Switchable Ultrastrong Coupling in Circuit QED

We propose different designs of switchable coupling between a superconducting flux qubit and a microwave transmission line. They are based on two or more loops of Josephson junctions which are directly connected to a closed (cavity) or open transmission line. In both cases the circuit induces a coupling that can be modulated in strength, reaching the so-called ultrastrong coupling regime in which the coupling is comparable to the qubit and photon frequencies. Furthermore, we suggest a wide set of applications for the introduced architectures.

Figure 1

Schemes for ultrastrong coupling between a qubit and a transmission line. (a) Basic setup of a qubit coupled directly to the line. $\Delta \psi$ is the phase difference between the nodes in which the qubit and line intersect. (b) With a second loop, the coupling can be modulated. (c) A slightly improved setup in which the qubit is better decoupled from the flux $f_2$.

Figure 2

For the Fig. 1b setup, coupling strengths as a function of the external flux $f_1$ and the qubit junction size $\alpha =E_{J2}/E_{J1}$, for $f_2=\pi$. We plot (a) the normalized first-order coupling along the $Z$ direction, $c_z^1{\sigma }_z\Delta \psi$, and (b) across the $XY$ plane.

Figure 3

(a) Following Eq. (5), normalized transverse coupling $c_x^1$ as a function of external fluxes $f_1$ and $f_2$ for the setup in Fig. 1c, using $\alpha =2.0$ and ${\alpha }_4=0.1$. (b) Cut at $f_1=0.5$ shows first-order (solid line) and second-order couplings (dashed line) of longitudinal ($c_z$, blue line) and transverse ($c_x$, red line).