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Resolution of strongly competitive product channels with optimal dynamic discrimination: Application to flavins
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Image of FIG. 1.
FIG. 1.

ODD seeks to dynamically discriminate a number of statically similar quantum systems. The state vectors for quantum systems ν = 1, 2, … are initially nearly parallel, which reflects their static indistinguishability. An optimal control pulse creates dynamic evolution of the state vectors to align the targeted quantum system parallel to the detection state and all other background systems (ν ≠ ξ) orthogonal to the detection state. Such discrimination is achieved on a coherent time scale, after which all state vectors again resume their free evolution.

Image of FIG. 2.
FIG. 2.

Molecular structure of RBF (a) and FMN (b) with numbering of specific atoms in the isoalloxazine ring moiety.

Image of FIG. 3.
FIG. 3.

Linear absorption and fluorescence spectra of RBF (solid) and FMN (dashed) in aqueous media at 298 K. Arrows at 400 and 530 nm indicate the control and collected fluorescence wavelengths, respectively.

Image of FIG. 4.
FIG. 4.

Energy level diagram illustrating ODD-relevant electronic transitions for RBF and FMN; the corresponding absorption and fluorescence spectra are shown on the left. The 400 nm shaped UV control field creates a unique wavepacket in a vibrational band {ν} of electronic state . A time-delayed, unshaped IR pulse at 800 nm interrupts the carefully created wavepackets on and re-excites the population to higher states , thus depleting the population and eventual fluorescence at 530 nm. The coherent interplay between the shaped preparation pulse, wavepacket evolution, and delayed depletion pulse induces a detectable difference in the RBF and FMN depletion efficiencies.

Image of FIG. 5.
FIG. 5.

Highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals involved in the initial type electronic transition of RBF. Localization of electron density on the central isoalloxazine ring is consistent with the minor influence of the ribityl side chain on the observed photophysics. Electronic structure obtained with GAUSSIAN 03 at the B3LYP/DGTZVP level of theory.

Image of FIG. 6.
FIG. 6.

Experimental layout for closed-loop ODD. The shaped UV pulse and unshaped IR pulse are recombined in duplicate flow cells each containing aqueous solutions of RBF or FMN. For the discrimination stage of the experiments, the two flow cells are replaced with a single flow cell containing an aqueous mixture of RBF and FMN. Temporally depleted fluorescence induced by the IR pulse is detected with photomultiplier modules.

Image of FIG. 7.
FIG. 7.

Raw fluorescence for RBF and FMN as a function of the delay time between the unshaped UV and IR pulses. The fluorescence depletion of FMN is offset by 5% for visual clarity. For delay times τ ≳ 0 ps the IR pulse depletes the population by 15–30% depending on experimental conditions. ODD discrimination is performed within a delay of 200 ≲ τ ≲ 600 (gray area). Simultaneous acquisition of RBF and FMN depletions ensures noise fluctuations are essentially equal and allows cancelation to first order.

Image of FIG. 8.
FIG. 8.

Absolute RBF and FMN depletions for optimal UV pulse shapes at a time-delay of τ = 500 fs. Depletions induced by a TL UV pulse are statistically indistinguishable at ∼21%. Optimal UV pulses are discovered that dynamically maximize (a) and minimize (b) the two flavin depletions. This separation of absolute fluorescence depletions enables reliable discrimination through as in Fig. 9(b).

Image of FIG. 9.
FIG. 9.

Closed-loop, adaptive optimization of the flavin depletion ratio . The GA discovers optimal UV pulses that maximize and minimize (a). The depletion induced by the TL pulse is also displayed as a reference. Discovery of optimal UV pulse shapes enable a statistically significant separation between RBF and FMN of ∼84% (16σ) (b). A histogram is constructed from 100 samples of 1000 averaged laser shots each.

Image of FIG. 10.
FIG. 10.

Scan of the depletion ratio as the delay time τ is varied between an optimal UV pulse (optimized at τ = 500 fs) and an unshaped IR pulse. The temporal discrimination provided by the TL pulse is shown for reference. The optimal UV pulse enables significant discrimination for a temporal window of ∼1.75 ps. For delay times longer than this window, any vibrational coherence created by the shaped pulses is lost and the two flavins again exhibit identical depletion ratios.

Image of FIG. 11.
FIG. 11.

Absolute RBF and FMN temporal depletions for maximization of the depletion ratio as well as with the TL pulse. In order to separate the flavin dynamics, an optimal UV pulse lowers the absolute flavin depletions. After a delay time of τ ∼ 1 ps, the individual flavin depletions return to their TL values, which indicates a loss of vibrational coherence and population relaxation. These absolute depletions correspond to the depletion ratio depicted in Fig. 10.

Image of FIG. 12.
FIG. 12.

Spectrograms of UV pulse pairs resultant from four distinct GA runs that alternatively maximize (left column) and minimize (right column) the flavin depletion ratio . Each spectrogram is created with a short-time Fourier transform of the recovered SD-FROG fields.

Image of FIG. 13.
FIG. 13.

SD-FROG retrieved optimal UV fields corresponding to the first pulse set of Fig. 12. Considerable temporal overlap of and is observed (a), which suggests that both fields engage a common vibrational mode and the resultant discrimination is dependent upon the relative subpulse phasing. Examination of reveals an in-phase subpulse structure (b) while exhibits an antiphased sequence (c). In both panels (b) and (c), the slowly varying temporal envelope is shown for reference. High-frequency oscillations in (a) result from noise in the FROG inversion procedure.

Image of FIG. 14.
FIG. 14.

SD-FROG retrieved optimal UV spectral phases corresponding to the fields shown in Fig. 13. Each spectral phase exhibits a triangle-like pattern (a), which creates the observed two subpulses spaced at ∼1.4 ps. A phase discontinuity of ∼π is also evident in (b) in order to craft the antiphased subpulses of . For comparison, with the π discontinuity removed at ∼398.5 nm is also displayed (blue) in panel (a).

Image of FIG. 15.
FIG. 15.

Experimentally measured depleted fluorescence signals for both a pure solution of RBF and a solution containing a mixture of both RBF and FMN. Linearly independent data are obtained by recording the fluorescence signals as the delay time τ between the optimal UV and IR pulses is varied. The extracted slope of 0.36 is the fractional context, , of RBF reported in the third row of Table I.

Image of FIG. 16.
FIG. 16.

Optimal UV field for maximization of the depletion ratio that corresponds to the second pulse set of Fig. 12. The subpulse sequence with a spacing exhibits an antiphased relationship (a). The optimal spectral phase again expresses a triangle-like pattern (b) with a noticeable phase discontinuity of ∼π at ∼399.5 nm (c). For comparison, the optimal phase with the π discontinuity removed is also displayed (blue) in panel (b). The slowly varying temporal envelope is shown in (a) for reference.


Generic image for table
Table I.

Discrimination experiments for independent determination of RBF and FMN concentrations in a mixture. Although two experiments could reveal the flavin concentrations within statistical uncertainty (rows 1 and 2), overdetermination of Eq. (2) by measuring the depleted fluorescence at multiple UV–IR delay times τ significantly reduces the uncertainty of the retrieved concentrations (row 3).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Resolution of strongly competitive product channels with optimal dynamic discrimination: Application to flavins