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Readout SQUID

Readout SQUID. Measurements of the 1/f noise in Josephson Junctions and the implications for qubits Jan Kycia, Chas Mugford- University of Waterloo Michael Mueck- University of Giessen, Germany John Clarke- University of California, Berkeley. The Group. Chas Mugford 1/f noise. Shuchao Meng

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Readout SQUID

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  1. Readout SQUID Measurements of the 1/f noise in Josephson Junctions and the implications for qubitsJan Kycia, Chas Mugford- University of WaterlooMichael Mueck- University of Giessen, GermanyJohn Clarke- University of California, Berkeley

  2. The Group Chas Mugford 1/f noise Shuchao Meng SQUID-sSET Lauren Lettress TES sensors Jeff Quilliam Ho: YLiF4 Nat Persaud Liquifier Jeff Mason SQUID NMR

  3. dc-SQUID The most sensitive magnetometer ~1 µFo/ (Hz) 1/2 Ib Io Io V L Lin

  4. Josephson Junctions Oxide barrier Superconductor, 1 2 2 IC The superconducting order parameters are: The phase difference between the superconductors is  =  2 -  1. As the two superconductors are brought closer together, allowing electrons to tunnel, the phases start to interact. Josephson (1962) predicted a phase dependent energy = -EJ cos, where EJ = = . , 1 = |1(x)| ei1 , 2 = |2| ei2 hIco h D(0) 2e (2e)2 RN d2eV dt h = IS = Ico sin (),

  5. Resistively and Capacitively Shunted Junction Model EJ VdV R dt I = Icosin  + + C C h d 2e dt Use V = , R hC d2 h d 2e dt2 2eR dt + + Ico sin  = I IS = Ico sin (), d2eV dt h = h D(0) (2e)2 RN EJ = Tilt  I position   velocity  V One period =Fo Tilted washboard model is the mechanical analog, with a particle of mass ~ C, moving along an axis, , in a potential, U() = -Icocos  - I, with a viscous drag force, . h d 2eR dt

  6. J F/2L Fo/L Imax F/Fo 1 2 F/Fo 1 2 The DC SQUID I J I/2 +J I/2 -J F V F/Fo 1 2

  7. Lfeedback Ib Io Io V L Lin A flux locked loop using a high frequency flux modulation is used to provide a flux to voltage converter with fixed gain and large dynamic range. V dV F/Fo 1 2 dF

  8. Magnified Image of DC SQUID dc SQUID 2x2µm Junctions Input coil Shunts provide required dissipation but also produce noise. Palladium Shunt resistor

  9. SQUID as a near-quantum-limited amplifier at 0.5 GHz M. Mueck, J. B. Kycia, and John Clarke, APL 78, 967 (2001). Find “Self Heating” at low temperatures Loss of temperature dependence, at low temperatures, is frequency independent Wellstood et al found that self heating can be reduced by adding a cooling pad to the shunt resistor.

  10. The Hamiltonian, H = -EJcos1-EJcos2 + Ec(Q/e)2 if EJ / EC > 1,  is a good quantum number, Q fluctuates. if EJ / EC < 1,  fluctuates, Q is a good quantum number. Phase fluctuations allow the particle to diffuse down the washboard; d  d t  0  V  0

  11. Transport Measurement Circuit with filters Screened room Lock-in reference input. . AC bias  0.1 nA x100 . . x1000 Copper powder filters LC filters 300 K RC filters 4.2 K Cu filters Follow design of Martinis, Devoret, Clarke, Phys. Rev. B, 35, 4682 (1987). Cu filters 20 mK Sample

  12. Temperature and dissipation dependence of sSET RK Rg • dissipation, g = g T2 G ~ ; ohmic G ~ ; transmission line (Ingold, Grabert PRL 1999) g1/3 T5/3 (Wilhelm, Schön, and Zimanyi)

  13. New configuration Provides in situ control of EJ , Ec ,g and T. H = -EJ(f)cos1-EJ (f)cos2 + Ec(Q/e)2 + H(R2deg)

  14. 1 m SEM image courtesy of Dan Grupp.

  15. Rimberg, Ho, Kurdak, Clarke PRL 1997 Wagenblast, Otterlo, Schon, Zimanyi PRL 1997 Good review: Leggett, Chakravarty, Dorsey, Fisher, Garg, Zwerger Rev Mod Phys (1987).

  16. Superconducting Qubits: Charge based qubits: “Cooper pair box” Demonstrated Rabi oscillation: Nakamura et al, Nature 398, 786 (1999). Improved read out scheme, decoherence time ~ 0.5 ms (Q = 25,000): Vion et al, Science 296, 886 (2002). Flux based qubits: Demonstrated energy splitting dependence on applied magnetic flux: Friedman et al, Nature 406 43 (2000), van der Wal et al, Science 290, 773 (2000).Coherent Oscillations observed with a dephasing time of 20 ns and a Relaxation time of 900 ns: Chiorescu et al, Science 299, 1869 (2003). Phase based qubits: Exhibited Rabi oscillations between ground state and 1st excited state of a current biased Josephson junction in its zero-voltage regime: Yu et al, Science 296, 889 (2002), Martinis et al PRL 89, 117901 (2002).

  17. External flux noise • Nyquist noise currents in nearby metal objects • Noise in the measurement scheme • Motion of trapped charge • 1/f “flicker” noise in the critical current of the Josephson Junction Sources of Decoherence: • The goal of our experiment is to measure the level of 1/f noise in the critical current of a resistively shunted Josephson Junction. • Once the measurement is made, we can: • Measure the temperature, time, material, and fabrication parameter dependence of the 1/f noise level. • Estimate the upper limit of the coherence time of superconducting qubits due to these noise sources. • Make optimal qubits by selecting the device configuration to minimize the noise sources.

  18. Flux Qubit • Small loop with three Josephson junctions produces the flux qubit. - Hysteretic DC SQUID is used to read the flux state. van der Wal et al, Science 290, 773 (2000). Chiorescu et al, Science 299, 1869 (2003).

  19. Ramsey Fringes in Flux Qubit I. Chiorescu, Y. Nakamura, C.J.P.M. Harmans, and J.E. Mooij, Science 299, 1869 (2003).

  20. “Quantronium” D. Vion, A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina,D. Esteve, M. H. Devoret, “Manipulating the Quantum State of an Electrical Circuit”, SCIENCE, 296,886 (2002).

  21. “Phase” Qubit Decoherence in Josephson Phase Qubits from Junction Resonators Simmonds, Lang, Hite, Nam, Pappas, and Martinis, Phys Rev Lett, 93, 077003-1, (2004).

  22. a b c e f d Resonances Observed -- likely due to defects (fluctuators) Decoherence in Josephson Phase Qubits from Junction Resonators Simmonds, Lang, Hite, Nam, Pappas, and Martinis, Phys Rev Lett, 93, 077003-1, (2004).

  23. 1/f Noise: Dutta-Horn ModelDutta and Horn, Rev Mod Phys, 53, 497 (1981)Random telegraph signal is produced by random transitions between the states of a double potential well. Define 1/t1and 1/t2as the probability of a transition from state 1 to 2 and 2 to 1 respectively. If 1/t = 1/t1 = 1/t2then the power spectrum is a Lorentzian of the formS(f)  t / [1+(2pft)2]If the transitions are thermally activated then the characteristic time is given byti = toexp(Ui/kBT), where 1/tois an attempt frequency.S(f,T) is linear in T because the kernel moves through the distribution of RTS’s as the temperature varies, selecting only those processes that have characteristic frequencies in the window of interest.

  24. electron barrier I trapped s.c.1 height no electron barrier trapped s.c.2 trap z V Mechanism Behind 1/ƒ Critical Current Fluctuations in Josephson Junctions The currently accepted picture of the mechanism behind critical current fluctuations involves traps within a Josephson junction. An electron is trapped in the tunnel barrier and is subsequently released. While trapped, the barrier height and hence critical current is modified temporarily. For a junction of area A the change in critical current is modified by the change in area due to an electron A. Ic=(A/A)Ic

  25. Dephasing due to current fluctuations and critical current fluctuations Critical current fluctuations with a l/f spectral density are potentially a limiting source of intrinsic decoherence in superconducting qubits.. W= the frequency of oscillation between the +0.5Foand –0.5Fostate.

  26. Dale Van Harlingen et al, PRB (2004).

  27. Methods of Measuring 1/ƒ Noise of the Critical Current of a Josephson Junction • Critical current fluctuations have been measured in the non-zero voltage state. • Is the 1/f noise the same when the junction is in the zero voltage state? We measured the critical current fluctuations using the same SQUID operated as an RF SQUID in the dispersive regime. F.C.Wellstood, PhD thesis, University of California, Berkeley 1988. B.Savo, F.C.Wellstood,, and J.Clarke, APL 49, 593 (1986). V.Foglietti et al., APL, 49, 1393 (1986) R.H.Koch, D.J. van Harlingen, and J.Clarke, APL, 41, 197 (1982). F.C. Wellstood, C. Urbina, John Clarke, APL, 5296, 85 (2004). Fred Wellstood’s Thesis Berkeley

  28. Comparing different junctions:Invariant noise parameter Normalize current noise spectrum to the critical current Choose T = 4.2K and 1Hz. But this does not take into account junction area. For a junction of area Aand if the area blocked by a single trap isDA, then change in critical current for a single fluctuator isDIc = (DA /A)Ic If nis the number of traps per area, then the critical current spectrum should scale as: SI2~n A (DA /A)2Ic2 = n DA2 (Ic2 /A) Van Harlingen et al found thatall values of n DA2 remarkably similar for all measured junctions. SI2scales as(Ic2 /A)

  29. Scaled quantity invariant quantity (van Harlingen et al. PRB 2004) Wellstood et al. average value of 6 junctions 26 Lukens et al. IEEE 2005 Also see “slower than linear” T dependence

  30. Measuring 1/ƒ Noise Due to Critical Current Fluctuations in the Non-Zero Voltage State Readout SQUID DC SQUID and read-out SQUID circuit • The sample SQUID is voltage biases. • The readout SQUID measured the current running though the 2W resistor. • Fluctuation in the critical current leads to a redistribution of the currents • flowing through the junction and the resistor.

  31. rf tight - low field -superconducting sample container rf tight SMA connectors Readout SQUID Sample SQUID Superconducting lead shield rf tight copper sample container Coaxial µ-metal shields

  32. 1/f noise in DC biased junction

  33. Applying Current Bias Reversal DC current bias method Current bias reversal eliminates 1/f noise, therefore this 1/f noise is not due to flux noise.

  34. Critical current fluctuations due to a single fluctuator Ic = 2.5uA DIc = 0.65nA This corresponds to a trap radius of ~ 5.6nm

  35. Reading out an rf SQUID in the Dispersive Regime Vrf ƒmod rf SQUID and FET amplifier circuit • A tank circuit is driven off-resonance with a 360-MHz current of fixed amplitude. • - The tank circuit voltage is read out with a low noise amplifier cooled to 4.2K. • Fluctuations in the critical currents of the two junctions modulate the SQUID • inductance and thus the resonant frequency of the tank circuit.

  36. Comparing the zero-voltage noise measurement method to the non-zero voltage noise measurement method • No difference between the measurements. • The 1/f noise is temperature dependent.

  37. Annealing Study Annealing lowers critical current and lowers noise

  38. Comparison of Noise Parameter Best Sample Van Harlingen et al. 12 Wellstood et al. 26 Lukens et al. 1.5

  39. Conclusion We have demonstrated that the l/f noise in a dc SQUID due to critical current fluctuations has the same magnitude in the zero voltage and non-zero voltage regime. Thus, the levels of critical current l/f noise measured by others in the nonzero voltage state should pertain to qubits operated at zero voltage. Measured noise of different junctions, reduce 1/f noise. Future Experiments Temperature dependence of 1/f noise down to dilution refrigerator temperatures. The dispersive method has no dissipation - best for low temperatures. We can cut away the shunt resistors to see if they are somehow responsible for noise. Continue varying processing parameters. Study dissipation is submicron Josephson junction.

  40. New Device will allow the in situ control of EJ, EC, and dissipation.

  41. Temperature and dissipation dependence of sSET

  42. Outline Describe how Josephson Junctions and SQUIDS work. Describe how superconducting qubits work. Explain why 1/f noise is relevant to superconducting qubits. - Present results on 1/f noise measurements.

  43. Tunable coupling via curent B.L.T. Plourde, J. Zhang, K.B. Whaley, F.K.W., T.L. Robertson, T. Hime, S. Linzen, P.A. Reichardt, C.E. Wu, and J. Clarke PRB 70, 140501(R) (2004). Bias current: Screening current: • Extra flux at constant bias • directly increases screening • increases γ → indirectly reduces screening

  44. rf SQUID • The SQUID hysteresis parameter is defined as: • If rf <1 the SQUID is dispersive. Ic is never exceeded • If rf >1 the SQUID is hysteretic or dissipative. Two kinds of behaviour are observed in rf SQUID loops depending of the “SQUID hysteresis parameter” rf. The difference is seen in the applied flux e vs the flux threading the loop . 1 rf <1 0 -1 0 1 rf >1 1 R IS 0 F F L -1 e 0 1

  45. Abstract Critical current fluctuations may be a major source of intrinsic decoherence of qubits made from Josephson junctions. We have measured the 1/f noise due to critical current fluctuations in macroscopic ( area  2  2 m2 ) Josephson junctions. We have exploited two ways for measuring critical current fluctuations, one way where we directly measure changes in the critical current of a voltage biased junction, and a second way in which we measure 1/f flux noise in an rf SQUID running in the dispersive mode. With both methods, we find the magnitude of the critical current fluctuations, at a temperature of 4.2K, to be Ic/Ic 10-5 at a frequency of 1 Hz.

  46. The Bloch sphere Convenient representation of the two-state Hamiltonian and state Beff

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