Superconducting Qubit with Purcell Protection and Tunable Coupling

We present a superconducting qubit for the circuit quantum electrodynamics architecture that has a tunable qubit-resonator coupling strength $g$. This coupling can be tuned from zero to values that are comparable with other superconducting qubits. At $g=0$, the qubit is in a decoherence-free subspace with respect to spontaneous emission induced by the Purcell effect. Furthermore, we show that in this decoherence-free subspace, the state of the qubit can still be measured by either a dispersive shift on the resonance frequency of the resonator or by a cycling-type measurement.

Figure 1

(a) Schematic of the circuit QED architecture. (b) Schematic of the proposed three island device. The islands are connected by SQUIDs and the arrows are used to indicated the dipole and quadrupole moments of the device. (c) Circuit model of the device. The variables are explained in the text.

Figure 2

(a) Eigenenergies of the TCQ Hamiltonian as a function of $E_I/E_C$ for $E_{J_{\pm }}=50E_C$. Solid lines are from numerical diagonalization and dashed lines are from the coupled anharmonic oscillator model. (b) Charge dispersion $|{\epsilon }_{q(m)}|$ as a function of the ratio $E_J/E_C$ for $E_I=-E_C$ (solid lines) and $E_I=0$ (dashed lines).

Figure 3

(a) Matrix element for the coupling operator ($n_{+}+n_{-}$) and (b) the qubit transition energy as a function of the energy ratio $E_{J_{+}}/E_C$. Other parameters are $n_{g_{\pm }}=0$, $E_I=-E_C$, and $E_{J_{-}}$ is numerically solved to ensure that only the coupling strength [dark (blue)] and frequency [light (red)] are changed. Solid lines are from a numerical diagonalization and dashed lines are from the coupled anharmonic oscillator model.