We demonstrate how heating of an environment can invert the line shape of a driven cavity. We consider a superconducting coplanar cavity coupled to multiple artificial atoms. The measuredcavity transmission is characterized by Fano-type resonances with a shape that is continuously tunable by bias current through nearby (magnetic flux) control lines. In particular, the same dispersive shift of the microwave cavity can be observed as a peak or a dip. We find that this Fano-peak inversion is possible due to a tunable interference between a microwave transmission through a background, with reactive and dissipative properties, and through the cavity, affected by bias-current induced heating. The background transmission occurs due to crosstalk with the multiple control lines. We show how such background can be accounted for by a Jaynes- or Tavis-Cummings model with modified boundary conditions between the cavity and transmission-line microwave fields. A dip emerges when cavity transmission is comparable with background transmission and dissipation. We find generally that resonance positions determine system energy levels, whereas resonance shapes give information on system fluctuations and dissipation.
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.
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 mostcases, 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.
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 cleaningprocess 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.
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 transversalinteraction. 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.
The Jordan-Wigner transformation maps a one-dimensional spin-1/2 system onto a Fermionic model without spin degree of freedom. Here we show that a double chain of qubits with XX andZZ couplings of neighboring qubits along and between the chains, respectively, can be mapped on a spin-full 1D Fermi-Hubbard model. The qubit system can thus be used to emulate the quantum properties of this model. We analyze physical implementations of such analog quantum simulators, including one based on transmon qubits, where the ZZ interaction arises due to an inductive coupling and the XX interaction due to a capacitive interaction. We propose protocols to gain confidence in the results of the simulation through measurements of local operators.
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-offlithography, 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.
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 energylevels 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.
Short review on advanced superconducting circuits and devices.
We present a superconducting qubit design that is fabricated in a 2D geometry
over a superconducting ground plane to enhance the lifetime. The qubit is
coupled to a microstrip resonatorfor readout. The circuit is fabricated on a
silicon substrate using low loss, stoichiometric titanium nitride for capacitor
pads and small, shadow-evaporated aluminum/aluminum-oxide junctions. We observe
qubit relaxation and coherence times ($T_1$ and $T_2$) of 11.7 $pm$ 0.2 $mu$s
and 8.7 $pm$ 0.3 $mu$s, respectively. Calculations show that the proximity of
the superconducting plane suppresses the otherwise high radiation loss of the
qubit. A significant increase in $T_1$ is projected for a reduced
qubit-to-superconducting plane separation.