Exploring parasitic Material Defects with superconducting Qubits

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1 Exploring parasitic Material Defects with superconducting Qubits Jürgen Lisenfeld, Alexander Bilmes, Georg Weiss, and A.V. Ustinov Physikalisches Institut, Karlsruhe Institute of Technology, Karlsruhe, Germany Two-Level-Systems (TLS): a major source of noise in microfabricated quantum devices Utilizing qubits to study individual TLS: - TLS tuning by mechanical strain, strain spectroscopy - mutual TLS interactions: origin of time-dependent fluctuations - noise spectroscopy - TLS-quasiparticle interactions KIT University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association

2 Two-Level-Systems: Tunneling Atom Model [1,2] in amorphous materials, atoms may tunnel between two positions: these tunneling systems couple via electric dipole moment mechanical strain energy classical quantum coordinate E tunnel energy [1] W.A. Phillips, J. Low Temp. Phys (1972) 2 [2] J. Lisenfeld: Anderson, Exploring Halperin, Material and Varma, Defects Philosophical with superconducting Mag. 25, Qubits 1 (1972) ε E E = TLS asymmetry 2 ε + ε 2, strain

3 TLS in microfabricated circuits and Josephson junctions TLS on surface oxides TLS are found in surface oxides in / on the substrate at interfaces in tunnel junctions in tunnel junctions TLS on substrate in Josephson junctions: E at interfaces TLS generate noise & dissipation in MOSFETs & single-electron transistors micro-mechanical resonators single-photon detectors, nanowires superconducting resonators and qubits hydroxide defects Appl. Phys. Lett. 97, (21) dangling bonds electrons trapped at interfaces: PRL 95, 4685 (25) Kondo- / Andreev Fluctuators PRB 84, (211) phononically dressed electrons PRB 87, (213) tunneling atoms Phys. Rev. Lett. 95, 2153 (25) 3 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

4 The Phase Qubit complete circuit J.M. Martinis et al., PRL 93, 773 (24) Hamilton-Operator Φext. 9 Φ 4 E J / E C 1 Potential for E J >> E C : EE E Φext. 9 Φ qubit manipulation via Rabi oscillation ϕ 4 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

5 Phase Qubit sample used in this work M. Steffen, J.M. Martinis et al., PRL 97, 552 (26) qubit junction flux bias coil Qubit coil fabricated at UCSB & CNF Al/AlOx JJ, SiN capacitor large junction ~ 1 µm 2 contains many TLS short coherence time: T 1 ~1 ns, T 2 ~ 1 ns qubit inductance Φˆ DC-SQUID loop qubit readout SQUID 5 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

6 Defect-Qubit - interaction t = 2 nm Φˆ qubit readout SQUID Qubit-TLS interaction: via TLS electrical dipole moment p Qubit: Φˆ 2 Qˆ 2 H ˆ = + + 2L 2C el. Field: Qˆ E = t C 6 J. Lisenfeld: Exploring Material Defects with superconducting Qubits E J 1 V/m Dipole interaction: for p g = 2 D = 2.2 eå = p E h 1 MHz qubit-tls coupling strength

7 Defect Qubit - Interaction Frequency Domain: defects cause avoided level crossings Time Domain: qubit decays due to energy relaxation.3 1 MHz 2g.5 T 1 1ns f (GHz) t (ns) frequency f (GHz) flux bias Φ.9 t (ns) 1 frequency cf.: R.W. Simmonds, K.M. Lang, D.A. Hite, D.P. Pappas, and J.M. Martinis, PRL Decoherence 93, 773 (24) Mechanisms in sc. Qubits II (DiSQII), 9 J. Yoni Lisenfeld: Shalibo, Exploring Matthew Material Neeley, Defects John with M. superconducting Martinis, NadavQubits Katz et al., PRL 15, 1771 (21).

8 Defect Qubit - Interaction Frequency Domain: defects cause avoided level crossings Time Domain: energy oscillates between qubit and defects.3 1 MHz 2g 1/ g.5 f (GHz) t (ns) frequency f (GHz) flux bias Φ.9 t (ns) 1 frequency cf.: R.W. Simmonds, K.M. Lang, D.A. Hite, D.P. Pappas, and J.M. Martinis, PRL Decoherence 93, 773 (24) Mechanisms in sc. Qubits II (DiSQII), 1 J. Yoni Lisenfeld: Shalibo, Exploring Matthew Material Neeley, Defects John with M. superconducting Martinis, NadavQubits Katz et al., PRL 15, 1771 (21).

9 Defect Qubit - Interaction Frequency Domain: defects cause avoided level crossings Time Domain: energy oscillates between qubit and defects.3 1 MHz.5 δp : qubit population loss TLS signal f (GHz) t (ns) δp 8 frequency f (GHz) flux bias Φ.9 4 t (ns) TLS signals for fixed t = 4 ns 11 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

10 TLS Strain Spectroscopy G. Grabovskij, J. Lisenfeld, G. Weiss, A.V. Ustinov et al., Science 338, 232 (212) electrical dipole moment TLS strain tuning qubit chip piezo V by deforming the sample using a piezo δp - tiny deformations L 1 7 /V L (compress 1 nm by 1-16 m) change TLS asymmetry: ε 2 MHz/V TLS signals for fixed t = 4 ns mechanical strain 4 t (ns) J. Lisenfeld: Exploring Material Defects with superconducting Qubits

11 TLS Strain Spectroscopy G. Grabovskij, J. Lisenfeld, G. Weiss, A.V. Ustinov et al., Science 338, 232 (212) TLS frequency ω 1 9 ω 1 TLS asymmetry 2 ε = + ε 2, strain TLS strain tuning qubit chip piezo V by deforming the sample using a piezo δp - tiny deformations L 1 7 /V L (compress 1 nm by 1-16 m) change TLS asymmetry: ε 2 MHz/V frequency (GHz) 6 piezo voltage V / strain ε δp 4 t (ns) TLS signals for fixed t = 4 ns 13 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

12 TLS Strain Spectroscopy G. Grabovskij, J. Lisenfeld, G. Weiss, A.V. Ustinov et al., Science 338, 232 (212) J. Lisenfeld, G. Grabovskij, J. Cole, C. Müller, G. Weiss, and A.V. Ustinov, Nature Commun. 6, 6182 (215) 9 frequency (GHz) 8 7 δp J. Lisenfeld: Exploring Material Defects with superconducting Qubits 5 75 strain / piezo voltage (V)

13 TLS Strain Spectroscopy G. Grabovskij, J. Lisenfeld, G. Weiss, A.V. Ustinov et al., Science 338, 232 (212) J. Lisenfeld, G. Grabovskij, J. Cole, C. Müller, G. Weiss, and A.V. Ustinov, Nature Commun. 6, 6182 (215) 9 frequency (GHz) 8 time-dependent frequency fluctuations 7 avoided level-crossings -25 strain / piezo voltage (V) J. Lisenfeld: Exploring Material Defects with superconducting Qubits

14 TLS Strain Spectroscopy G. Grabovskij, J. Lisenfeld, G. Weiss, A.V. Ustinov et al., Science 338, 232 (212) J. Lisenfeld, G. Grabovskij, J. Cole, C. Müller, G. Weiss, and A.V. Ustinov, Nature Commun. 6, 6182 (215) telegraphic switching two coherently coupled TLS irreversible shift 16 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

15 coherently interacting defects J. Lisenfeld, G. Grabovskij, C. Müller, J.H. Cole, G. Weiss, and A.V. Ustinov, Nature Communications 6, 6182 (215) signature in defect spectroscopy simulated spectrum of 2 coupled TLSs frequency (GHz) frequency (GHz) strain / piezo voltage (V) J. Lisenfeld: Exploring Material Defects with superconducting Qubits -4-2 strain / piezo voltage (V)

16 coherently interacting defects J. Lisenfeld, G. Weiss, A.V. Ustinov et al., Nature Communications 6, 6182 (215) interaction Hamiltonian: rotate to eigenbasis by angle, where minor contributions frequency (GHz) frequency (GHz) strain / piezo voltage (V) J. Lisenfeld: Exploring Material Defects with superconducting Qubits -4-2 strain / piezo voltage (V)

17 coherently interacting defects J. Lisenfeld, G. Weiss, A.V. Ustinov et al., Nature Communications 6, 6182 (215) frequency (GHz) strain / piezo voltage (V) 2 19 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

18 coherently interacting defects J. Lisenfeld, G. Weiss, A.V. Ustinov et al., Nature Communications 6, 6182 (215) frequency (GHz) strain / piezo voltage (V) 2 2 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

19 TLS interactions: source of fluctuations in qubits C. Müller, J. Lisenfeld, A. Shnirman, and S. Poletto, Phys. Rev. B 92, (215) cf. L. Faoro and L.B. Ioffe, PRB 91, 1421 (215): origin of phase noise in resonators fluctuations in energy relaxation rate e.g. 3D-Transmon (IBM) qubit origin: coupling between high-frequency TLS and thermal TLS fluctuations in TLS resonance frequency results in fluctuations of qubit s noise density TLS 21 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

20 coherent control of individual TLS J. Lisenfeld et al., Phys. Rev. B 81, 1511 (21) 8. frequency [GHz] TLS resonantly absorbs photons via a Raman transition involving a virtual qubit excitation full NMR-like TLS control via microwave pulse sequences TLS operation not degraded by qubit decoherence.5 P( 1 ) 7.8 bias flux [arb. units] 22 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

21 Noise Spectroscopy using single TLS as Quantum Spectrum Analyzers rotate TLS eigenbasis by strain γ, which depends linearily on applied piezo Voltage matrix elements: 1σ z = ω 1 measure decoherence rates with different protocols, ε ( γ ) 1σ z 1 = ω 1 frequency 2 ε ω = + 1 TLS asymmetry ε 2, strain γ energy relaxation ωs 6 1GHz obtain noise spectral density at different frequencies ω s Sγ ( ω s ) Ramsey ω S.5 MHz Γ ( ) 1 S γ ω1 ω 1 2 energy relaxation 6 1GHz ω S Spin-echo ω S 1 5 MHz Γ ϕ ε ω 1 2 ( ) Sγ ω S dephasing ω S 5MHz 23 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

22 Strain-dependence of TLS coherence times J. Lisenfeld, G. Schön, A. Shnirman, G. Weiss, A.V. Ustinov et al., Scientific Reports 6, (215) energy relaxation (1/T 1 ) symmetric pattern in Γ 1 can not originate in mutual TLS interactions S ( ω 1 ) golden rule: Γ S( ) 1 ω ε 2 (MHz) several TLS have a common maximum in Γ 1 around 7.4 GHz possibly coupling to same phonon mode 25 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

23 Strain-dependence of TLS coherence times J. Lisenfeld, G. Schön, A. Shnirman, G. Weiss, A.V. Ustinov et al., Scientific Reports 6, (215) energy relaxation Spin echo (T 2 *) Ramsey (T 2 ) 27 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

24 Temperature dependence of TLS coherence J. Lisenfeld et al., Phys. Rev. Lett. 15, 2354 (21) TLS energy relaxation rate exceeds phonon contribution 4 (ns) 2 T 1 excited state life time coth( E/2k B T) TLS decay at higher temperatures [1] caused by quasiparticles? c.f. J. L. Black, Glassy Metals I, Topics in Applied Physics 46, 167 (1981). Γ 1 decay rate coth( E/2k quasiparticles B temperature (K) T) test : 1) generate quasiparticles by injection or by raising the sample temperature 2) calibrate QP density using the qubit 3) measure TLS coherence times 28 [1] J. Lisenfeld: J. Lisenfeld Exploring et al., Material Phys. Defects Rev. with Lett. superconducting 15, 2354 Qubits (21)

25 injection of quasiparticles cf. M. Lenander et al., PRB 84, 2451 (211) drive 2 nd on-chip DC-SQUID with current I b > I C generated QPs diffuse to qubit s Josephson junction where they interact with TLS we expect a difference in QP density on the two JJ electrodes because of the sample layout qubit loop DC-SQUID 1 µm 29 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

26 Quasiparticle density calibration A. Bilmes, J. Lisenfeld, M. Marthaler, A.V. Ustinov et al., to be published (216) Use the qubit as a QP-detecor [1,2] the local superconduncting gap shrinks: Qubit resonance shift - increased energy relaxation pulsed QP injection, time domain x 1e6 x 1e-5 x 1e-4 cf. M. Lenander, H. Wang, Radoslaw C. Bialczak et al., PRB 84, 2451 Decoherence (211) Mechanisms in sc. Qubits II (DiSQII), 3 J. Lisenfeld: G. Catelani, Exploring J. Koch, Material R.J. Defects Schoelkopf, with superconducting M.H. Devoret Qubits, L.I. Glazman et al., PRL 16, 772 (211)

27 QP-induced decoherence of Two-Level Systems A. Bilmes, J. Lisenfeld, G. Weiss, A.V. Ustinov et al., to be published (216) Korringa-like QP-TLS-interaction: QP-TLS coupling depends on TLS location QP densities differ in injection experiment: fit [1] estimation of TLS location TLS1 TLS2 we observe: Imb=X qp (L) /X qp (R) [1] S. Zanker, M. Marthaler, and G. Schön, arxiv: v1 (216) 31 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

28 Summary: Exploring TLS with superconducting Qubits TLS are an important decoherence source for various microfabricated devices fluctuating qubit relaxation frequency-dependent Γ 1 R. Barends et al., PRL 111, 852 (213) superconducting qubits are ideal tools to study single TLS: TLS strain spectroscopy coherently coupled TLS noise spectroscopy frequency strain 32 J. Lisenfeld: Exploring Material Defects with superconducting Qubits

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