Multidimensional Spectroscopy with Classical Fields vs Entangled Photons: Selecting Liouville Space Pathways

Sergey K. Andrukhovich, A.V. Berestov, B. A. Martsynkevich +2 more

Konstantin E. Dorfman, Shaul Mukamel

Eric R. Bittner, Carlos Silva-Acuña, Hao Li

Liouville pathways provide the conceptual foundation for interpreting multidimensional spectroscopies and are commonly represented as independent contributions to the nonlinear response. In open quantum systems, however, the effective reduced Liouvillian need not preserve this observational pathway decomposition. Environmental interactions can transport amplitude between pathway sectors during the free-evolution intervals, generating measurable signatures in the nonlinear spectroscopic response.} We develop a geometric framework in which pathway transport is governed by a Liouvillian connection, its associated curvature, and the resulting observational holonomy. The framework applies to open quantum systems in which the environment selects a pointer basis distinct from the observational basis used to construct the spectroscopic response. This basis incompatibility induces transport among Liouville pathways, generating characteristic spectral distortions and a nontrivial Liouvillian curvature. Using a Duhamel expansion of the Liouvillian propagator, we derive a reconstruction procedure that identifies the transport operators responsible for the observed redistribution of pathway weight, accurate throughout the full range of basis misalignment. This perspective reframes spectral features as determined not only by which pathways exist but by how amplitude is transported among them. Spectral distortions, peak shifts, and otherwise-forbidden pathway contributions become geometric signatures of a curved Liouville-space manifold rather than phenomenological broadening corrections, identifying pathway geometry as a complementary layer of organization in nonlinear spectroscopy.

S. Kielich

Oleksiy Roslyak, Shaul Mukamel

In response to quantum optical fields, pairs of molecules generate coherent nonlinear spectroscopy signals. Homodyne signals are given by sums over terms each being a product of Liouville space pathways of the pair of molecules times the corresponding optical field correlation function. For classical fields all field correlation functions may be factorized and become identical products of field amplitudes. The signal is then given by the absolute square of a susceptibility which in turn is a sum over pathways of a single molecule. The molecular pathways of different molecules in the pair are uncorrelated in this case (each path of a given molecule can be accompanied by any path of the other). However, entangled photons create an entanglement between the molecular pathways.We use the superoperator nonequlibrium Green's functions formalism to demonstrate the signatures of this pathway-entanglement in the difference frequency generation signal. Comparison is made with an analogous incoherent two-photon fluorescence signal.

Oleg P. Varnavski, Juan P. Villabona-Monsalve, Audrey V. Eshun +2 more