The description of excited state dynamics in multichromophoric systems constitutes both a theoretical and experimental challenge in modern physical chemistry. An experimental protocol which can systematically characterize both coherent and dissipative processes at the level of the evolving quantum state of the chromophores is desired. In this article, we show that a carefully chosen set of polarization controlled two-color heterodyned photon-echo experiments can be used to reconstruct the time-evolving density matrix of the one-exciton manifold of a heterodimer. This possibility in turn allows for a complete description of the excited state dynamics via quantum process tomography (QPT). Calculations on the dimer show that QPT can reveal rich information about system-bath interactions, which otherwise appear nontrivially hidden in the polarization monitored in standard four-wave mixing experiments. Our study presents a novel method for analyzing condensed phase experiments with a quantum information processing perspective.
The description of excited state dynamics in multichromophoric systems constitutes both a theoretical and experimental challenge in modern physical chemistry. An experimental protocol which can systematically characterize both coherent and dissipative processes at the level of the evolving quantum state of the chromophores is desired. In this article, we show that a carefully chosen set of polarization controlled two-color heterodyned photon-echo experiments can be used to reconstruct the time-evolving density matrix of the one-exciton manifold of a heterodimer. This possibility in turn allows for a complete description of the excited state dynamics via quantum process tomography (QPT). Calculations on the dimer show that QPT can reveal rich information about system-bath interactions, which otherwise appear nontrivially hidden in the polarization monitored in standard four-wave mixing experiments. Our study presents a novel method for analyzing condensed phase experiments with a quantum information processing perspective.
The description of excited state dynamics in energy transfer systems constitutes a theoretical and experimental challenge in modern chemical physics. A spectroscopic protocol that systematically characterizes both coherent and dissipative processes of the probed chromophores is desired. Here, we show that a set of two-color photon-echo experiments performs quantum state tomography (QST) of the one-exciton manifold of a dimer by reconstructing its density matrix in real time. This possibility in turn allows for a complete description of excited state dynamics via quantum process tomography (QPT). Simulations of a noisy QPT experiment for an inhomogeneously broadened ensemble of model excitonic dimers show that the protocol distills rich information about dissipative excitonic dynamics, which appears nontrivially hidden in the signal monitored in single realizations of four-wave mixing experiments.
In the first part of the dissertation, we develop a theoretical approach to analyze nonlinear spectroscopy experiments based on the formalism of quantum state (QST) and process tomography (QPT). In it, a quantum system is regarded as a black box which can be systematically tested in its performance, very much like an electric circuit is tested by sending a series of inputs and measuring the corresponding outputs, but in the quantum sense. We show how to collect a series of pump-probe or photon-echo experiments, and by varying polarizations and frequency components of the perturbations, reconstruct the quantum state (density matrix) of the probed system for a set of different initial conditions, hence simultaneously achieving QST and QPT. Furthermore, we establish the conditions under which a set of two-dimensional optical spectra also yield the desired results. Simulations of noisy experiments with inhomogeneous broadening show the feasibility of the protocol. A spin-off of this work is our suggestion of a witness that distinguishes between spectroscopic time-oscillations corresponding to vibronic only coherences against their electronic counterparts. We conclude by noting that the QST/QPT approach to nonlinear spectroscopy sheds light on the amount of quantum information contained in the output of an experiment, and hence, is a convenient theoretical and experimental paradigm even when the goal is not to perform a full QPT. In the second part of the thesis, we discuss a methodology to study the electronic dynamics of complex molecular systems, such as photosynthetic units, in the framework of time-dependent density functional theory (TD-DFT). By treating the electronic degrees of freedom as the system and the nuclear ones as the bath, we develop an open quantum systems (OQS) approach to TD-DFT. We formally extend the theoretical backbone of TD-DFT to OQS, and suggest a Markovian bath functional which can be readily included in electronic structure codes.
Long-lived electronic coherences in various photosynthetic complexes at cryogenic and room temperature have generated vigorous efforts both in theory and experiment to understand their origins and explore their potential role to biological function. The ultrafast signals resulting from the experiments that show evidence for these coherences result from many contributions to the molecular polarization. Quantum process tomography (QPT) is a technique whose goal is that of obtaining the time-evolution of all the density matrix elements based on a designed set of experiments with different preparation and measurements. The QPT procedure was conceived in the context of quantum information processing to characterize and understand general quantum evolution of controllable quantum systems, for example while carrying out quantum computational tasks. We introduce our QPT method for ultrafast experiments, and as an illustrative example, apply it to a simulation of a two-chromophore subsystem of the Fenna-Matthews-Olson photosynthetic complex, which was recently shown to have long-lived quantum coherences. Our Fenna-Matthews-Olson model is constructed using an atomistic approach to extract relevant parameters for the simulation of photosynthetic complexes that consists of a quantum mechanics/molecular mechanics approach combined with molecular dynamics and the use of state-of-the-art quantum master equations. We provide a set of methods that allow for quantifying the role of quantum coherence, dephasing, relaxation and other elementary processes in energy transfer efficiency in photosynthetic complexes, based on the information obtained from the atomistic simulations, or, using QPT, directly from the experiment. The ultimate goal of the combination of this diverse set of methodologies is to provide a reliable way of quantifying the role of long-lived quantum coherences and obtain atomistic insight of their causes.
Quantum Process Tomography (QPT) methods aim at identifying, i.e. estimating, a quantum process. QPT is a major quantum information processing tool, since it especially allows one to experimentally characterize the actual behavior of quantum gates, that may be used as the building blocks of quantum computers. We here consider unitary (possibly dense, i.e. without sparsity constraints) processes, which corresponds to isolated systems. Moreover, we develop a QPT method applicable to a significant number of qubits and hence to a high state space dimension, which allows one to tackle more complex problems. Using the unitarity of the process allows us to propose a method that first achieves part of QPT by performing an eigenanalysis of the estimated density matrix of a process output. We then complete the QPT by using another state differently. The relevance of our method is validated by means of simulations.
Reconstruction of the dynamics (quantum process tomography) of the single-exciton manifold in energy transfer systems is proposed here on the basis of two-dimensional fluorescence spectroscopy (2D-FS) with phase-modulation. The quantum-process-tomography protocol introduced here benefits from, e.g., the sensitivity enhancement ascribed to 2D-FS. Although the isotropically averaged spectroscopic signals depend on the quantum yield parameter Γ of the doubly excited-exciton manifold, it is shown that the reconstruction of the dynamics is insensitive to this parameter. Applications to foundational and applied problems, as well as further extensions, are discussed.
An arbitrary quantum-optical process (channel) can be completely characterized by probing it with coherent states using the recently developed coherent-state quantum process tomography (QPT) [Lobino et al., Science 322, 563 (2008)]. In general, precise QPT is possible if an infinite set of probes is available. Thus, realistic QPT of infinite-dimensional systems is approximate due to a finite experimentally feasible set of coherent states and its related energy-cutoff approximation. We show with explicit formulas that one can completely identify a quantum-optical Gaussian process just with a few different coherent states without approximations like the energy cutoff. For tomography of multimode processes, our method exponentially reduces the number of different test states, compared with existing methods.