Two-dimensional fluorescence spectroscopy with quantum entangled photons: Idler-referenced timing without pump detection

TL;DR

This work analyzes the feasibility of using idler-photon arrival times as the temporal reference for time-resolved two-dimensional fluorescence spectroscopy with entangled photons, aiming to remove the pump-timing channel. By treating the SPDC-produced twin-photon state with a central pump time $t_P$ as a free parameter, the authors show that an idler-referenced scheme can recover time-resolved dynamics when the photon pair exhibits negative or negligible frequency correlations. They derive the two-photon coincidence signals, separating rephasing and non-rephasing pathways, and show that negative frequency correlations yield a 2D spectroscopic signal with timing set by $t_F-t_I$, while positive correlations generally invalidate the idler-referenced approach unless specific conditions are met. The results provide design guidelines for entangled-photon sources and detection schemes, indicating a simplified experimental layout is achievable, but emphasize careful matching of temporal characteristics to the experiment’s timescale to fully harness non-classical correlations.

Abstract

Entangled photons have attracted increasing interest as resources for developing time-resolved spectroscopic techniques. Theoretical studies suggest that their non-classical correlations enable time-resolved spectroscopy with monochromatic pumping and can selectively isolate specific Liouville pathways in nonlinear optical signals. In an earlier study, we proposed a fluorescence detection scheme that could, in principle, be implemented using existing single-photon detectors [Y. Fujihashi et al., arXiv:2502.02073 (2025)]. In that design, the time origin was defined by detecting the arrival of the pulsed laser used to pump the nonlinear crystal for spontaneous parametric down-conversion, a requirement that made the overall experiment cumbersome. This study theoretically examines an alternative protocol that defines the reference time based on the arrival of idler photons. We demonstrate that this idler-referenced scheme functions effectively when the entangled photons exhibit either negative or negligible frequency correlations. Eliminating the pump-timing channel simplifies the optical layout and lowers the experimental barrier to realizing time-resolved two-dimensional fluorescence spectroscopy with entangled photons. Although the photons may exhibit frequency correlations in isolation, their frequency-time degrees of freedom can behave as effectively uncorrelated when considered over the full measurement timescale. Therefore, fully exploiting non-classical correlations requires an entangled photon source whose temporal characteristics are carefully matched to the overall timescale of the experiment.

Figures (5)

• Figure 1: Schematic of the quantum spectroscopy configuration proposed in a previous study Fujihashi:2025tw. (b) Setup considered in this study. BS: beam splitter; SPDC: spontaneous parametric down-conversion; PBS: polarized beam splitter; TCSPC: time-correlated single-photon counting device.
• Figure 2: Schematic of detection schemes corresponding to the two experimental configurations, as shown in Fig. \ref{['fig1']}. (a) In the pump-referenced setup, the detector system records the arrival-time difference between the photodiode and each single-photon camera. Setting the pump-pulse center to $t_\mathrm{P}=0$ and considering entangled pairs with the negative temporal correlation $t_\mathrm{S}=- t_\mathrm{I}$, the elapsed time from excitation by the signal photon to fluorescence emission can be expressed $\Delta t_\mathrm{FS}=t_\mathrm{F}-t_\mathrm{S}=t_\mathrm{F}+t_\mathrm{I}$. Accordingly, plotting the coincidence counts as a function of $t_\mathrm{F}+t_\mathrm{I}$ yields a time-resolved picture of the excited-state dynamics of the molecular sample. (b) In the idler-referenced scheme, the detector system records only the arrival-time difference between the two single-photon cameras, $t_\mathrm{F}-t_\mathrm{I}$. The figure illustrates the case of negatively frequency-correlated photon pairs, which are generated almost simultaneously within the time window of the entanglement time $T_\mathrm{e}$. Under this condition, $t_\mathrm{F}-t_\mathrm{I}$ is equal to the interval $\Delta t_\mathrm{FS}=t_\mathrm{F}-t_\mathrm{S}$ between sample excitation by the signal photon and the subsequent fluorescence emission, enabling access to excited-state dynamics without any timing signal from the pump.
• Figure 3: Joint spectral intensity $|f(\omega_\mathrm{S},\omega_\mathrm{I})|^2$ and the corresponding joint temporal intensity $|f(t_\mathrm{S},t_\mathrm{I})|^2$ of the two-photon state. Panels (a) and (b) show the cases of negative frequency correlation, whereas panels (c) and (d) show the cases of positive frequency correlation. The joint spectral intensities in panels (a) and (c) are computed using Eqs. \ref{['eq:psi-twin-negative']} and \ref{['eq:psi-twin-positive']}, respectively, while the joint temporal intensities in panels (b) and (d) are based on Eqs. \ref{['eq:temporal1']} and \ref{['eq:temporal2']}, respectively. For clarity, the delta functions in panels (b) and (d) are rendered as finite-width rectangular functions.
• Figure 4: Schematic of photon detection events. The light-pink shaded region illustrates the temporal distribution of $F_\mathrm{t}(t,t_\mathrm{I})$ in Eq. \ref{['eq:time-gate-function']}. The arrival times of the idler photons are blurred by the finite temporal resolution of the single-photon camera. The fluorescence photons experience the same temporal blurring.
• Figure 5: Double-sided Feynman diagrams representing the Liouville space pathways contributing to the two-photon coincidence signal in Eq. \ref{['eq:tpc-signal2']}.