Tunneling Spectroscopy of Two-Level Systems Inside a Josephson Junction

We consider a two-level system (TLS) with energy level separation $\hslash {\Omega }_0$ inside a Josephson junction. The junction is shunted by a resistor $R$ and is voltage $V$ biased. If the TLS modulates the Josephson energy and/or is optically active, it is Rabi driven by the Josephson oscillations in the running phase regime near the resonance $2eV=\hslash {\Omega }_0$. The Rabi oscillations, in turn, translate into oscillations of current and voltage that can be detected in noise measurements. This effect provides an option to fully characterize the TLS inside Josephson junction and to find the TLS’s contribution to the decoherence when the junction is used as a qubit.

Figure 1

Model. The system is a Josephson junction with an embedded TLS. The TLS can be modeled as a charged particle that can tunnel between two nearby positions in the insulator. It modulates the Josephson coupling and/or interacts with the Josephson oscillation via dipole moment. When Josephson oscillations resonantly drive TLS, its Rabi oscillations can be detected on the resistor $R$.