Granular aluminum: A superconducting material for high impedance quantum circuits

  1. Lukas Grünhaupt,
  2. Martin Spiecker,
  3. Daria Gusenkova,
  4. Nataliya Maleeva,
  5. Sebastian T. Skacel,
  6. Ivan Takmakov,
  7. Francesco Valenti,
  8. Patrick Winkel,
  9. Hannes Rotzinger,
  10. Alexey V. Ustinov,
  11. and Ioan M. Pop
Superconducting quantum information processing machines are predominantly based on microwave circuits with relatively low characteristic impedance, of about 100 Ohm, and small anharmonicity,
which can limit their coherence and logic gate fidelity. A promising alternative are circuits based on so-called superinductors, with characteristic impedances exceeding the resistance quantum RQ=6.4 kΩ. However, previous implementations of superinductors, consisting of mesoscopic Josephson junction arrays, can introduce unintended nonlinearity or parasitic resonant modes in the qubit vicinity, degrading its coherence. Here we present a fluxonium qubit design using a granular aluminum (grAl) superinductor strip. Granular aluminum is a particularly attractive material, as it self-assembles into an effective junction array with a remarkably high kinetic inductance, and its fabrication can be in-situ integrated with standard aluminum circuit processing. The measured qubit coherence time TR2 up to 30 μs illustrates the potential of grAl for applications ranging from protected qubit designs to quantum limited amplifiers and detectors.

Quasiparticle dynamics in granular aluminum close to the superconductor to insulator transition

  1. Lukas Grünhaupt,
  2. Nataliya Maleeva,
  3. Sebastian T. Skacel,
  4. Martino Calvo,
  5. Florence Levy-Bertrand,
  6. Alexey V. Ustinov,
  7. Hannes Rotzinger,
  8. Alessandro Monfardini,
  9. Gianluigi Catelani,
  10. and Ioan M. Pop
Superconducting high kinetic inductance elements constitute a valuable resource for quantum circuit design and millimeter-wave detection. Granular aluminum (GrAl) in the superconducting
regime is a particularly interesting material since it has already shown a kinetic inductance in the range of nH/◻ and its deposition is compatible with conventional Al/AlOx/Al Josephson junction fabrication. We characterize microwave resonators fabricated from GrAl with a room temperature resistivity of 4×103μΩ⋅cm, which is a factor of 3 below the superconductor to insulator transition, showing a kinetic inductance fraction close to unity. The measured internal quality factors are on the order of Qi=105 in the single photon regime, and we demonstrate that non-equilibrium quasiparticles (QP) constitute the dominant loss mechanism. We extract QP relaxation times in the range of 1 s and we observe QP bursts every ∼20 s. The current level of coherence of GrAl resonators makes them attractive for integration in quantum devices, while it also evidences the need to reduce the density of non-equilibrium QPs.

Local Sensing with an AC Stark Spectrum Analyzer

  1. Andre Schneider,
  2. Jochen Braumüller,
  3. Lingzhen Guo,
  4. Patrizia Stehle,
  5. Hannes Rotzinger,
  6. Michael Marthaler,
  7. Alexey V. Ustinov,
  8. and Martin Weides
Analyzing weak microwave signals in the GHz regime is a challenging task if the signal level is very low and the photon energy widely undefined. Due to its discrete level structure,
a superconducting qubit is only sensitive to photons of certain energies. With a multi-level quantum system (qudit) in contrast, the unknown photon frequency can be deduced from the higher level AC Stark shift. The measurement accuracy is given by the signal amplitude, its detuning from the discrete qudit energy level structure and the anharmonicity. We demonstrate an energy sensitivity in the order of 10−4 with a measurement range of 1 GHz. Here, using a transmon qubit, we experimentally observe shifts in the transition frequencies involving up to three excited levels. These shifts are in good agreement with an analytic circuit model and master equation simulations. For large detunings, we find the shifts to scale linearly with the power of the applied microwave drive.

An argon ion beam milling process for native AlOx layers enabling coherent superconducting contacts

  1. Lukas Grünhaupt,
  2. Uwe von Lüpke,
  3. Daria Gusenkova,
  4. Sebastian T. Skacel,
  5. Nataliya Maleeva,
  6. Steffen Schlör,
  7. Alexander Bilmes,
  8. Hannes Rotzinger,
  9. Alexey V. Ustinov,
  10. Martin Weides,
  11. and Ioan M. Pop
We present an argon ion beam milling process to remove the native oxide layer forming on aluminum thin films due to their exposure to atmosphere in between lithographic steps. Our cleaning
process is readily integrable with conventional fabrication of Josephson junction quantum circuits. From measurements of the internal quality factors of superconducting microwave resonators with and without contacts, we place an upper bound on the residual resistance of an ion beam milled contact of 50mΩ⋅μm2 at a frequency of 4.5 GHz. Resonators for which only 6% of the total foot-print was exposed to the ion beam milling, in areas of low electric and high magnetic field, showed quality factors above 106 in the single photon regime, and no degradation compared to single layer samples. We believe these results will enable the development of increasingly complex superconducting circuits for quantum information processing.

Analog quantum simulation of the Rabi model in the ultra-strong coupling regime

  1. Jochen Braumüller,
  2. Michael Marthaler,
  3. Andre Schneider,
  4. Alexander Stehli,
  5. Hannes Rotzinger,
  6. Martin Weides,
  7. and Alexey V. Ustinov
The quantum Rabi model describes the fundamental mechanism of light-matter interaction. It consists of a two-level atom or qubit coupled to a quantized harmonic mode via a transversal
interaction. In the weak coupling regime, a rotating wave approximation can be applied and the quantum Rabi Hamiltonian reduces to the well-known Jaynes-Cummings Hamiltonian. In the ultra-strong coupling regime, where the effective coupling strength g is comparable to the energy ω of the bosonic mode, the counter rotating terms can no longer be neglected, revealing remarkable features in the system dynamics. Here, we demonstrate an analog quantum simulation of the quantum Rabi model in the ultra-strong coupling regime of variable strength. The quantum hardware of the simulator is a superconducting circuit embedded in a cQED setup. The simulation scheme is based on the application of two transversal microwave drive tones used to engineer the desired effective Hamiltonian. We observe a fast quantum state collapse followed by periodically recurring quantum revivals of the initial qubit state, which is the most distinct signature of the synthesized model. We achieve a relative coupling ratio of g/ω∼0.7, approaching the deep strong coupling regime.

Concentric transmon qubit featuring fast tunability and site-selective Z coupling

  1. Jochen Braumüller,
  2. Martin Sandberg,
  3. Michael R. Vissers,
  4. Andre Schneider,
  5. Steffen Schlör,
  6. Lukas Grünhaupt,
  7. Hannes Rotzinger,
  8. Michael Marthaler,
  9. Alexander Lukashenko,
  10. Amadeus Dieter,
  11. Alexey V. Ustinov,
  12. Martin Weides,
  13. and David P. Pappas
We present a planar qubit design based on a superconducting circuit that we call concentric transmon. While employing a simple fabrication process using Al evaporation and lift-off
lithography, we observe qubit lifetimes and coherence times in the order of 10us. We systematically characterize loss channels such as incoherent dielectric loss, Purcell decay and radiative losses. The implementation of a gradiometric SQUID loop allows for a fast tuning of the qubit transition frequency and therefore for full tomographic control of the quantum circuit. The presented qubit design features a passive direct Z coupling between neighboring qubits, being a pending quest in the field of quantum simulation.

Multi-photon dressing of an anharmonic superconducting many-level quantum circuit

  1. Jochen Braumüller,
  2. Joel Cramer,
  3. Steffen Schlör,
  4. Hannes Rotzinger,
  5. Lucas Radtke,
  6. Alexander Lukashenko,
  7. Ping Yang,
  8. Michael Marthaler,
  9. Lingzhen Guo,
  10. Alexey V. Ustinov,
  11. and Martin Weides
We report on the investigation of a superconducting anharmonic multi-level circuit that is coupled to a harmonic readout resonator. We observe multi-photon transitions via virtual energy
levels of our system up to the fifth excited state. The back-action of these higher-order excitations on our readout device is analyzed quantitatively and demonstrated to be in accordance with theoretical expectation. By applying a strong microwave drive we achieve multi-photon dressing of our system which is dynamically coupled by a weak probe tone. The emerging higher-order Rabi sidebands and associated Autler-Townes splittings involving up to five levels of the investigated anharmonic circuit are observed. Experimental results are in good agreement with master equation simulations.