We introduce a rate formalism to treat classically forbidden electron transport through a quantum dot (cotunneling) in the presence of a coupled measurement device. We demonstrate this formalism for a toy model case of cotunneling through a single-level dot while being coupled to a strongly pinched-off quantum point contact (QPC). We find that the detector generates three types of back-action: the measurement collapses the coherent transport through the virtual state, but at the same time allows for QPC-assisted incoherent transport, and widens the dot level. Last, we obtain the measured cotunneling time from the cross correlation between dot and QPC currents.
A recent experiment [arXiv:2507.08795] has reported measurements of the interwire
X-parity lifetime in a Majorana tetron device via the quantum capacitance of an auxiliary readout dot. Motivated by these measurements, we theoretically study the interwire parity lifetime in a minimal model of the coupled dot-tetron system subject to electrostatic noise. We show that coupling to the measurement dot can itself strongly modify the parity dynamics by generating an energy splitting that shifts noise-induced transitions to finite frequency and thereby stabilizes the measured states against low-frequency fluctuations. For representative noise strengths motivated by disordered nanowire devices, we find
X-parity switching lifetimes of order microseconds in the measurement configuration even when the corresponding bare-tetron coherence time is only tens of nanoseconds long. We analyze both the dispersive regime, where the dot can be integrated out and the dynamics reduces to an effective two-level system, and the near-resonant regime, where all four low-energy states participate. In the latter case, rapid transitions organize the spectrum into two long-lived manifolds that approximately correspond to sectors of the combined dot-tetron
X-loop parity, yielding effective two-state switching despite the underlying multilevel structure. Our results show that measurement-induced stabilization can substantially enhance the observed
X-parity switching lifetime, such that the lifetime measured under continuous readout can greatly exceed the intrinsic idle
T2∗ coherence time of the isolated Majorana tetron qubit.
Coupled quantum dots are an example of the ubiquitous quantum double potential well. In a typical transport experiment, each quantum dot is also coupled to a continuum of states. Our approach takes this into account by using a Green’s function formalism to solve the full system. The time-dependent solution is then explored in different limiting cases. In general, a combination of coherent and incoherent behavior is observed. In the case that the coupling of each dot to the macroscopic world is equal, however, the time evolution is purely coherent. The double-well potential is one of the simplest and best understood problems in modern quantum mechanics. Its utility is likewise unparalleled. Potential applications of double-well devices have been noted in Refs. [1-5]. For such devices to be useful, an understanding of the processes which couple the microscopic device to the macroscopic environment is paramount. That is to say, the decoherence processes of such systems must be well understood. To this end, we consider a simple exactly solvable model of two coupled quantum dots. An excellent review of related systems and some approximate solutions are given in Ref. [6]. Each dot is coupled to an environment (a triple-barrier system) as in Fig. 1. The environment consists of a continuum of states, as would be appropriate for a macroscopic lead. Only one state in each quantum dot is considered, which amounts to the assumption that the tunneling parameters connecting our two states to any neglected state are much less than the energy differences with that state. The Hamiltonian of the system can be written as the sum of two terms, H = H0 + Hc. The first term, H0, represents the dynamics of the simple two-state system, H0 = ε1d † 1d1 + ε2d † 2 d2 + V (d† 1d2 + d†