Rabi enhanced tunneling from solid-state spin qubits: a Lindblad equation for Rabi driven spins in tunneling contact with a reservoir

Lindblad equations describe the dissipative dynamics of a quantum system interacting with a (typically larger and often memoryless) second system such as a thermal bath. When the system Hamiltonian is not time dependent a complete set of its eigenstates can be used as a basis for expanding the system-bath interaction Hamiltonian, and there is a standard method for obtaining a Lindblad equation by tracing over the bath.



However, for a spin in a solid-state qubit, driving Rabi oscillations with an oscillating magnetic field yields a time-dependent Hamiltonian. If an electron experiencing this Rabi driving also has a weak tunneling contact to a nearby lead, there should be a Lindblad equation describing this driven-dissipative behavior. We have used the unitary time evolution operator that solves the Rabi problem to transform into the interaction picture with respect to the system Hamiltonian, which, along with typical assumptions about the bath and the secular approximation, gives a matrix form of the Lindblad equation. This equation predicts that the Rabi driving can enhance emptying of the dot while maintaining the lead chemical potential at the average energy of the two Zeeman-split energy levels (spin up and spin down). The enhanced rate could have implications for the performance of spin-based quantum computation. Eliminating the need for large excursions of the applied voltage for emptying the dot could reduce errors.



This Lindblad equation may also see application in spin-informed scanning tunneling microscopy (STM), in which the tip of an STM is enhanced by adding a single spin on the end for magnetic sensing.