Quantifying and Controlling Quantum Coherence through Femtosecond Pulse Shaping

Quantum coherence, a fundamental aspect of quantum mechanics, defines the extent of non-classicality in a physical system. To gain a deeper and quantitative understanding of this property, a well-defined theoretical framework is essential. Among the many complex measures proposed for quantifying coherence, we introduce a simple, intuitive, and easily computable approach that is non-negative, self-normalized, and monotonic under any incoherent operation.

Coherent control represents a powerful quantum-mechanical strategy for steering molecular dynamics using light. The central idea is to manipulate quantum interference phenomena by tailoring the phase of a laser pulse. When a quantum system can reach a final state through multiple pathways, the transition rate can be modified by adjusting the relative phases of the interfering amplitudes. Since these quantum phases can be tuned via the optical phase of the excitation field, the essence of quantum coherent control lies in laser pulse shaping.

Maintaining coherence is critical; any coupling to an uncontrolled environment can cause phase randomization and diminish the effectiveness of control. By coherently manipulating molecular states, coherent control effectively bypasses some of the practical limits imposed by the uncertainty principle in ultrafast laser interactions. Because the control dynamics must occur within timescales shorter than molecular dephasing times, arbitrary pulse shaping at femtosecond durations becomes indispensable.

Theoretical insights and numerical simulations play a vital role in evaluating the feasibility of these control schemes. A major advancement in this field is the introduction of programmable pulse shaping with feedback loops, which enables the dynamic optimization of control outcomes. In this work, we emphasize the experimental realization of arbitrary femtosecond pulse shaping, complemented by a density matrix–based theoretical framework to describe quantum coherence and its evolution. Collectively, these approaches provide a unified perspective on quantifying and exploiting coherence for controlled molecular dynamics.