6 Coherent Control of Nonadiabatic Dynamics of Electron-Phonon …
131
their interaction with electrons through μ i and ν. In order to clarify the mechanism
of this effect, further discussion on the entanglement entropy in multipartite systems
[21–23] will be helpful.
6.4 Summary
We calculated the wavepacket dynamics of electron-phonon-photon systems by
numerical calculations focusing on the interplay of the electron-phonon nonadiabaticity and the Raman processes. While the effect of the Raman processes is small
on the wavepacket motion starting with empty Stokes/anti-Stokes modes, the stimulated Raman processes enhance the electronic transition, which shows that we should
take into account them to obtain accurate trajectories of wavepackets. In particular,
the interference between Stokes and anti-Stokes Raman processes suppresses the
absorption of pump-mode photons, although the electronic excitation is induced and
the excited-state population N (t) takes a large value. Furthermore, when both λ and
ν i are present, large deviation from semiclassical calculations is obtained, which
shows that the bifurcation of wavepackets should be carefully treated in the presence
of both the electron-phonon adiabaticity and the Raman processes.
As an example of coherent control of phonon states by external light, we show that
the relative phase between photon modes is directly reflected to the created phonon
states. However, the role of the CI on the phonon creation mechanism is still an open
question, and we need further study on the modulation of the wavepacket trajectory
which induces the change of the winding number around the CI [15], for example.
References
1. R.S. Judson, H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992)
2. D.G. England, K.A.G. Fisher, J.W. MacLean, P.J. Bustard, K. Heshami, K.J. Resch, B.J. Sussman, Phys. Rev. Lett. 117, 073603 (2016)
3. R.M. Bowman, M. Dantus, A.H. Zewail, Chem. Phys. Lett. 174, 546 (1990)
4. K.G. Nakamura, K. Ohya, H. Takahashi, T. Tsuruta, H. Sasaki, S. Uozumi, K. Norimatsu, M.
Kitajima, Y. Shikano, Y. Kayanuma, Phys. Rev. B 94, 024303 (2016)
5. M. Gallart, M. Ziegler, O. Crégut, E. Feltin, J.-F. Carlin, R. Butté, N. Grandjean, B. Hönerlage,
P. Gilliot, Phys. Rev. B96, 041303 (2017)
6. T. Ghosh, S. Aharon, A. Shpatz, L. Etgar, S. Ruhman, ACS Nano. 12, 5719 (2018)
7. M. Gao, C. Lu, H. Jean-Ruel, L.C. Liu, A. Marx, K. Onda, S. Koshihara, Y. Nakano, X. Shao, T.
Hiramatsu, G. Saito, H. Yamochi, R.R. Cooney, G. Moriena, G. Sciaini, R.J.D. Miller, Nature
496, 343 (2013)
8. K.H. Kim, J.G. Kim, S. Nozawa, T. Sato, K.Y. Oang, T.W. Kim, H. Ki, J. Jo, S. Park, C. Song,
T. Sato, K. Ogawa, T. Togashi, K. Tono, M. Yabashi, T. Ishikawa, J. Kim, R. Ryoo, J. Kim, H.
Ihee, S. Adachi, Nature 518, 385 (2015)
9. M. Först, A.D. Caviglia, R. Scherwitzl, R. Mankowsky, P. Zubko, V. Khanna, H. Bromberger,
S.B. Wilkins, Y.-D. Chuang, W.S. Lee, W.F. Schlotter, J.J. Turner, G.L. Dakovski, M.P. Minitti,
131
their interaction with electrons through μ i and ν. In order to clarify the mechanism
of this effect, further discussion on the entanglement entropy in multipartite systems
[21–23] will be helpful.
6.4 Summary
We calculated the wavepacket dynamics of electron-phonon-photon systems by
numerical calculations focusing on the interplay of the electron-phonon nonadiabaticity and the Raman processes. While the effect of the Raman processes is small
on the wavepacket motion starting with empty Stokes/anti-Stokes modes, the stimulated Raman processes enhance the electronic transition, which shows that we should
take into account them to obtain accurate trajectories of wavepackets. In particular,
the interference between Stokes and anti-Stokes Raman processes suppresses the
absorption of pump-mode photons, although the electronic excitation is induced and
the excited-state population N (t) takes a large value. Furthermore, when both λ and
ν i are present, large deviation from semiclassical calculations is obtained, which
shows that the bifurcation of wavepackets should be carefully treated in the presence
of both the electron-phonon adiabaticity and the Raman processes.
As an example of coherent control of phonon states by external light, we show that
the relative phase between photon modes is directly reflected to the created phonon
states. However, the role of the CI on the phonon creation mechanism is still an open
question, and we need further study on the modulation of the wavepacket trajectory
which induces the change of the winding number around the CI [15], for example.
References
1. R.S. Judson, H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992)
2. D.G. England, K.A.G. Fisher, J.W. MacLean, P.J. Bustard, K. Heshami, K.J. Resch, B.J. Sussman, Phys. Rev. Lett. 117, 073603 (2016)
3. R.M. Bowman, M. Dantus, A.H. Zewail, Chem. Phys. Lett. 174, 546 (1990)
4. K.G. Nakamura, K. Ohya, H. Takahashi, T. Tsuruta, H. Sasaki, S. Uozumi, K. Norimatsu, M.
Kitajima, Y. Shikano, Y. Kayanuma, Phys. Rev. B 94, 024303 (2016)
5. M. Gallart, M. Ziegler, O. Crégut, E. Feltin, J.-F. Carlin, R. Butté, N. Grandjean, B. Hönerlage,
P. Gilliot, Phys. Rev. B96, 041303 (2017)
6. T. Ghosh, S. Aharon, A. Shpatz, L. Etgar, S. Ruhman, ACS Nano. 12, 5719 (2018)
7. M. Gao, C. Lu, H. Jean-Ruel, L.C. Liu, A. Marx, K. Onda, S. Koshihara, Y. Nakano, X. Shao, T.
Hiramatsu, G. Saito, H. Yamochi, R.R. Cooney, G. Moriena, G. Sciaini, R.J.D. Miller, Nature
496, 343 (2013)
8. K.H. Kim, J.G. Kim, S. Nozawa, T. Sato, K.Y. Oang, T.W. Kim, H. Ki, J. Jo, S. Park, C. Song,
T. Sato, K. Ogawa, T. Togashi, K. Tono, M. Yabashi, T. Ishikawa, J. Kim, R. Ryoo, J. Kim, H.
Ihee, S. Adachi, Nature 518, 385 (2015)
9. M. Först, A.D. Caviglia, R. Scherwitzl, R. Mankowsky, P. Zubko, V. Khanna, H. Bromberger,
S.B. Wilkins, Y.-D. Chuang, W.S. Lee, W.F. Schlotter, J.J. Turner, G.L. Dakovski, M.P. Minitti,