We demonstrate the local control of up to eight two-level systems interacting strongly with a microwave cavity. Following calibration, the frequency of each individual two-level system(qubit) is tunable without influencing the others. Bringing the qubits one by one on resonance with the cavity, we observe the collective coupling strength of the qubit ensemble. The splitting scales up with the square root of the number of the qubits, being the hallmark of the Tavis-Cummings model. The local control circuitry causes a bypass shunting the resonator, and a Fano interference in the microwave readout, whose contribution can be calibrated away to recover the pure cavity spectrum. The simulator’s attainable size of dressed states is limited by reduced signal visibility, and -if uncalibrated- by off-resonance shifts of sub-components. Our work demonstrates control and readout of quantum coherent mesoscopic multi-qubit system of intermediate scale under conditions of noise.
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.
The interaction between propagating microwave fields and Cooper-pair tunneling across a DC voltage-biased Josephson junction can be highly nonlinear. We show theoretically that thisnonlinearity can be used to convert an incoming single microwave photon into an outgoing n-photon Fock state in a different mode. In this process the Coulomb energy released by Cooper-pair tunneling is transferred to the outgoing Fock state, providing energy gain. The conversion can be made reflectionless (impedance-matched) so that all incoming photons are converted to n-photon states. With realistic parameters multiplication ratios n>2 can be reached. By cascading two to three such multiplication stages, the outgoing Fock-states can be sufficiently large to accurately discriminate them from vacuum with linear post-amplification and classical power measurement, implying that our scheme can be used as single-photon detector for itinerant microwave photons without dead time.
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.
A metamaterial formed by superconducting circuits or quantum dots can serve as active lasing medium when coupled to a microwave resonator. For these artificial atoms, in contrast toreal atoms, variations in their parameters cannot be avoided. In this paper, we examine the influence of disorder on such a multi-atom lasing setup. We find that the lasing process evolves into a self-organized stationary state that is quite robust against disorder. The reason is that photons created by those atoms which are in or close to resonance with the resonator stimulate the emission also of more detuned atoms. Not only the number of photons grows with the number of atoms, but also the width of the resonance as function of the detuning. Similar properties are found for other types of disorder such as variations in the individual coupling. We present relations how the allowed disorder scales with the number of atoms and confirm it by a numerical analysis. We also provide estimates for the sample-to-sample variations to be expected for setups with moderate numbers of atoms.
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 study dephasing of a superconducting qubit due to quasiparticle tunneling through a Josephson junction. While qubit decay due to tunneling processes is well understood within a goldenrule approximation, pure dephasing due to BCS quasiparticles gives rise to a divergent golden rule rate. We calculate qubit dephasing due to quasiparticle tunneling beyond lowest order approximation in coupling between qubit and quasiparticles. Summing up a certain class of diagrams we show that qubit dephasing due to purely longitudinal coupling to quasiparticles leads to a dephasing ∼exp(−x(t)) where x(t) is not linear in time on short time scales while it tends towards a selfconsistent calculated dephasing rate for longer times.