Quasiparticle Decoherence in $d$-Wave Superconducting Qubits

It is usually argued that the presence of gapless quasiparticle excitations at the nodes of the $d$-wave superconducting gap should strongly decohere the quantum states of a $d$-wave qubit, making quantum effects practically unobservable. Using a self-consistent linear response nonequilibrium quasiclassical formalism, we show that this is not necessarily true. We find quasiparticle conductance of a $d$-wave grain boundary junction to be strongly phase dependent. Midgap states as well as nodal quasiparticles contribute to the conductance and therefore decoherence. Quantum behavior is estimated to be detectable in a qubit containing a $d$-wave junction with appropriate parameters.

Figure 1

(a) Angle resolved conductance, normalized to $G_0=e^2{N}_F{v}_{F}S$, for $\varphi =0$ (dashed line) and $\varphi =\pi /2$ (solid line) at $T=0.01T_c$. (b) Quasiparticle trajectories crossing the grain boundary. Trajectories along $\alpha$ and $\beta$ directions see sign change of the order parameter. Other parameters are $\omega =0.02T_c$ and $\eta =0.05T_c$.

Figure 2

$\varphi$ (a) and $T$ (b) dependence of $G$ for the same set of parameters as in Fig. 1.

Figure 3

Dependence of $G$ on $\omega$ (a) and $\eta$ (b) at $T={10}^{-4}{T}_c$. $\eta$ in (a) and $\omega$ in (b) are equal to $0.01T_c$.