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ACS Physical Chemistry Au

Deep Learning Parameter Estimation and Quantum Control of Single Molecules

Juan M. Scarpetta, Omar Calderón-Losada, Morten Hjorth-Jensen, John Henry Reina

Published Jun 12, 2026• 0 citations
Publisher

Abstract

Coherent control, a central concept in physics and chemistry, has sparked significant interest due to its ability to fine-tune interference effects in atoms and individual molecules for applications ranging from light-harvesting complexes to molecular qubits. However, precise characterization of the system's dissipative dynamics is required for its implementation, especially at high temperatures. In a quantum control experiment, this means learning system-bath parameters and driving coupling strengths. Here, we demonstrate how to infer key physical parameters of a single molecule driven by spectrally modulated pulses at room temperature. We develop and compare two computational approaches based on two-photon absorption photoluminescence signals: an optimization-based minimization scheme and a feed-forward neural network. The robustness of our approach highlights the importance of reliable parameter estimation in designing effective coherent control protocols. Our results have direct applications in ultrafast spectroscopy, quantum materials, and technology.

DOI
10.1021/acsphyschemau.6c00048

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Coherent control, a central concept in physics and chemistry, has sparked significant interest due to its ability to fine-tune interference effects in atoms and individual molecules for applications ranging from light-harvesting complexes to molecular qubits. However, precise characterization of the system's dissipative dynamics is required for its implementation, especially at high temperatures. In a quantum control experiment, this means learning system-bath parameters and driving coupling strengths. Here, we demonstrate how to infer key physical parameters of a single molecule driven by spectrally modulated pulses at room temperature. We develop and compare two computational approaches based on two-photon absorption photoluminescence signals: an optimization-based minimization scheme and a feed-forward neural network. The robustness of our approach highlights the importance of reliable parameter estimation in designing effective coherent control protocols. Our results have direct applications in ultrafast spectroscopy, quantum materials, and technology.
Coherent control, a central concept in physics and chemistry, has sparked significant interest due to its ability to fine-tune interference effects in atoms and individual molecules for applications ranging from light-harvesting complexes to molecular qubits. However, precise characterization of the system's dissipative dynamics is required for its implementation, especially at high temperature. In a quantum control experiment, this means learning system-bath parameters and driving coupling strengths. Here, we demonstrate how to infer key physical parameters of a single molecule driven by spectrally modulated pulses at room temperature. We develop and compare two computational approaches based on two-photon absorption photoluminescence signals: an optimization-based minimization scheme and a feed-forward neural network. The robustness of our approach highlights the importance of reliable parameter estimation in designing effective coherent control protocols. Our results have direct applications in ultrafast spectroscopy, quantum materials and technology.
Ultrafast pulses allow observation of molecular dynamics with femtosecond time resolution through pump probe experiments. However, averaging over an ensemble of molecules tends to wash out phase sensitive information, necessary to probe quantum effects, due to the intrinsic inhomogeneity in molecular conformations, orientations and interactions that lead to unique potential energy landscapes for each molecule. It is therefore important to go beyond the ensemble average when looking at quantum dynamics of organic systems at room temperature, and resolve the behaviour of specific molecules on an individual basis. In this thesis, we show the creation, manipulation and observation of ultrafast coherent effects in single molecules at room temperature, and resolve a certain measure of environmental influence on the specific dynamics of each molecule. Moreover, we apply this insight to investigate a functional light harvesting biosystem, and lay the basis for a technique that has the time and space resolution required to observe these systems in vivo. In chapter 1, we introduce the concepts and techniques the research in this thesis is built on. In chapter 2, we treat the possibility of controlling ultrafast pulses at the high-NA diffraction limit, and come to conclusions about the procedure to follow there that hold for all pulse-shaping experiments. We show in proof of principle experiments that we can control the ultrafast characteristics of optical pulses in nanometric excitation volumes. In chapters 3 and 4 we report the creation, detection and control of ultrafast quantum dynamics in single organic molecules at room temperature. We show that manipulation of superposition states is possible in these systems within a coherence dephasing time of ~50 fs. This leads to the first observation of rabi-oscillations in room temperature single molecules, to ultrafast operation of an organic qubit, and to the creation of non-stationary superposition states (vibrational wavepackets). We probe the influence of the local environment on the composition and dynamics of these wavepackets and show we can optimize the state preparation protocol for each individual molecule in its own nanoenvironment, leading to high fidelity coherent control. In these chapters we lay out the proof of principle work of detecting the quantumdynamics of a complex system in interaction with its environment at room temperature. In chapter 5 we discuss application of these techniques to the investigation of long lived coherence in photosynthetic systems. We show that electronic coherence between different rings of the LH2 system persists to time scales of 100s of femtoseconds at room temperature. Moreover we show that the energy transfer pathways in LH2 adapt to environmentally induced changes in the molecule and that the nature of the transfer remains coherent for each pathway, providing strong evidence that coherent energy transfer is the optimum process for energy transfer in photosynthesis. Finally, in chapter 6 we take the technical development one step further and report on the creation of a framework based on plasmonic antennas that allows for control of the amplitude-phase characteristics in nanometric sized hotspot fields. We show for the first time that the ultrafast characteristics of plasmonic hotspots can directly be engineered through design of the plasmonic system and experimentally demonstrate two much-anticipated examples: a sub-diffraction resolution phase shaper and an ultrafast plasmonic switch for pump probe experiments. The results presented in this thesis form the first creation and observation of ultrafast coherent dynamics in individual molecular systems at room temperature. This is a necessary step to be able to do true quantum tomography in complex systems, resolve the influence of the environment on molecular dynamics, and investigate the physics that determines evolutionary optimization and functionality in biomolecules.
Quantum computing requires the optimization of control pulses to achieve high-fidelity quantum gates. We propose a machine learning-based protocol to address the challenges of evaluating gradients and modeling complex system dynamics. By training a recurrent neural network (RNN) to predict qubit behavior, our approach enables efficient gradient-based pulse optimization without the need for a detailed system model. First, we sample qubit dynamics using random control pulses with weak prior assumptions. We then train the RNN on the system's observed responses, and use the trained model to optimize high-fidelity control pulses. We demonstrate the effectiveness of this approach through simulations on a single ST0ST_0ST0​ qubit.
Coherence is a key aspect of a large variety of processes, ranging from the coherent delocalisation of excitation energy, which is important for energy transfer in supramolecular nanostructures, to coherence between electronic states of a single quantum system, which is essential for quantum optical applications. Coherent control schemes exploit this quantum mechanical property by actively manipulating the outcome of dynamical processes. Moreover, this technique allows measuring dynamical processes under the influence of dephasing. However, going beyond the ensemble averaged situation, i.e. working on the level of single quantum systems, is highly challenging for quantum systems embedded in a solid matrix at elevated temperature. Since interactions between the quantum system and its specific local environment are a priori unknown, this requires a reliable approach to retrieve the relevant parameters governing the ultrafast coherent dynamics. Here, we present measurements of the ultrafast coherence decay of two-photon accessible excited states in single organic molecules embedded in a disordered environment at room temperature. We combine this experimental approach with a quantum dynamics identification procedure, which yields a minimum three-level model to describe the obtained data with very good agreement. In particular, we are able to retrieve the ultrafast (coherent) excited state dynamics in single molecules and demonstrate its sensitivity to the local nanoenvironment from molecule to molecule. This work provides a robust approach to measure and analyse ultrafast quantum dynamics in complex nanosystems.
The combination of single particle detection and ultrafast laser pulses is an instrumental method to track dynamics at the femtosecond time scale in single molecules, quantum dots and plasmonic nanoparticles. Optimal control of the extremely short-lived coherences of these individual systems has so far remained elusive, yet its successful implementation would enable arbitrary external manipulation of otherwise inaccessible nanoscale dynamics. In ensemble measurements, such control is often achieved by resorting to a closed-loop optimization strategy, where the spectral phase of a broadband laser field is iteratively optimized. This scheme needs long measurement times and strong signals to converge to the optimal solution. This requirement is in conflict with the nature of single emitters whose signals are weak and unstable. Here we demonstrate an effective closed-loop optimization strategy capable of addressing single quantum dots at room temperature, using as feedback observable the two-photon photoluminescence induced by a phase-controlled broadband femtosecond laser. Crucial to the optimization loop is the use of a deterministic and robust-against-noise search algorithm converging to the theoretically predicted solution in a reduced amount of steps, even when operating at the few-photon level. Full optimization of the single dot luminescence is obtained within ~100 trials, with a typical integration time of 100 ms per trial. These times are faster than the typical photobleaching times in single molecules at room temperature. Our results show the suitability of the novel approach to perform closed-loop optimizations on single molecules, thus extending the available experimental toolbox to the active control of nanoscale coherences. Femtosecond laser control allows to harness short-lived coherences and study molecular ultrafast dynamics. Translating such coherent-control schemes from the ensemble to single molecules is challenging due to signal fluctuation and photo-dissociation. Now, Nicolò Accanto and Pablo de Roque from ICFO - the Institute of Photonic Sciences in Barcelona, and colleagues, have reduced the time needed to perform closed-loop optimisations. By employing a new simple deterministic algorithm, and assuming simple optimisation landscapes, they accomplished a phase-only optimisation of the two-photon photoluminescence of a single quantum dot. Combining this rapid feedback process within the search algorithm with a sensitive microscopy technique, they were able to optimise on signals even at the few-photon level, enabling the coherent control of individual quantum-dots at room temperature in a matter of seconds - a speedup critical for capturing details of biomolecular interactions, for instance.
The ability to characterise a Hamiltonian with high precision is crucial for the implementation of quantum technologies. In addition to the well-developed approaches utilising optimal probe states and optimal measurements, the method of optimal control can be used to identify time-dependent pulses applied to the system to achieve higher precision in the estimation of Hamiltonian parameters, especially in the presence of noise. Here, we extend optimally controlled estimation schemes for single qubits to non-commuting dynamics as well as two interacting qubits, demonstrating improvements in terms of maximal precision, time-stability, as well as robustness over uncontrolled protocols.