284
M. Sato
ME coupling. In fact, it has been predicted [26] that a topological spin liquid can be
created if we apply a circularly polarized laser to a honeycomb Kitaev model [71–73]
with a striction type ME coupling.
11.5 Summary and Outlook
In this chapter, I have reviewed the basic theoretical part of Floquet engineering [20–
23], focusing on isolated periodically-driven quantum systems. Floquet theorem,
Floquet-Magnus expansion for deriving the effective Floquet Hamiltonian, and its
physical meanings have been explained in Sect. 11.2. The truncated Floquet Hamiltonian can be used to correctly describe the short-time behavior of driven systems.
Then, in Sect. 11.3, I have discussed some information about currently-available
laser and electromagnetic waves which is important to perform Floquet engineering
in materials, especially, solids. The intensity of 1 [MV/cm] gives a reference amplitude of AC electric field for effective engineering of physical quantities. Finally, I
have explained two examples of Floquet engineering in magnetic insulators: inverse
Faraday effect with THz laser in generic magnetic insulators [24, 68] and ultrafast
control of spin chirality in multiferroics [25].
Further development of Floquet theory is necessary to more accurately predict
Floquet engineered quantities in materials. An important research direction is the
development of sophisticated theories treating effect of environment (i.e., dissipation) because dissipation effect cannot be ignored in real materials driven by laser.
Approaches based on non-equilibrium Green’s function [12, 14] and quantum master equation [15, 18, 19] have high potential to provide a deep insight to dissipative
periodically driven systems. These studies would also contribute to the development
of the fundamental of non-equilibrium physics.
Acknowledgements I would like to thank all the collaborators of our recent works for laser-driven
phenomena, especially, Shintaro Takayoshi, Takashi Oka, Tatsuhiko N. Ikeda, Hiroaki Ishizuka,
Horoyuki Fujita, and Sho Higashikawa. I was supported by JSPS KAKENHI (Grant No. 17K05513
and No. 20H01830) and a Grant-in-Aid for Scientific Research on Innovative Areas “Quantum
Liquid Crystals” (Grant No. JP19H05825).
References
1. H. Hirori, A. Doi, F. Blanchard, K. Tanaka, Appl. Phys. Lett. 98, 91106 (2011)
2. Y. Mukai, H. Hirori, T. Yamamoto, H. Kageyama, K. Tanaka, New J. Phys. 18, 013045 (2016)
3. B. Liu, H. Bromberger, A. Cartella, T. Gebert, M. Forst, A. Cavalleri, Opt. Lett. 42, 129 (2017)
4. M. Sato, T. Higuchi, N. Kanda, K. Konishi, K. Yoshioka, T. Suzuki, K. Misawa, M. KuwatoGonokami, Nature Photo. 7, 724 (2013)
5. P. Nemec, M. Fiebig, T. Kampfrath, A.V. Kimel, Nature Phys. 14, 229 (2018)
6. C.P. Slichter, Principles of Magnetic Resonance (Springer, 1989)
7. H. Nojiri, Z.W. Ouyang, Terahertz Sci. Tech. 5, 1 (2012)
M. Sato
ME coupling. In fact, it has been predicted [26] that a topological spin liquid can be
created if we apply a circularly polarized laser to a honeycomb Kitaev model [71–73]
with a striction type ME coupling.
11.5 Summary and Outlook
In this chapter, I have reviewed the basic theoretical part of Floquet engineering [20–
23], focusing on isolated periodically-driven quantum systems. Floquet theorem,
Floquet-Magnus expansion for deriving the effective Floquet Hamiltonian, and its
physical meanings have been explained in Sect. 11.2. The truncated Floquet Hamiltonian can be used to correctly describe the short-time behavior of driven systems.
Then, in Sect. 11.3, I have discussed some information about currently-available
laser and electromagnetic waves which is important to perform Floquet engineering
in materials, especially, solids. The intensity of 1 [MV/cm] gives a reference amplitude of AC electric field for effective engineering of physical quantities. Finally, I
have explained two examples of Floquet engineering in magnetic insulators: inverse
Faraday effect with THz laser in generic magnetic insulators [24, 68] and ultrafast
control of spin chirality in multiferroics [25].
Further development of Floquet theory is necessary to more accurately predict
Floquet engineered quantities in materials. An important research direction is the
development of sophisticated theories treating effect of environment (i.e., dissipation) because dissipation effect cannot be ignored in real materials driven by laser.
Approaches based on non-equilibrium Green’s function [12, 14] and quantum master equation [15, 18, 19] have high potential to provide a deep insight to dissipative
periodically driven systems. These studies would also contribute to the development
of the fundamental of non-equilibrium physics.
Acknowledgements I would like to thank all the collaborators of our recent works for laser-driven
phenomena, especially, Shintaro Takayoshi, Takashi Oka, Tatsuhiko N. Ikeda, Hiroaki Ishizuka,
Horoyuki Fujita, and Sho Higashikawa. I was supported by JSPS KAKENHI (Grant No. 17K05513
and No. 20H01830) and a Grant-in-Aid for Scientific Research on Innovative Areas “Quantum
Liquid Crystals” (Grant No. JP19H05825).
References
1. H. Hirori, A. Doi, F. Blanchard, K. Tanaka, Appl. Phys. Lett. 98, 91106 (2011)
2. Y. Mukai, H. Hirori, T. Yamamoto, H. Kageyama, K. Tanaka, New J. Phys. 18, 013045 (2016)
3. B. Liu, H. Bromberger, A. Cartella, T. Gebert, M. Forst, A. Cavalleri, Opt. Lett. 42, 129 (2017)
4. M. Sato, T. Higuchi, N. Kanda, K. Konishi, K. Yoshioka, T. Suzuki, K. Misawa, M. KuwatoGonokami, Nature Photo. 7, 724 (2013)
5. P. Nemec, M. Fiebig, T. Kampfrath, A.V. Kimel, Nature Phys. 14, 229 (2018)
6. C.P. Slichter, Principles of Magnetic Resonance (Springer, 1989)
7. H. Nojiri, Z.W. Ouyang, Terahertz Sci. Tech. 5, 1 (2012)