Leo Uhre Jakobsen

Low-energy spectrum of double-junction superconducting circuits in the Born-Oppenheimer approximation

  1. Leo Uhre Jakobsen,
  2. Ksenia Shagalov,
  3. David Feldstein-Bofill,
  4. Morten Kjaergaard,
  5. Karsten Flensberg,
  6. and Svend Krøjer
The superconductor-insulator-superconductor Josephson junction is the fundamental nonlinear element of superconducting circuits. Connecting two junctions in series gives rise to higher-harmonic
content in the total energy-phase relation, enabling new design opportunities in multimode circuits. However, the double-junction element hosts an internal mode whose spectrum is set by the finite capacitances of the individual junctions. Using a Born-Oppenheimer approximation that treats the additional mode as fast compared to the qubit mode, we analyze the double-junction circuit element shunted by a large capacitor. Here, we derive an effective single-mode model of the qubit containing a correction term owing to the presence of the internal mode. We explore experimentally relevant parameter regimes and find that our model accurately describes the low-energy spectrum of the qubit. We further discuss how eliminating the internal degree of freedom affects the system’s periodic boundary conditions and how this leads to non-uniqueness in performing the Born-Oppenheimer approximation. Finally, we analyze the harmonic content of the double-junction element and discuss its sensitivity to charge noise.
arxiv pdf

Higher Josephson harmonics in a tunable double-junction transmon qubit

  1. Ksenia Shagalov,
  2. David Feldstein-Bofill,
  3. Leo Uhre Jakobsen,
  4. Zhenhai Sun,
  5. Casper Wied,
  6. Amalie T. J. Paulsen,
  7. Johann Bock Severin,
  8. Malthe A. Marciniak,
  9. Clinton A. Potts,
  10. Anders Kringhøj,
  11. Jacob Hastrup,
  12. Karsten Flensberg,
  13. Svend Krøjer,
  14. and Morten Kjaergaard
Tunable Josephson harmonics open up for new qubit design. We demonstrate a superconducting circuit element with a tunnel junction in series with a SQUID loop, yielding a highly magnetic-flux
tunable harmonic content of the Josephson potential. We analyze spectroscopy of the first four qubit transitions with a circuit model which includes the internal mode, revealing a second harmonic up to ∼10% of the fundamental harmonic. Interestingly, a sweet spot where the dispersive shift vanishes is achieved by balancing the dispersive couplings to the internal and qubit modes. The highly tunable set-up provides a route toward protected qubits, and customizable nonlinear microwave devices.
arxiv pdf