Qubits: Supraleitende Quantenschaltungen. (i) Grundlagen und Messung

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1 Braunschweiger Supraleiter-Seminar Seminar Qubits: Supraleitende Quantenschaltungen (i) Grundlagen und Messung Jens Könemann, Bundesallee 100, Braunschweig Q Φ 26. Mai 0/ 16

2 Braunschweiger Supraleiter-Seminar Qubits: Der Quanten-Computer auf Festkörperbasis (Supraleitende Quantenschaltungen) Inhalt Motivation/Einführung Experimentelle Technik Charge-Phase Qubits in der PTB Zusammenfassung 26. Mai 1/ 16

3 States of a quantum bit - qubit (2-level quantum system) excited state 1 Basis states ground state 0 ψ = a 0 + b 1, where a and b are two complex numbers, a 2 + b 2 = 1. For example: a = 1, b = 0 or a = 1/ 2, b = i/ Mai 2/ 16

4 Possible realizations of qubits: hardware Ions, neutral atoms, Optical/microwave Single quanta in cavity... Solid State realizations Quantum dots Solid state NMR Josephson junction (building-block of superconducting circuits) [parametric inductance with low intrinsic dissipation]... Advantage of Solid state approach is its potential scalability! 26. Mai 3/ 16

5 Possible realizations of qubits: hardware Ions, neutral atoms, Optical/microwave Single quanta in cavity... Solid State realizations Quantum dots Solid state NMR Josephson junction (superconducting circuits)... S I S Classical: nonlinear classical element Quantum: Duality of charge and phase 26. Mai 4/ 16

6 Quantum Effects in Josephson Junctions: Josephson Qubit classical Josephson effect Provides hardware for quantum-limited measurements Good variable Φ or ϕ Good variable Q or N E J /E c» 1 Quantum behavior E J /E c «1 classical SET effect λ=e J /E c Phase qubit Flux qubit Charge qubit Charge-phase qubit A Josephson qubit: 2-level system

7 Superconducting (Josephson) qubits Based on large JJ Based on small JJ Phase Flux Charge-phase Charge CP box ϕ Φ Φ/ϕ Q Q ϕ NIST Φ TU-Delft Q ϕ CEA-Saclay Q Chalmers

8 Charge-Phase-Qubits Schematic diagram Two lowest bands form basis { 0>, 1>} Φ Q Curvature of qubitenergy surface: Josephson-Inductance Microwaves n = 1 Degeneracy point n = 0 [A. Zorin, JETP 98, 1250 (2004)] Qubit microwave spectroscopy, see e.g. Born et al., PRB 70, (2004)

9 Charge-phase qubits at PTB Mesurement set-up 26. Mai 8/ 16

10 Measurement technique Josephson-Physics (70s): non-hysteretic rf-squids Idea: Measurement of reactive part of Qubit-impedance [ R. Rifkin and B.S. Deaver, Phys. Rev. B 13, 3894 (1976)]. I RF I 0 sin ω RF t Circuit acts as qubit or electrometer Zorin, Physica C 2002 V 0 (ψ)sin[ω RF t + θ(ψ)] V g L QUBIT = L Jos + L L Jos Dispersive, read-out (Zero dc voltage across the junction -> vanishing dissipation at low frequency drive!) -> minimum back-action [E. Il'ichev et al., Rev. Sci. Instrum. 72, 1882 (2001).] 26. Mai 9/ 16

11 Experimental set-up Dilution refrigerator T=20 mk 26. Mai 10 / 16

12 Charge-phase qubits at PTB Investigations of Nb qubits 26. Mai 11 / 16

13 Sample layout Nb tank coil Gradiometer-Design 1 mm Nb Drain Island Josephson contact Source Integrated Qubit-test structure with Nb-tank circuit and Nb-Bloch transistor (fabricated using CMP-technology) Gate [ R. Dolata et al., J. Appl. Phys. 97, (2005) ]

14 Resonance curves 0,08 0,06 T = 20 mk ϕ dc =0 ϕ dc =π I rf =16 na 0,16 0,12 V T (mv) 0, MHz 0.36 MHz 0,08 a / a 0 (1) 0,02 0,04 L I S L J T L T L ϕ J M 2e h ϕ 2 ( ϕ,... ) ( ϕ,... ) E( ϕ,... ) ( ϕ,... ) = I ( ϕ,... ) S 1 I 0,00 rf =8 na 0,00 75,5 76,0 76,5 77,0 f 0 f (MHz) Frequency shift: δf = k 2 Φ βl L J (2πI C) ( ϕ, Q) f 13 / 16

15 Mapping of the ground state of Nb charge-phase qubits E J =50μeV, E c =80μeV E J =95μeV, E c =45μeV Zangerle et al., PRB 73, (2006) α -> L J -1 ~ (d 2 E/dϕ 2 ) -Observed gate-modulation period is 1e due to qp poisoning of the island Large (small) α corresponds to large (small) surface curvature

16 Charge-phase qubits at PTB Investigations of Al qubits 26. Mai 15 / 16

17 Peculiarities in Al-gate curves: Quasiparticles dispersive read-out Q Φ I V I cos ωt V cos (ωt + α) Δφ ±30 20 qp-tunneling (suppressed) qp-tunneling (active) Angle α (degrees) e -2e -e 0 e 2e Q Φ Φ 0 /2: Admixture excited qubit state Voltage V G (mv) Könemann et al., Phys. Rev. B (2007)

18 Summary Chalmers Experiment at PTB: Investigation of charge-phase qubit with dispersive rf-readout Mapping of qubit energy surface (ground state with admixture of excited state) New phenomenon of quasiparticle-induced qubit excitations CEA TUD PTB CNRS SNS UNIKARL IPHT CNR UBARI UNIBASEL INN LMU Support by EU: Project EuroSQUIP (6th framework programm) LANDAU