Chain-boson model for the decoherence and relaxation of a few coupled SQUIDs in a phonon bath

Abstract

We develop a "chain-boson model" master equation, within the Born-Markov approximation, for a few superconducting quantum interference devices ͑SQUIDs͒ coupled into a chain and exchanging their angular momenta with a low-temperature phonon bath. Our master equation has four generators; we concentrate on the damping and diffusion and use them to study the relaxation and decoherence of a Heisenberg SQUID chain whose spectrum exhibits critical-point energy-level crossings, entangled states, and pairs of resonant transitions. We note that at an energy-level crossing, the relevant bath wavelengths are so long that even well-spaced large SQUIDs can partially exhibit collective coupling to the bath, dramatically reducing certain relaxation and decoherence rates. Also, transitions into entangled states can occur even in the case of an independent coupling of each SQUID to the bath. Finally, the pairs of resonant transitions can cause decaying oscillations to emerge in a lower-energy subspace.

Dephasing due to quasiparticle tunneling in fluxonium qubits: a phenomenological approach

“…The situation we have in mind is some stationary nonequilibrium quasiparticle distribution on the fluxonium qubit. As mentioned above, we model this distribution by an effective temperature, in order to keep the discussion simple 8 . In particular, we treat the situation where one side of the black-sheep Josephson junction is at an elevated temperature T T T 2 δ = + with respect to the other which is at temperature T T 1 = , see figure 1(a).…”

“…The heat current Q flowing into the cold reservoir, which is held at 7 Importantly, in contrast to the procedure employed here, perturbative approaches in the tunnel coupling such as used in [24,25], need to introduce artificial cutoff energies to avoid emerging divergencies for 1 2 Δ Δ ≈ . 8 Note that more general nonequilibrium quasiparticle distributions can be analyzed by replacing the Fermi functions (entering through the cosh term in equations (6)-(9) by arbitrary distribution functions. temperature T T 1 = (or equivalently in the heat current flowing out of the hot reservoir, kept at temperature 9 T T T 2 δ = + ) is given by the sum of two terms…”

“…This is important since both effects in general limit the performance of the qubits by introducing relaxation and dephasing processes. Indeed, over the last few years considerable effort has been made in order to understand, and consequently to reduce, the causes of relaxation and decoherence in different types of superconducting circuits [1,[6][7][8][9].…”

Linear-algebraic bath transformation for simulating complex open quantum systems

“…In this approach, then, the bath transformation from the noninteracting bath model (figure 1(A)) to the 1-D Wilson chain (figure 1(B)) [23][24][25] is necessary. The collective modes of the bath oscillators in the chain model have been used widely in various fields such as quantum molecular dynamics [26,27], open quantum dynamics [28][29][30][31][32], quantum information [33] and nuclear physics [34,35].…”

“…1B) [22] is necessary. The collective modes of the bath oscillators in the chain model has been used widely in various fields such as quantum molecular dynamics [23,24], open quantum dynamics [25][26][27][28][29], quantum information [30] and nuclear physics [31,32].…”