As superconductors are cooled below their critical temperature, stray magnetic flux can become trapped in regions that remain normal. The presence of trapped flux facilitates dissipationof ac current in a superconductor, leading to losses in superconducting elements of microwave devices. In type II superconductors, dissipation is well-understood in terms of the dynamics of vortices hosting a single flux quantum. In contrast, the ac response of type I superconductors with trapped flux has not received much attention. Building on Andreev’s early work [Sov. Phys. JETP 24, 1019 (1967)], here we show theoretically that the dominant dissipation mechanism is the absorption of the ac field at the exposed surfaces of the normal regions, while the deformation of the superconducting/normal interfaces is unimportant. We use the developed theory to estimate the degradation of the quality factors in field-cooled cavities, and we satisfactorily compare these theoretical estimates to the measured field dependence of the quality factors of two aluminum cavities.
We investigate inelastic microwave photon scattering by a transmon qubit embedded in a high-impedance circuit. The transmon undergoes a charge-localization (Schmid) transition uponthe impedance reaching the critical value. Due to the unique transmon level structure, the fluorescence spectrum carries a signature of the transition point. At higher circuit impedance, quasielastic photon scattering may account for the main part of the inelastic scattering cross-section; we find its dependence on the qubit and circuit parameters.
We evaluate the rates of energy and phase relaxation of a superconducting qubit caused by stray photons with energy exceeding the threshold for breaking a Cooper pair. All channelsof relaxation within this mechanism are associated with the change in the charge parity of the qubit, enabling the separation of the photon-assisted processes from other contributions to the relaxation rates. Among the signatures of the new mechanism is the same order of rates of the transitions in which a qubit looses or gains energy.
Controlling quasiparticle dynamics can improve the performance of superconducting devices. For example, it has been demonstrated effective in increasing lifetime and stability of superconductingqubits. Here we study how to optimize the placement of normal-metal traps in transmon-type qubits. When the trap size increases beyond a certain characteristic length, the details of the geometry and trap position, and even the number of traps, become important. We discuss for some experimentally relevant examples how to shorten the decay time of the excess quasiparticle density. Moreover, we show that a trap in the vicinity of a Josephson junction can reduce the steady-state quasiparticle density near that junction, thus suppressing the quasiparticle-induced relaxation rate of the qubit. Such a trap also reduces the impact of fluctuations in the generation rate of quasiparticles, rendering the qubit more stable.
Engineered quantum systems allow us to observe phenomena that are not easily accessible naturally. The LEGO-like nature of superconducting circuits makes them particularly suited forbuilding and coupling artificial atoms. Here, we introduce an artificial molecule, composed of two strongly coupled fluxonium atoms, which possesses a tunable magnetic moment. Using an applied external flux, one can tune the molecule between two regimes: one in which the ground-excited state manifold has a magnetic dipole moment and one in which the ground-excited state manifold has only a magnetic quadrupole moment. By varying the applied external flux, we find the coherence of the molecule to be limited by local flux noise. The ability to engineer and control artificial molecules paves the way for building more complex circuits for protected qubits and quantum simulation.
The presence of quasiparticles in superconducting qubits emerges as an intrinsic constraint on their coherence. While it is difficult to prevent the generation of quasiparticles, keepingthem away from active elements of the qubit provides a viable way of improving the device performance. Here we develop theoretically and validate experimentally a model for the effect of a single small trap on the dynamics of the excess quasiparticles injected in a transmon-type qubit. The model allows one to evaluate the time it takes to evacuate the injected quasiparticles from the transmon as a function of trap parameters. With the increase of the trap size, this time decreases monotonically, saturating at the level determined by the quasiparticles diffusion constant and the qubit geometry. We determine the characteristic trap size needed for the relaxation time to approach that saturation value.
In superconducting qubits, the interaction of the qubit degree of freedom
with quasiparticles defines a fundamental limitation for the qubit coherence.
We develop a theory of the puredephasing rate Gamma_{phi} caused by
quasiparticles tunneling through a Josephson junction and of the inhomogeneous
broadening due to changes in the occupations of Andreev states in the junction.
To estimate Gamma_{phi}, we derive a master equation for the qubit dynamics.
The tunneling rate of free quasiparticles is enhanced by their large density of
states at energies close to the superconducting gap. Nevertheless, we find that
Gamma_{phi} is small compared to the rates determined by extrinsic factors in
most of the current qubit designs (phase and flux qubits, transmon, fluxonium).
The split transmon, in which a single junction is replaced by a SQUID loop,
represents an exception that could make possible the measurement of
Gamma_{phi}. Fluctuations of the qubit frequency leading to inhomogeneous
broadening may be caused by the fluctuations in the occupation numbers of the
Andreev states associated with a phase-biased Josephson junction. This
mechanism may be revealed in qubits with small-area junctions, since the
smallest relative change in frequency it causes is of the order of the inverse
number of transmission channels in the junction.
We study the photon shot noise dephasing of a superconducting transmon qubit
in the strong-dispersive limit, due to the coupling of the qubit to its readout
cavity. As each random arrivalor departure of a photon is expected to
completely dephase the qubit, we can control the rate at which the qubit
experiences dephasing events by varying textit{in situ} the cavity mode
population and decay rate. This allows us to verify a pure dephasing mechanism
that matches theoretical predictions, and in fact explains the increased
dephasing seen in recent transmon experiments as a function of cryostat
temperature. We investigate photon dynamics in this limit and observe large
increases in coherence times as the cavity is decoupled from the environment.
Our experiments suggest that the intrinsic coherence of small Josephson
junctions, when corrected with a single Hahn echo, is greater than several
hundred microseconds.