Jump Operators for Rabi oscillating electrons tunneling between a quantum dot and a classical lead

Electron spins on quantum dots can serve as qubits, with rotations between spin states driven by an AC magnetic field.  When such driven electrons are also able to tunnel between the dot and a lead, the state they tunnel from/to is no longer a simple spin-up or spin-down state.  An accurate Lindbladian master equation should take into account these coherent oscillations when deriving the dissipative dynamics due to tunneling. We have derived expressions for the Lindbladian jump operators for tunneling between a quantum dot and a classical Markovian lead, when the electron spin on the dot is Rabi driven by an AC magnetic field, on- or off- resonance, and the chemical potential of the lead is between the spin-up and spin-down Zeeman split levels.  Similar to Cohen-Tannoudji's dressed state picture for describing the AC Stark shift [1], the secular approximation applied in the case when the Rabi frequency is high compared to the tunneling rate with the lead yields a master equation with an additional level splitting.  We have used this equation to show that on-resonance Rabi-driving changes the steady-state occupation of the dot [2].  Here we use the method of Kasatkin et al. [3] to show that this master equation is a Lindblad equation and derive the jump operators, which consist of linear combinations of jumping on and off the dot and into (and out of) spin-up and spin-down states.  On-resonance they may be simplified such that each operator represents only jumps on or off the dot.

 

[1] C. Cohen-Tannoudji and S. Reynaud, Journal of Physics B: Atomic and Molecular Physics 10, 345 (1977).

[2] E. Townsend, J. Pomeroy and G. Bryant  arXiv:2503.17481 (2025)

[3] V. Kasatkin, L. Gu and D. Lidar, Phys. Rev. Research 5, 043163 (2023).