Dissipation in a superconducting artificial atom due to a single nonequilibrium quasiparticle

Abstract

We study a superconducting artificial atom which is represented by a single Josephson junction or a Josephson junction chain, capacitively coupled to a coherently driven transmission line, and which contains exactly one residual quasiparticle (or less than one quasiparticle per island in a chain). We study the dissipation in the atom induced by the quasiparticle tunneling, taking into account the quasiparticle heating by the drive. We calculate the transmission coefficient in the transmission line for drive frequencies near resonance and show that, when the artificial atom spectrum is nearly harmonic, the intrinsic quality factor of the resonance increases with the drive power. This counterintuitive behavior is due to the energy dependence of the quasiparticle density of states.

Report on scipost_201811_00008v1

“…With these values both the highand low-energy formulas, Eqs. (18) and (19), fit well the numerical solution, see Fig 2. Finally, to find the proper normalization, we can use the numerical result…”

“…The largest values of T * /ω 0 are reached for low-frequency qubits made of small islands, since the rate Γ 0 is inversely proportional to the volume. Considering a typical aluminum island of volume ∼ 0.02 µm 3 , we have Γ 0 ∼ 10 5 Hz [18]. For the time τ ph , we use the relation in [27] and the experimental results for thin films in Refs.…”

Non-equilibrium quasiparticles in superconducting circuits: photons vs. phonons

“…In principle, one can write coupled equations for the photon density matrix and f ( ), as in Ref. [18]; their solution in the presence of phonons remains an open question. Also, we neglect multiphoton absorption/emission and assume the photon system to be either strictly two-level or strictly harmonic; then each act of absorbtion/emission involves only energy ω 0 , and the photon state enters only vian.…”

“…The two terms on the right-hand side represent collision integrals due to absorption/emission of phoTons and phoNons, respectively. The photon term can be written as [18] St…”

“…In the numerical work [16], the external circuit was treated classically, so it tended to heat the quasiparticles to infinite temperature, and the distribution was stabilized by phonon emission only (see also [17] and references therein for related experiments). In [18], the quasiparticle distribution was assumed to be entirely determined by the external circuit (both heating by the drive and cooling by photon emission were included at the quantum level), while phonon emission was neglected.…”