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.

Fluxon-Based Quantum Simulation in Circuit QED

  1. Alexandru Petrescu,
  2. Hakan E. Türeci,
  3. Alexey V. Ustinov,
  4. and Ioan M. Pop
Long-lived fluxon excitations can be trapped inside a superinductor ring, which is divided into an array of loops by a periodic sequence of Josephson junctions in the quantum regime,
thereby allowing fluxons to tunnel between neighboring sites. By tuning the Josephson couplings, and implicitly the fluxon tunneling probability amplitudes, a wide class of 1D tight-binding lattice models may be implemented and populated with a stable number of fluxons. We illustrate the use of this quantum simulation platform by discussing the Su-Schrieffer-Heeger model in the 1-fluxon subspace, which hosts a symmetry protected topological phase with fractionally charged bound states at the edges. This pair of localized edge states could be used to implement a superconducting qubit increasingly decoupled from decoherence mechanisms.

Quantum simulation of the spin-boson model in a microwave circuit

  1. Juha Leppäkangas,
  2. Jochen Braumüller,
  3. Alexey V. Ustinov,
  4. Martin Weides,
  5. and Michael Marthaler
We consider superconducting circuits for the purpose of simulating the spin-boson model. The spin-boson model consists of a single two-level system coupled to bosonic modes. In most
cases, the model is considered in a limit where the bosonic modes are sufficiently dense to form a continuous spectral bath. A very well known case is the Ohmic bath, where the density of states grows linearly with the frequency. In the limit of weak coupling or large temperature, this problem can be solved numerically. If the coupling is strong, the bosonic modes can become sufficiently excited to make a classical simulation impossible. Quantum simulation of this problem can be done by coupling a superconducting qubit to a specifically engineered electromagnetic environment. We discuss in detail how to build a bosonic bath using superconducting resonators and how to achieve strong couplings by additional driving. We also discuss how interesting spin dynamics with different initialization conditions can be probed by using standard techniques from circuit quantum electrodynamics.

Transmission-line resonators for the study of individual two-level tunneling systems

  1. Jan David Brehm,
  2. Alexander Bilmes,
  3. Georg Weiss,
  4. Alexey V. Ustinov,
  5. and Jürgen Lisenfeld
Parasitic two-level tunneling systems (TLS) emerge in amorphous dielectrics and constitute a serious nuisance for various microfabricated devices, where they act as a source of noise
and decoherence. Here, we demonstrate a new test bed for the study of TLS in various materials which provides access to properties of individual TLS as well as their ensemble response. We terminate a superconducting transmission-line resonator with a capacitor that hosts TLS in its dielectric. By tuning TLS via applied mechanical strain, we observe the signatures of individual TLS strongly coupled to the resonator in its transmission characteristics and extract the coupling components of their dipole moments and energy relaxation rates. The strong and well-defined coupling to the TLS bath results in pronounced resonator frequency fluctuations and excess phase noise, through which we can study TLS ensemble effects such as spectral diffusion, and probe theoretical models of TLS interaction.

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.

Dispersive Response of a Disordered Superconducting Quantum Metamaterial

  1. Dmitriy S. Shapiro,
  2. Pascal Macha,
  3. Alexey N. Rubtsov,
  4. and Alexey V. Ustinov
We consider a disordered quantum metamaterial formed by an array of superconducting flux qubits coupled to microwave photons in a cavity. We map the system on the Tavis-Cummings model
accounting for the disorder in frequencies of the qubits. The complex transmittance is calculated with the parameters taken from state-of-the-art experiments. We demonstrate that photon phase shift measurements allow to distinguish individual resonances in the metamaterial with up to 100 qubits, in spite of the decoherence spectral width being remarkably larger than the effective coupling constant. Our simulations are in agreement with the results of the recently reported experiment.

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.