Abstract
We present generalized adiabatic theorems for closed and open quantum systems that can be applied to slow modulations of rapidly varying fields, such as oscillatory fields that occur in optical experiments and light induced processes. The generalized adiabatic theorems show that a sufficiently slow modulation conserves the dynamical modes of time dependent reference Hamiltonians. In the limiting case of modulations of static fields, the standard adiabatic theorems are recovered. Applying these results to periodic fields shows that they remain in Floquet states rather than in energy eigenstates. More generally, these adiabatic theorems can be applied to transformations of arbitrary time-dependent fields, by accounting for the rapidly varying part of the field through the dynamical normal modes, and treating the slow modulation adiabatically. As examples, we apply the generalized theorem to (a) predict the dynamics of a two level system driven by a frequency modulated resonant oscillation, a pathological situation beyond the applicability of earlier results, and (b) to show that open quantum systems driven by slowly turned-on incoherent light, such as biomolecules under natural illumination conditions, can only display coherences that survive in the steady state.
Highlights
Quantum systems driven by slowly varying external fields play an important role in atomic, molecular, and optical physics
These results express the dynamics of the modulated field in terms of the dynamical normal modes of time-dependent reference Hamiltonians
These results significantly extend the applicability of the adiabatic theorem and its underlying intuition to, e.g., the domain of optical excitations that play a central role in atomic, molecular, and optical physics
Summary
Quantum systems driven by slowly varying external fields play an important role in atomic, molecular, and optical physics. We derive generalized ATs, termed adiabatic modulation theorems, for open and closed quantum systems that apply to oscillatory and other rapidly varying fields, extending adiabaticity conditions to optically driven processes and providing faster pathways to adiabaticity, with the potential to accelerate AQC. We show that the adiabatic transformation time is limited not by the energy gaps in the system but rather by the frequency differences of the instantaneous normal modes, that are often easier to manipulate These constructions allow for the design of experimental techniques that go beyond the preparation of time-independent states and allow for the preparation of specific dynamics using the well-developed intuition of adiabatic theory.
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