A modified Lindblad equation for a Rabi driven electron-spin qubit with tunneling to a Markovian lead

Abstract: We derive a modified Lindblad equation for the state of quantum dot tunnel coupled to a Markovian lead when the spin state of the dot is driven by an oscillating magnetic field. We show that the equation is a completely positive, trace-preserving map and find the jump operators. This is a driven-dissipative regime in which coherent driving is relevant to the tunneling and cannot be treated as simply a rotation modifying the system with a bath derived under a static magnetic field. This work was motivated by an experimental desire to determine the Zeeman splitting of an electron spin on a quantum dot (a spin qubit), and in a related work we show that this splitting energy can be found by measuring the charge occupancy of the dot while sweeping the frequency of the driving field \ arXiv:2503.17481. Here we cover the full derivation of the equation and give the jump operators. These jump operators are potentially useful for describing the stochastic behavior of more complex systems with coherent driving of a spin capable of tunneling on or off of a device, such as in electron spin resonance scanning tunneling microscopy. The jump operators have the interesting feature of combining jumps of electrons onto and off of the device.