We study a simple model for photoinduced electron transfer reactions for the case of many donor-acceptor pairs that are collectively and homogeneously coupled to a photon mode of a cavity. We describe both coherent and dissipative collective effects resulting from this coupling within the framework of a quantum optics Lindblad master equation. We introduce a method to derive an effective rate equation for electron transfer by adiabatically eliminating donor and acceptor states and the cavity mode. The resulting rate equation is valid for both weak and strong coupling to the cavity mode and describes electronic transfer through both the cavity-coupled bright states and the uncoupled dark states. We derive an analytic expression for the instantaneous electron transfer rate that depends non-trivially on the time-varying number of pairs in the ground state. We find that under proper resonance conditions, and in the presence of an incoherent drive, reaction rates can be enhanced by the cavity. This enhancement persists, and can even be largest, in the weak light-matter coupling regime. We discuss how the cavity effect is relevant for realistic experiments.
We investigated the electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schrodinger equation for the whole system can be reduced to new Bloch-type rate equations describing the time development of the detector and the measured system at once. Using these equations we find that the continuous measurement of the unstable system does not affect its exponential decay, exp(-gammat), contrary to expectations based on the quantum Zeno effect. However, the width of the energy distribution of the tunneling electron is no longer gamma, but increases due to the decoherence, generated by the detector.
In the preceding chapter electron rate equations of bimolecular form were derived. In this chapter these equations are generalized to include higher order non-linear terms. Such terms occur in rate equations for electrons, phonons, photons, etc., either if many-particle interaction operators are taken into account, or (and) if powers of oneparticle interaction operators are included. The latter case takes place if the transition probabilities (1.5.15) with respect to one-particle interaction operators are evaluated in higher orders. An estimate of the physical consequences of such transitions is, at present, not possible, since for higher order transitions the derivation of rate equations becomes more and more complicated. Hence a rigorous mathematical justification of higher order effects in rate equations starting from first principles seems at present to be extraordinarily hard and has not yet been undertaken. Thus in the following we consider only such interactions which already lead to higher order non-linear terms in the rate equations for first order (resonance) transition probabilities. In particular we concentrate on the electronic many-particle interactions. We will use the same model as in Chapter 3 and in principle the calculations will run along the same lines as in the previous chapter, but the calculation effort will become much greater.
A universal energy eigenvalue equation is proposed in this paper. It is proven that the unique set of eigenfunctions or preferred basis exists for any non-isolated sub-system. Applying the new eigenvalue equation to the relative motion of a hydrogen atom together with the derived relativistic Hamiltonian to quantify the impact of finite proton mass to the fine structure, correction to the fine structure is obtained as a result of the entanglement of the relative motion and the center-of-mass motion, which can be used to verify the correctness of the proposed eigenvalue equation. Applying the equation to the measurement of electron double-slit interference, it is analyzed that the photon packets with Lorentzian spectral lineshape, the domain and state density of the sub-system, and the energy of the incident electron together determines the spontaneous emission rate of the incident electron. Photons generated in this process excite electrons from the valence band to the conduction band of the detector. Corresponding to any emitted or absorbed photon, the sub-system is found to be uniquely determined by maximizing the transition rate. This new principle is valid for atoms too. Closed-form expressions are obtained for the transition rates and example numerical results show good correlation between calculation and the position measurement experiment. The discovered common mechanisms that determine the sub-systems, the preferred bases, and transition rates form the foundation of a new, general, and consistent theory of quantum measurement.