Ultrawide-range photon number calibration using a hybrid system combining nano-electromechanics and superconducting circuit quantum electrodynamics

  1. Philip Schmidt,
  2. Daniel Schwienbacher,
  3. Matthias Pernpeintner,
  4. Friedrich Wulschner,
  5. Frank Deppe,
  6. Achim Marx,
  7. Rudolf Gross,
  8. and Hans Huebl
We present a hybrid system consisting of a superconducting coplanar waveguide resonator coupled to a nanomechanical string and a transmon qubit acting as nonlinear circuit element.
We perform spectroscopy for both the transmon qubit and the nanomechanical string. Measuring the ac-Stark shift on the transmon qubit as well as the electromechanically induced absorption on the string allows us to determine the average photon number in the microwave resonator in both the low and high power regimes. In this way, we measure photon numbers that are up to nine orders of magnitude apart. We find a quantitative agreement between the calibration of photon numbers in the microwave resonator using the two methods. Our experiments demonstrate the successful combination of superconducting circuit quantum electrodynamics and nano-electromechanics on a single chip.

Flux-driven Josephson parametric amplifiers: Hysteretic flux response and nondegenerate gain measurements

  1. Stefan Pogorzalek,
  2. Kirill G. Fedorov,
  3. Ling Zhong,
  4. Jan Goetz,
  5. Friedrich Wulschner,
  6. Michael Fischer,
  7. Peter Eder,
  8. Edwar Xie,
  9. Kunihiro Inomata,
  10. Tsuyoshi Yamamoto,
  11. Yasunobu Nakamura,
  12. Achim Marx,
  13. Frank Deppe,
  14. and Rudolf Gross
Josephson parametric amplifiers (JPA) have become key devices in quantum science and technology with superconducting circuits. In particular, they can be utilized as quantum-limited
amplifiers or as a source of squeezed microwave fields. Here, we report on the detailed measurements of five flux-driven JPAs, three of them exhibiting a hysteretic dependence of the resonant frequency versus the applied magnetic flux. We model the measured characteristics by numerical simulations based on the two-dimensional potential landscape of the dc superconducting quantum interference devices (dc-SQUID), which provide the JPA nonlinearity, for a finite screening parameter βL>0 and demonstrate excellent agreement between the numerical results and the experimental data. Furthermore, we study the nondegenerate response of different JPAs and accurately describe the experimental results with our theory.

Loss mechanisms in superconducting thin film microwave resonators

  1. Jan Goetz,
  2. Frank Deppe,
  3. Max Haeberlein,
  4. Friedrich Wulschner,
  5. Christoph W. Zollitsch,
  6. Sebastian Meier,
  7. Michael Fischer,
  8. Peter Eder,
  9. Edwar Xie,
  10. Kirill G. Fedorov,
  11. Edwin P. Menzel,
  12. Achim Marx,
  13. and Rudolf Gross
We present a systematic analysis of the internal losses of superconducting coplanar waveguide microwave resonators based on niobium thin films on silicon substrates. At millikelvin
temperatures and low power, we find that the characteristic saturation power of two-level state (TLS) losses shows a pronounced temperature dependence. Furthermore, TLS losses can also be introduced by Nb/Al interfaces in the center conductor, when the interfaces are not positioned at current nodes of the resonator. In addition, we confirm that TLS losses can be reduced by proper surface treatment. For resonators including Al, quasiparticle losses become relevant above \SI{200}{\milli\kelvin}. Finally, we investigate how losses generated by eddy currents in the conductive material on the backside of the substrate can be minimized by using thick enough substrates or metals with high conductivity on the substrate backside.

Spin-boson model with an engineered reservoir in circuit quantum electrodynamics

  1. Max Haeberlein,
  2. Frank Deppe,
  3. Andreas Kurcz,
  4. Jan Goetz,
  5. Alexander Baust,
  6. Peter Eder,
  7. Kirill Fedorov,
  8. Michael Fischer,
  9. Edwin P. Menzel,
  10. Manuel J. Schwarz,
  11. Friedrich Wulschner,
  12. Edwar Xie,
  13. Ling Zhong,
  14. Enrique Solano,
  15. Achim Marx,
  16. Juan José García-Ripoll,
  17. and Rudolf Gross
A superconducting qubit coupled to an open transmission line represents an implementation of the spin-boson model with a broadband environment. We show that this environment can be
engineered by introducing partial reflectors into the transmission line, allowing to shape the spectral function, J({\omega}), of the spin-boson model. The spectral function can be accessed by measuring the resonance fluorescence of the qubit, which provides information on both the engineered environment and the coupling between qubit and transmission line. The spectral function of a transmission line without partial reflectors is found to be Ohmic over a wide frequency range, whereas a peaked spectral density is found for the shaped environment. Our work lays the ground for future quantum simulations of other, more involved, impurity models with superconducting circuits.