Relaxation process of periodically driven quantum systems in the high-frequency regime

by Takashi Mori (Department of Physics, The University of Tokyo)

Tuesday 21 Jun 2016, 13:30 → 14:30 Asia/Tokyo

Room 433, Main Research Building (RIKEN Wako)

QHP seminars Date: June 21 (Tue) Time: 13:30 - Place: Main Research bldg. 433 Speaker: Takashi Mori (Department of Physics, The University of Tokyo) Title: Relaxation process of periodically driven quantum systems in the high-frequency regime Abstract: Recently, quantum dynamics under periodic driving fields is paid much attention as a tool of quantum engineering, i.e. manipulating and controlling a quantum system and realizing a novel phase of matter [1-3]. Theoretically, however, quantum dynamics of periodically driven quantum systems is not well understood. The Floquet theory with the truncation of the Magnus expansion is a familiar method to analyze such a system, but its applicability has not been made clear. In this talk, I would like to present our study based on the mathematically rigorous treatment of the Magnus expansion. In thermally isolated spin systems, it is rigorously shown that, in the high frequency regime, the Floquet theory with the truncation of the Magnus expansion gives a good approximation for an exponentially long time in frequency [4,5]. As a result, it is shown that the heating (energy absorption due to periodic driving) is very slow in the high frequency regime, which leads to the general relaxation process found in such systems; the system will first reach the quasi-stationary state that is described by the Floquet theory with the truncation of the Magnus expansion, and then after an exponentially long time in frequency, the system will approach the true stationary state, which is often the state of infinite temperature. I will also comment on open systems. It is shown that even if a periodically driven closed system is described by the effective Hamiltonian obtained by the Floquet theory with the truncation of the Magnus expansion, the stationary state is in general not described by the Gibbs state of this effective Hamiltonian when the system is in contact with a thermal reservoir [6,7]. References: [1] M. Bukov, L. D’Alessio, and A. Polkovnikov, Adv. Phys. 64, 139 (2015) [2] A. Zenesini, H. Lignier, D. Ciampini, O. Morsch, and E. Arimondo, Phys. Rev. Lett. 102, 100403 (2009) [3] M. Aidelsburger, M. Atala, M. Lohse, J. T. Barreiro, B. Paredes, and I. Bloch, Phys. Rev. Lett. 111, 185301 (2013) [4] T. Mori, T. Kuwahara, and K. Saito, Phys. Rev. Lett. 116, 120401 (2016) [5] T. Kuwahara, T. Mori, and K. Saito, Ann. Phys. (Berlin) 367, 96 (2016) [6] T. Shirai, T. Mori, and S. Miyashita, Physical Review E 91, 030101 (2015) [7] T Shirai, J Thingna, T Mori, S Denisov, P Hänggi, and S Miyashita, New J. Phys. 18, 053008 (2016)