Fractal superconducting resonators for the interrogation of two-level systems
Doktorsavhandling, 2014

In this thesis we use high-Q superconducting thin-film microwave resonators to interact with several types of quantum mechanical two-level systems. Such a resonator is used as the central building block in a cryogenic near-field scanning microwave microscope (NSMM) to reach a completely new regime of NSMM operation. In this regime where the superconducting resonator is only populated with a small number of photons, we demonstrate a capacitance sensitivity down to 64x10^(-21) Farad/rtHz and nanoscale resolution, which is sufficient to apply this scanning probe technique to quantum coherent objects. Such a 'coherent'-NSMM enables several new applications: for example to study the interaction of the NSMM probe with two-level defects in samples and to characterize artificial two-level systems (qubits), which eventually could lead to better understanding of decoherence mechanisms in superconducting quantum circuits. We demonstrate the ability to reach this regime in a sample consisting of a Cooper-pair box (CPB) weakly coupled to a superconducting resonator. In the strong driving regime we observe Landau-Zener-Stückelberg interference and we discover a new type of relaxation mechanism in the strongly driven CPB that involves pair breaking and quasiparticle tunneling. It results in a recovered parity of the CPB and a population inversion of the dressed states. Not only does this demonstrate the applicability of NSMM for qubit characterization, but the quasiparticle mediated population inversion also becomes suitable for robust charge sensing in a scanning probe setup. To integrate the superconducting resonator onto our NSMM probe we develop a new type of resonator design - the fractal design - that have a very small external dipole moment allowing for a compact resonator. Another advantage of the fractal resonator is its resilience to magnetic fields. We show that the fractal resonator, after further optimization, can maintain quality factors above 10^5 in applied fields of more than 400 mT, something that becomes particularly useful for the interrogation of spin ensembles coupled to the resonator. We demonstrate that it is possible to detect down to 5x10^5 spins/rtHz in a very small volume coupled to a fractal resonator. Furthermore, the low dipole moment of the fractal resonator allows us to also introduce DC bias into the resonator without degrading its Q-factor. This is an important technological step that allows us to interact with new materials where spins can be quickly and locally manipulated using electric fields and we demonstrate the first steps in this direction with ensembles of manganese doped ZnO nanowires and frustrated molecular Cu spin triangles. The measurements achieve a very high sensitivity thanks to the Pound-Drever-Hall locking technique used. We develop this technique such that both resonance frequency and quality factor can be monitored with very high accuracy in real time. The demonstrated stability is ~30 Hz/rtHz for frequency readout and we can determine the Q-factor with a precision of 34 dB/rtHz.

Cooper-pair box


electron spin resonance

two-level systems

atomic force microscopy


near-field scanning microwave microscopy

Superconducting resonators

circuit quantum electrodynamics

Kollektorn, MC2
Opponent: Prof. Oleg Astafiev, Royal Holloway, University of London


Sebastian Erik de Graaf

Chalmers, Mikroteknologi och nanovetenskap (MC2), Kvantkomponentfysik

Effects of quasiparticle tunnelling in a circuit-QED realization of a strongly driven two-level system

Journal of Physics B: Atomic, Molecular and Optical Physics,; Vol. 46(2013)p. Art. no. 224019-

Artikel i vetenskaplig tidskrift

Magnetic field resilient superconducting fractal resonators for coupling to free spins

Journal of Applied Physics,; Vol. 112(2012)p. 123905-

Artikel i vetenskaplig tidskrift

A near-field scanning microwave microscope based on a superconducting resonator for low power measurements

Review of Scientific Instruments,; Vol. 84(2013)p. 023706-

Paper i proceeding


Nanovetenskap och nanoteknik (SO 2010-2017, EI 2018-)




Den kondenserade materiens fysik



Technical report MC2 - Department of Microtechnology and Nanoscience, Chalmers University of Technology: 269

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 3630

Kollektorn, MC2

Opponent: Prof. Oleg Astafiev, Royal Holloway, University of London

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