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Surface Dielectric and Quasiparticle Loss in Transmon Qubits Chen Wang

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Surface Dielectric and Quasiparticle Loss in Transmon Qubits Chen Wang Surface Dielectric and Quasiparticle Loss in Transmon Qubits Chen Wang Department of Applied Physics, Yale University Acknowledgments Yvonne Gao, Chris Axline,… All members of Schoelkopf lab & Devoret lab & Yale cQED theorists Workshop on Decoherence in superconducting qubits—JQI, College Park, MD, 2016/4/22 List of Contents Mechanisms of qubit relaxation (T1) to be discussed: Ø Surface dielectric loss: C. Wang et al. Appl. Phys. Lett. 107, 162601 (2015) Ø Quasiparticle-induced dissipation: C. Wang et al. Nat. Commun. 5, 5836 (2014) Ø Seam conduction loss: T. Brecht et al. Appl. Phys. Lett. 107, 192603 (2015) Seamless design: C. Axline et al. (in preparation) Circa 2012 T1 ~ 1-3 µs e.g. A. Houck et al. (2008) T1 ~ 50-100 µs JJ 1 mm H. Paik et al. (2011) Questions: Why, and what’s next? 250 μm 5 Dissipation Channels in Qubit Circuit environment junction junction environment capacitance capacitance inductance inductance Transmon: 95% 5% 95% 5% C CE J LJ LE cap cap ind ind G G Grad E J GJ GE TLS? TLS? QP? QP? radiation Total Loss Rate = ∑ Loss rate contribution from each element = ∑ (Relative weight of element) x (Lossiness of element) Participation ratio 1/Quality factor Lessons Learned “The small Josephson junction is (or can be) very very good.” From fluxonium (I. Pop et al. Nature 2014) and Cooper-pair box (Z. Kim et al. PRL 2011) “Planar resonators with larger feature size have better Q.” From several studies of resonator Q vs. geometry (H. Wang et al. APL 2009; J. M. Sage et al. JAP 2009; K. Geerlings et al. APL 2012; A. Megrant et al. APL 2012, …) C CE J LJ LE cap cap ind G G ind Grad E J GJ GE TLS? TLS? QP? QP? radiation Transmon in 3D Cavity as a Test-bed of Surface Loss Type B ü No uncontrollable radiation (“Gap Capacitor”) loss in a 3D cavity Type A ü Fab together for consistent (“Big pads”) material quality 2 mm 1 mm Similar idea: o. Dial et al. SuST 29, 044001 (2016) A Tale of Two Transmons Type B Extra filters, Semi-rigid cables, Type A Replace S-S infra-red Teflon-retracted absorbers components couplers s) µ ( 2 mm 1 mm 1 T 4 consecutive cooldowns in 2013 Magnetic Field Dependence of Gap-Capacitor Transmon in Al Cavity Cooling the qubit in a moderate magnetic field improves T1 ! Field polarity does not matter (zero field point confirmed) Data from Device B2 (10 µm gap capacitor) 1 mA ~ 8 mG Magnetic Field Dependence of Gap-Capacitor Transmon in Al Cavity 2 Two sharp transitions with applied field Bk ~ Φ0/L Device B2 Magnetic Field Dependence of Large-Pad Transmon in Al Cavity “Type A device” Microwave Injection of Quasiparticles C. Wang et al. Nature Communications 5, 5836 (2014) Similar technique applied to fluxonium qubit: U. Vool et al. PRL 113, 247001 (2014) Measurement of Quasiparticle Decay Transmon Qubit t = 0 Measurement of Quasiparticle Decay Transmon Qubit T1 = 1.0 µs Short Time Scale Measurement of Quasiparticle Decay T1 = 2.3 µs T1 = 1.0 µs Measurement of Quasiparticle Decay T1 = 5.5 µs T1 = 2.3 µs T1 = 1.0 µs Earlier experiment on quasiparticle decay in a phase qubit M. Lenander et al. PRB (2011) Demonstration of Quasiparticle Recombination ! !!!! !! = = ! !!" + !!"! Type B transmon !! ℏ! 1/t High QP density Fast QP decay Low QP density 5 5 Slow QP decay τss = 18 ms < 3x10-6 Settling !! !" = −!!! + !! !" !" “QP decay time towards a steady-state” τ = 18 ms B = 0 ss Demonstration of Quasiparticle Trapping one decay rate for large range of QP densities ! Type A transmon 250 µm High QP density Fast QP decay Low QP density Same fast QP decay τss = 1.5 ms < 3x10-7 !! !" = −!! + !! !" !" Single exponential suggests a single-particle loss mechanism. B = 0 “QP trapping”, trapping rate s = 1/τss = 1/(1.5 ms) Controlling QP Dynamics In-situ by Magnetic Field Type B Device B1 5 5 QP dynamics crosses over from recombination-dominated to trapping-dominated with increasing cooling magnetic field. C. Wang et al. Nat. Commun. 5, 5836 (2014) Quasiparticle Trapping due to Magnetic Field Penetration 15 µm for B1 15 µm for B1 10 µm for B2 10 µm for B2 Individual vortices!! Previous observation of QP loss in magnetic field of several Gauss: J. N. Ullom et al., Appl. Phys. Lett. (1998) Quantized Trapping Rate due to Individual Vortices All vortices are created equal! • Subtract a “background trapping rate” (yet to be understood) • Multiply by total device area (A) Single vortex “trapping power”: P C. Wang et al. Nat. Commun. 5, 5836 (2014) Single Vortex Trapping Power 2P ≈ 0.12 cm2/s P ≈ 0.06 cm2/s 0 Trapping rate x Device area Total trapping power of N vortices the macroscopic observable the microscopic intrinsic property Interplay of QP Trapping and Diffusion For high magnetic field: • Enough trapping power to deplete QP in the pad • Trapping rate limited by diffusion through the lead • QP diffusion constant at 20 mK measured: D = 18 cm2/s Single Vortex as a Quasiparticle Trap is Both Weak and Strong Weak: P << D A quasiparticle passing by a vortex is rarely trapped 0.067 cm2/s 18 cm2/s A vortex is the dominant quasiparticle decay Strong: P >> R x A 0 channel compared with weak recombination 0 vortex 1 vortex Improved Qubit Coherence by Vortices! Unambiguous evidence of non-equilibrium quasiparticles limiting T1 of a transmon Vortices reduce QP lifetime T2E T 1 Background QP density is reduced τss Less dissipation due to QP tunneling Short live the quasiparticles, long live the qubit! Also show field-cool improvement: Fluxonium: U. Vool et al. PRL (2014); CPW resonator: I. Nsanzineza et al., PRL (2014) Improved Qubit Coherence by Vortices! Unambiguous evidence of non-equilibrium quasiparticles limiting T1 of a transmon Vortices reduce τss QP lifetime T2E Background QP density is reduced T1 Less dissipation due to QP tunneling Short live the quasiparticles, long live the qubit! Also show field-cool improvement: Fluxonium: U. Vool et al. PRL (2014); CPW resonator: I. Nsanzineza et al., PRL (2014) Analysis of QP Induced Qubit Dissipation and QP Generation Rate 1) Stray QP generation rate: g ~ 1 x 10-4 /s 2) Relaxation rate due to other mechanisms: Γex = 1 / (26 µs) for B1, 1 / (17 µs) for B2 Geometry Dependence of Transmon T1 Type A 250 µm Type B x x Measured with B ~ 30 mG A1 A2 A3 B4 (x=3) B2 (x=10) B1 (x=15) B3 (x=30) 75 µs 66 µs 95 µs 7.5 µs 19 µs 25 µs 31 µs Surface Dielectric Participation Ratio energy stored in element i 1 P P = = i i total energy cap ∑ Q Qi Example: Metal-air interface for a rectangular 3D cavity (TE101) E Energy in vacuum: 1 1 U = ε E 2 V = E 2 Ad vac 2 0 vac vac 2 vac E Energy in MA interface: 1 2 1 1 2 U MA = εrε0 EMA VMA = Evac 2AtMA 2 2 εr 1 2tMA 1 2×3nm −7 Pi = ≈ =1.2×10 εMA d 10 5mm Surface Dielectric Participation Ratio Example: Coplanar waveguide The participation ratio for all three types of interfaces scale inversely with the “pitch” size (w or g, assuming w/g is a constant or order unity): ε 2t 10−2 1 2t 10−4 r P ~ ~ PMS , PSA ~ ~ MA 10 g (g / µm) 10εr g (g / µm) Cross-sectional (2D) numerical simulation: (assuming translation symmetry) J. Wenner, Appl. Phys. Lett. 99, 113513 (2011) M. Sandberg, Appl. Phys. Lett. 100, 262605 (2012) The Challenge of Computing Surface Participation in 3D Qubits E&M simulation of 3D qubits: Have to discretize to < t ~ 3 nm for energy in surface layer to converge (Computationally infeasible) Surface charge distribution of a half-infinite metal plane: ++ + + + x A Two-Step Approach for Computing Surface Participation in 3D Qubits Assumption: Field scaling near the edge is independent of far-away boundary conditions Perimeter Area Energy = Line Energy x Scaling Factor C. Wang et al. Appl. Phys. Lett. 107, 162601 (2015) A Two-Step Approach for Computing Surface Participation in 3D Qubits C. Wang et al. Appl. Phys. Lett. 107, 162601 (2015) The Near-Junction Region Matters for Surface Participation Or maybe not? C Design B B (Gap-Capacitor) B Design A (Big-pads) Some other designs Design C Design D Proportionality of 1/T1 vs Surface Participation C B B C B Design A 1 PMS = ω + Γ0 T1 tanδMS −3 ⇒ tanδMS = 2.6 ×10 , Γ0 ≈ 1/ (300µs) Participation of the Three Interfaces Scale Similarly So we can not pinpoint which interface (MS, SA or MA) is responsible for loss 1 PMS = ω∑ + Γ0 T1 tanδMS −3 ⇒ tanδMS +1.2tanδSA + 0.1tanδMA = 2.6 ×10 , Γ0 ≈ 1/ (300µs) Summary on the Coherence of 3D Transmons* * of the “big-pad style” (Paik, et al. PRL 2011) Ø The major limiting factor is still surface dielectric loss ! Ø We have a good estimate of vortex microwave loss: B = 100 mG : Γ ~ 1/(100 µs) à Γ < 1/(1 ms) at B < 10 mG Ø We have a good estimate of quasiparticle dissipation: -4 -7 g ~ 1.0 x 10 , τss ~ 1 ms: xqp = 1 x 10 à Γ ~ 1/(250 µs) Ø We have a bound on the sapphire substrate quality: Q > 12 M or Γ < 1/(300 µs) Can We Further Reduce Surface Participation? By making bigger, more separated electrodes? It’s harder than you think… because of the junction leads C Design C B (Gap-Capacitor) B Design A (Big-pads) Can be Achieved with Suspended Josephson Junction A few attempts with qubits on silicon substrate XeF2 etch DRIE (Bosch process) 100 µm 500 nm ü Suspension improves T1 ✖ But on Si substrate, our surface loss tangent is much worse Y.
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