The University of Tokyo Seiji Miyashita 10 Aug. 2010 Kyoto Yukawa Reduction of the system dynamics from the total system including the environments The University of Tokyo Seiji Miyashita

Projection operator method

For the master equation

Real part

Phonon Bottleneck phenomena in V15 Plateau induced by thermal effect sample Heat flow Heat bath Chiorescu, W. Wernsdorfer, A. Mueller, H. Boegge, B. Barbara, Phys. Rev. Lett. 84 (2000) 3454.

Field sweeping with thermal bath Fast sweeping Slow sweeping Magnetic Foehn Effect LZS K. Saito & SM. JPSJ (2001) 3385.

Nonadiabatic Tr. & Heat-inflow LZ transition Magnetic Foehn Effect

Fe2 Fe-rings Y. Shapira, et al PRB59 (1999) 1046 Y. Ajiro & Y. Inagaki Y. Narumi & K. Kindo H. Nakano & SM, JPSJ 70(2001) 2151

Fast Magnetization Tunneling in Tetranicke(II) SMM [Ni(hmp)(dmb)Cl]4 v=0.0512, ...., 0.0002 V=0.002, ..... , 0.28T/s En-Che Yang,et al: Inorg. Chem. 45 (2006) 529

Boson system

Spin-boson system from QMEnote (SM and T. Mori)

Relation between the equation of motion and its steady solution Equation of motion up to the second order (a situational solution) we may add any traceless W The diagonal elements are arbitrary in the order of Master equation leads the system to the equilibrium of the system The off-diagonal elements aredetermined in the order of T. Mori and SM: JPSJ 77 (2008) 124005 (1-9). Complex admittance C. Uchiyama, M. Aihara, M. Saeki and S. Miyashita: PRE 80 (2009) 021128 (1-18). M. Saeki, C. Uchiyama, T. Mori and S. Miyashita: PRE 81, (2010) 031131 (1-33)

The University of Tokyo Seiji Miyashita 10 Aug. 2010 Kyoto Yukawa Study on the line shapes of the response function --Origins of the Width-- The University of Tokyo Seiji Miyashita

ESR line shape in strongly interacting spin systems Temperature-dependence of the shift and width in low-dimensional quantum spin systems Spin trimer: 3CuCl2 ・2Dioxane F F AF (S=1/2)x3 paramagnetic S=3/2 EPR correlated state Y. Ajiro, et al: JPSJ 63 (1994) 859.

Shift and width of the line shape Intrinsic width due to assembly of the delta-functions Quantum broadening due to quantum fluctuation of the field Transmission spectrum (input-output modes) Broadening width due to the interaction with the thermal bath

Microscopic expression of the line shape from　the Hamiltonian of the system R. Kubo & K.Tomita JPSJ (1954) 888. Kubo formula R. Kubo: JPSJ 12 (1957) 570. Isotropic models (Paramagnetic Resonance) Perturbation

Expression of the admittance Eigenvalue and eigenvectors of the Hamiltonian shift width

Frequency sweep and Field sweep

1D AF Heisenberg Chain

Nagata-Tazuke effect One-dimensional Heisenberg antiferromagnet K.Nagata and Y.Tazuke, JPSJ 32(1972)337. (J. Kanamori & M.Tachiki : JPSJ 48 (1962) 50) One-dimensional Heisenberg antiferromagnet 21

Demonstration of the Nagata-Tazuke effects R.E. Dietz, et al. PRL 26 (1971) 1186. T.T. Cheung, et al. PRB 17 (1978) 1266 SM, T. Yoshino, A. Ogasahara: JPSJ 68 (1999) 655.

Line shape of a spin chane with a staggered DM interaction S. El Shawish, O. Cepas, and SM: PRB81, 224421 (2010).

Line shape of a spin chain with a staggered DM interaction cf. S. El Shawish, O. Cepas, and SM: PRB81, 224421 (2010).

Models Staggered DM model XXZ model Equivalence Difference

Consideration on the line shape relaxation time moments of

Memory function (short time)

Memory function (long time)

Memory function (Gaussian form : KT)

Double peak structure

Estimated line shape in infinite chain Exact short range + spin diffusion long time tail with various cut-off times (tau_0,tau_c)

Width of the line shape self-consistent

Memory function (2D kagome)

Line shape and width (2D kagome)

Derivative of line shape ZnCu3(OH3)Cl2

Shift and width of the line shape Intrinsic width due to assembly of the delta-functions Quantum broadening due to quantum fluctuation of the field Transmission spectrum (input-output modes) Broadening width due to the interaction with the thermal bath

Coupling between spin system and cavity phonon system Cavity photon system Coupling Transmission

Coupling between spin system and cavity phonon system Cavity photon system Coupling Transmission

Jaynes-Cumming model and ESR spectrum I. Chiorescu and S. Miyashita: PRB (2010) in press Model for ESR Rabi-oscillation Absorption spectrum Jaynes-Cummings model

Interaction with photon The Jaynes-Cummings model Photon couples all the spins. Total spin is conserved

Enhancement of Rabi-oscillation and the vacuum-field Rabi splitting Y. Kaluzny, P. G. , M. Gross, J. M. Raimond and S. Haroche, PRL 51, 1175 (1983) The vacuum-field Rabi splitting in the transmission spectrum G. S. Agarwal:, PRL 53, 1732 (1984).

Splitting of PMR of DPPH The vacuum-field Rabi-splitting G. S. Agarwal:, PRL 53, 1732 (1984). DPPH I. Chiorescu, N. Groll, S. Bertaina, T. Mori and SM: PRB (2010) in press. (1004.3605)

N-diamond arXiv 1006.0251

arXiv 1006.0242 Rubby S=3/2 Cr3+

Multi-photon effect N=nmax ( , 0) ( , 1) ( , N) nmax: number of cavity Super-radiance? ( , 0) ... ( , 1) ... ( , N) ... At N=nmax, a wide distribution of the Rabi frequences nmax: number of cavity photons in the ground state of spin system

Eigenvalues and the transmission spectrum The vacuum-field Rabi-splitting G. S. Agarwal:, PRL 53, 1732 (1984).

Photon emission spectrum

Shift and width of the line shape Intrinsic width due to assembly of the delta-functions Quantum broadening due to quantum fluctuation of the field Transmission spectrum (input-output modes) Broadening width due to the interaction with the thermal bath

Line shape of the transmission

Thermal bath method

Transmission in a steady state j-1 j j+1 j=0

Input-output formulation

Shift and width of the line shape Intrinsic width due to assembly of the delta-functions Quantum broadening due to quantum fluctuation of the field Transmission spectrum (input-output modes) Broadening width due to the interaction with the thermal bath C. Uchiyama, M. Aihara, M. Saeki and S. Miyashita: PRE 80 (2009) 021128.

Summary Explicit expression of the the spectrum line shape: Quantum broadening due to quantum fluctuation of the field Transmission spectrum (steady flow method) vs Broadening width due to the interaction with the thermal bath Line shale of a ring Heisenberg model with DM interaction Coupling of spin system and cavity photons

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