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Precision Franck-Condon spectroscopy from highly-excited vibrational states
Published 18 Jan 2024 in physics.chem-ph and quant-ph | (2401.10384v2)
Abstract: As per the Franck-Condon principle, absorption spectroscopy reveals changes in nuclear geometry in molecules or solids upon electronic excitation. It is often assumed these changes cannot be resolved beyond the ground vibrational wavefunction width ($\sqrt{\hbar/m\omega}$). Here, we show this resolution dramatically improves with highly-excited vibrational initial states (with occupation number $\langle n\rangle$). These states magnify changes in geometry by $2\langle n\rangle +1$, a possibly counterintuitive result given the spatial uncertainty of Fock states grows with $n$. We also discuss generalizations of this result to multimode systems. Our result is relevant to optical spectroscopy, polariton condensates, and quantum simulators ($\textit{e.g.}$, boson samplers).
- A. Tokmakoff, Time-dependent quantum mechanics and spectroscopy (2014).
- M. Lax, “The Franck-Condon principle and its application to crystals,” J. Chem. Phys. 20, 1752–1760 (1952).
- K. Huang, A. Rhys, and N. F. Mott, “Theory of light absorption and non-radiative transitions in F-centres,” Proc. R. Soc. A 204, 406–423 (1950).
- J. Franck and E. Dymond, “Elementary processes of photochemical reactions,” Trans. Faraday Soc. 21, 536–542 (1926).
- E. U. Condon, “Nuclear motions associated with electron transitions in diatomic molecules,” Phys. Rev. 32, 858 (1928).
- F. Ansbacher, “A note on the overlap integral of two harmonic oscillator wave functions,” Z. Naturforsch. A 14, 889–892 (1959).
- J.-L. Chang, “A new formula to calculate Franck–Condon factors for displaced and distorted harmonic oscillators,” J. Mol. Spectrosc. 232, 102–104 (2005).
- P. T. Ruhoff and M. A. Ratner, “Algorithms for computing franck–condon overlap integrals,” Int. J. Quantum Chem. 77, 383–392 (2000).
- T. Zelevinsky, S. Kotochigova, and J. Ye, “Precision test of mass-ratio variations with lattice-confined ultracold molecules,” Phys. Rev. Lett. 100, 043201 (2008).
- D. DeMille, S. Sainis, J. Sage, T. Bergeman, S. Kotochigova, and E. Tiesinga, “Enhanced sensitivity to variation of me/mpsubscript𝑚𝑒subscript𝑚𝑝m_{e}/m_{p}italic_m start_POSTSUBSCRIPT italic_e end_POSTSUBSCRIPT / italic_m start_POSTSUBSCRIPT italic_p end_POSTSUBSCRIPT in molecular spectra,” Phys. Rev. Lett. 100, 043202 (2008).
- D. DeMille, S. B. Cahn, D. Murphree, D. A. Rahmlow, and M. G. Kozlov, “Using molecules to measure nuclear spin-dependent parity violation,” Phys. Rev. Lett. 100, 023003 (2008).
- I. Kozyryev and N. R. Hutzler, “Precision measurement of time-reversal symmetry violation with laser-cooled polyatomic molecules,” Phys. Rev. Lett. 119, 133002 (2017).
- A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990).
- J. A. Cina and V. Romero-Rochin, “Optical impulsive excitation of molecular pseudorotation in Jahn–Teller systems,” J. Chem. Phys. 93, 3844–3849 (1990).
- U. Banin, A. Bartana, S. Ruhman, and R. Kosloff, “Impulsive excitation of coherent vibrational motion ground surface dynamics induced by intense short pulses,” J. Chem. Phys. 101, 8461–8481 (1994).
- J. A. Cina, “Impulsive excitation of pseudo-rotation for geometric phase detection,” J. Raman Spectrosc. 31, 95–97 (2000).
- T. F. Crimmins, N. S. Stoyanov, and K. A. Nelson, “Heterodyned impulsive stimulated Raman scattering of phonon–polaritons in LiTaO33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT and LiNbO33{}_{3}start_FLOATSUBSCRIPT 3 end_FLOATSUBSCRIPT,” J. Chem. Phys. 117, 2882–2896 (2002).
- J. Huh, G. G. Guerreschi, B. Peropadre, J. R. McClean, and A. Aspuru-Guzik, “Boson sampling for molecular vibronic spectra,” Nat. Photonics 9, 615–620 (2015).
- F. Wolf, C. Shi, J. C. Heip, M. Gessner, L. Pezzè, A. Smerzi, M. Schulte, K. Hammerer, and P. O. Schmidt, “Motional Fock states for quantum-enhanced amplitude and phase measurements with trapped ions,” Nat. Commun. 10, 2929 (2019).
- K. A. Gilmore, M. Affolter, R. J. Lewis-Swan, D. Barberena, E. Jordan, A. M. Rey, and J. J. Bollinger, “Quantum-enhanced sensing of displacements and electric fields with two-dimensional trapped-ion crystals,” Science 373, 673–678 (2021).
- C. H. Valahu, V. C. Olaya-Agudelo, R. J. MacDonell, T. Navickas, A. D. Rao, M. J. Millican, J. B. Pérez-Sánchez, J. Yuen-Zhou, M. J. Biercuk, C. Hempel et al., “Direct observation of geometric-phase interference in dynamics around a conical intersection,” Nat. Chem. pp. 1–6 (2023).
- S. Pannir-Sivajothi, J. A. Campos-Gonzalez-Angulo, L. A. Martínez-Martínez, S. Sinha, and J. Yuen-Zhou, “Driving chemical reactions with polariton condensates,” Nat. Commun. 13, 1645 (2022).
- V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
- D. J. Tannor, Introduction to quantum mechanics: a time-dependent perspective (2007).
- J. Huh and R. Berger, “Application of time-independent cumulant expansion to calculation of Franck–Condon profiles for large molecular systems,” Faraday Discuss. 150, 363–373 (2011).
- L. Zuo, S. B. Jo, Y. Li, Y. Meng, R. J. Stoddard, Y. Liu, F. Lin, X. Shi, F. Liu, H. W. Hillhouse et al., “Dilution effect for highly efficient multiple-component organic solar cells,” Nat. Nanotechnol. 17, 53–60 (2022).
- M. de Jong, L. Seijo, A. Meijerink, and F. T. Rabouw, “Resolving the ambiguity in the relation between Stokes shift and Huang–Rhys parameter,” Phys. Chem. Chem. Phys. 17, 16959–16969 (2015).
- J. Luo, X. Wang, S. Li, J. Liu, Y. Guo, G. Niu, L. Yao, Y. Fu, L. Gao, Q. Dong et al., “Efficient and stable emission of warm-white light from lead-free halide double perovskites,” Nature 563, 541–545 (2018).
- W. Stadler, D. M. Hofmann, H. C. Alt, T. Muschik, B. K. Meyer, E. Weigel, G. Müller-Vogt, M. Salk, E. Rupp, and K. W. Benz, “Optical investigations of defects in Cd1−x1𝑥{}_{1-x}start_FLOATSUBSCRIPT 1 - italic_x end_FLOATSUBSCRIPTZnx𝑥{}_{x}start_FLOATSUBSCRIPT italic_x end_FLOATSUBSCRIPTTe,” Phys. Rev. B 51, 10619–10630 (1995).
- E. J. Heller, “The semiclassical way to molecular spectroscopy,” Acc. Chem. Res. 14, 368–375 (1981).
- N. Makri, “The linear response approximation and its lowest order corrections: An influence functional approach,” J. Phys. Chem. B 103, 2823–2829 (1999).
- Y. Georgievskii, C.-P. Hsu, and R. A. Marcus, “Linear response in theory of electron transfer reactions as an alternative to the molecular harmonic oscillator model,” J. Chem. Phys. 110, 5307–5317 (1999).
- T. Renger and R. A. Marcus, “On the relation of protein dynamics and exciton relaxation in pigment–protein complexes: An estimation of the spectral density and a theory for the calculation of optical spectra,” J. Chem. Phys. 116, 9997–10019 (2002).
- J. Cao, L. W. Ungar, and G. A. Voth, “A novel method for simulating quantum dissipative systems,” J. Chem. Phys. 104, 4189–4197 (1996).
- D. R. Reichman and R. J. Silbey, “On the relaxation of a two-level system: Beyond the weak-coupling approximation,” J. Chem. Phys. 104, 1506–1518 (1996).
- S. A. Egorov, E. Rabani, and B. J. Berne, “Vibronic spectra in condensed matter: A comparison of exact quantum mechanical and various semiclassical treatments for harmonic baths,” J. Chem. Phys. 108, 1407–1422 (1998).
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