Deep learning parameter estimation and quantum control of single molecule

TL;DR

It is demonstrated how to infer key physical parameters of a single molecule driven by spectrally modulated pulses at room temperature and the robustness of this approach highlights the importance of reliable parameter estimation in designing effective coherent control protocols.

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 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.

Figures (14)

• Figure 1: (a) Schematics of the individual molecules energy levels description. $E_i$ denotes the three-level energies of the molecule with corresponding two-photon absorption (2P abs.) transition between $E_0$ and $E_2$ at Rabi frequency $\Omega_{\text{2P}}$ and $|S_i\rangle \equiv|i\rangle$ represents the electronic states. The relaxation processes between levels $E_2 \to E_1$ occur at a rate $\Gamma_{12}$, and dephasing in the singlet state $S_2$ at a rate $\gamma_2$. (b) Molecular structure of the MeLPPP (R1, n-hexyl; R2, methyl; R3, 1,4-decylphenyl).
• Figure 2: (a) Frequency domain profile of the field. The solid line represents the normalized spectrum $A(\omega)$ with central frequency $\omega_0= 12~987 \text{\;cm}^{-1}$ and spectral width $\sigma_\text{FWHM}=400 \text{\;cm}^{-1}$. The dashed lines represent the spectral phase $\varphi(\omega)$ for chirped $(\beta\neq 0)$ and unchirped $(\beta=0)$ fields. (b) Normalized temporal profile of the chirped field (see Eq. \ref{['eq:phase_beta_mask']}) for different $\beta$ values. (c) Normalized temporal profile of the field with amplitude and phase modulation masks (see Eq. \ref{['eq:tau_mod_mask']}) for different $\tau$ values.
• Figure 3: Population dynamics of the MeLPPP molecule for $\Omega_{\text{2P}}=531\text{ cm}^{-1}$, $\gamma_2=1/61 \text{\;fs}^{-1}$, $\Gamma_{12}=1/190 \text{\;fs}^{-1}$ and control parameter values: (a) $\beta=0$ fs$^2$, (b) $\beta=500$ fs$^2$, (c) $\beta=1500$ fs$^2$, and (d) $\beta=2500$ fs$^2$.
• Figure 4: Ultrafast population dynamics of the MeLPPP molecule with values $\Omega_{\text{2P}}=531\text{ cm}^{-1}$, $\gamma_2=1/61 \text{\;fs}^{-1}$, $\Gamma_{12}=1/190 \text{\;fs}^{-1}$ and different control parameter: (a) $\tau=0$ fs (b) $\tau=50$ fs (c) $\tau=100$ fs and (d) $\tau=200$ fs.
• Figure 5: Full map of the ultrafast dynamics of the population $\rho_{11}$ of the MeLPPP molecule as a function of time and the control parameters $\beta$ and $\tau$. At steady-state times ($\sim1~\text{ps}$), the obtained values reproduce the shape of the PL signal, as indicated by the red solid line. Maximum values of $\rho_{11}$ occur at $\beta = 0$ and $\tau = 0$, while deviations from these conditions lead to distinct PL intensities.