Threshold to Oscillatory Zone Experimental Results Simulation Results Split Threshold

45. Hybrid zones Experimental Results SQUID Voltage Noise Level TD Statistics

49. Boundaries between local stable zones are observed in the periodic non-dissipative zone.

50. The variance of the SQUID inductance within a local stable state is observed.Stability diagram in the plane of Simulation results PDSZ PNDSZ PDSZ PNDSZ

52. Location and shape of PDSZ threshold is different.

53. Different βL fits the PNDSZ and the PDSZ.Experimental results Simulation results Exc. Heat Production Location and shape of threshold is different

54. Different βL fits the PNDSZ and the PDSZ. Only heat degree of Freedom Can explain this change Heat relaxation rates are comparable to the excitation frequency! Threshold point to PDSZ

55. DC-SQUID Model inc. heat balance equation EOM for the Josephson junction phases JJ Current Coupling represents the dependence of the kth JJ critical current of the temperature. Heat balance EOMs Parameters Heat Production Heat transfer to coolant

56. Numerical results inc. Heat production Stability diagram in the plane of + Stability Diagram in the plane of First Cycle Additional Cycles Time domain simulation Legend PDSZ PNDSZ

59. Question – Does stress or strain in Nano-beams affects material coherency ?

60. Method – Study the effect of a mechanical degree of freedom on the Aharonov-Bohm effect. 1um2 AB rings, 30x90nm2 cross section. I V Side electrode Side electrode 1um 30nm-thick Aluminum 100nm I V

63. Publication List E. Segev, B. Abdo, O. Shtempluck, and E. Buks, 'Fast Resonance Frequency Modulation in Superconducting Stripline Resonator', IEEE Trans. Appl. Sup., 16 (3), P. 1943 (2006). E. Segev, B. Abdo, O. Shtempluck, and E. Buks 'Novel Self-Sustained Modulation in Superconducting Stripline Resonators', Europhys. Lett. 78, 57002 (2007). E. Segev, B. Abdo, O. Shtempluck, and E. Buks 'Thermal Instability and Self-Sustained Modulation in Superconducting NbN Stripline Resonators', J. Phys. Cond. Matt. 19, 096206 (2007). E. Segev, B. Abdo, O. Shtempluck, and E. Buks 'Extreme Nonlinear Phenomena in NbN Superconducting Stripline Resonators', Phys. Lett. A 366, pp. 160-164 (2007). E. Segev, B. Abdo, O. Shtempluck, E. Buks, and B. Yurke'Prospects of Employing Superconducting Stripline Resonators for Studying the Dynamical Casimir Effect Experimentally', Phys. Lett. A 370, pp. 202-206 (2007). E. Segev, B. Abdo, O. Shtempluck, and E. Buks 'Utilizing Nonlinearity in a Superconducting NbN Stripline Resonator for Radiation Detection' , IEEE Trans. Appl. Sup., 17, pp. 271-274 (2007). E. Segev, B. Abdo, O. Shtempluck, and E. Buks 'Stochastic Resonance with a Single Metastable State: Thermal instability in NbN superconducting stripline resonators', Phys. Rev. B 77, 012501 (2008). E. Segev, O. Suchoi, O. Shtempluck, and E. Buks ‘Self-oscillations in a superconducting stripline resonator integrated with a dc superconducting quantum interference device', Appl. Phys. Lett. 95, 152509 (2009). E. Segev, O. Suchoi, O. Shtempluck, Fei Xue, and E. Buks ‘Metastability in a nano-bridge based hysteretic DC-SQUID embedded in superconducting microwave resonator, arXiv:1007.5225v1 (2010).

64. Publication List E. Buks, S. Zaitsev, E. Segev, B. Abdo, and M. P. Blencowe, ‘Displacement Detection with a Vibrating RF SQUID: Beating the Standard Linear Limit’, Phys. Rev. E 76, 026217 (2007). E. Buks, E. Segev, S. Zaitsev, B. Abdo, and M. P. Blencowe, ‘Quantum Nondemolition Measurement of Discrete Fock States of a Nanomechanical Resonator’, EuroPhys. Lett., 81 10001 (2008). B. Abdo, E. Segev, O. Shtempluck, and E. Buks, ‘Observation of Bifurcations and Hysteresis in Nonlinear NbN Superconducting Microwave Resonators’, IEEE Trans. Appl. Sup., 16 (4), p. 1976, (2006). B. Abdo, E. Segev, O. Shtempluck, and E. Buks, ‘Nonlinear dynamics in the resonance line-shape of NbN superconducting resonators’, Phys. Rev. B 73, 134513 (2006). B. Abdo, E. Segev, O. Shtempluck, and E. Buks,‘Intermodulation gain in nonlinear NbN superconducting microwave resonators’,App. Phys. Lett. 88 , 022508 (2006). B. Abdo, E. Segev, O. Shtempluck, and E. Buks, ‘Escape rate of metastable states in a driven NbN superconducting microwave resonator’, J. App. Phys., 101, 083909 (2007). B. Abdo, E. Segev, O. Shtempluck, and E. Buks, ‘Signal Amplification in NbN superconducting resonators via Stochastic Resonance’, Phys. Lett. A 370, p. 449 (2007). B. Abdo, O. Suchoi, E. Segev, O. Shtempluck, M. Blencowe and E. Buks, ‘Intermodulation and parametric amplification in a superconducting stripline resonator integrated with a dc-SQUID’, Europhys. Lett. 85, 68001 (2009). G. Bachar, E. Segev, O. Shtempluck, S. W. Shaw and E. Buks, ‘Noise Induced Intermittency in a Superconducting Microwave Resonator’, Europhys. Lett. 89, 17003 (2009). Oren Suchoi, BaleeghAbdo, Eran Segev, Oleg Shtempluck, Miles Blencowe and Eyal Buks, ‘IntermodeDephasing in a Superconducting Stripline Resonator’, Phys. Rev. B 81, 174525 (2010).