Decoherence dynamics in molecular qubits: Exponential, Gaussian and beyond

TL;DR

This paper investigates how system-bath interaction structures influence decoherence patterns in molecular qubits, revealing that decay is generally a complex oscillatory exponential rather than purely Gaussian or exponential, with implications for spectroscopic interpretations.

Contribution

It provides an analytical framework showing that decoherence in molecular qubits is often an oscillatory exponential, clarifies conditions for Gaussian and exponential decay, and links these dynamics to spectroscopic features.

Findings

Gaussian decay dominates at early times for unentangled states.

Exponential decay arises only in specific models and under certain conditions.

Gaussian spectral peaks can emerge without initial inhomogeneity.

Abstract

In this work, we examine how the structure of system-bath interactions can determine commonly encountered temporal decoherence patterns, such as Gaussian and exponential decay, in molecular and other qubits coupled to a thermal bosonic bath. The analysis, based on a pure dephasing picture that admits analytical treatment, shows that decoherence, in general, is neither purely Gaussian nor exponential but rather the exponential of oscillatory functions, with periods determined by the bath's frequencies. For initially unentangled qubit-bath states Gaussian decay is always present at early times. It becomes increasingly dominant with increasing temperature, qubit-bath interaction strength, and bath correlation time. Initial system-bath entanglement that arises due to displacement in the position of the bath states preserves the Gaussian decay. By contrast, strict exponential decay arises only in very specific models that we isolate. Still, it becomes dominant for times longer than the bath correlation time or for early times when there is initial entanglement due to momentum displacement of the bath states. For molecular electronic decoherence, the long-time exponential regime plays a limited role as it emerges after most coherence is lost. Thus, the Gaussian decay provides a more suitable (albeit imperfect) model of such decoherence. Further, we discuss the connection between electronic decoherence dynamics and electronic spectroscopic lineshape theory, where Gaussian spectral peaks correspond to Gaussian coherence decay and Lorentzian peaks correspond to exponential coherence decay. We find that Gaussian spectral peaks, usually associated with inhomogeneous broadening, can emerge from the entangling unitary system-bath dynamics even when there is no inhomogeneity in the initial conditions.