Abstract
In this chapter, we describe a unified quantum mechanical description for the generation and detection of coherent optical phonons using a simple model. Two electronic states coupled with displaced harmonic oscillators, which represent phonons, are used. The dipole interaction between an optical pulse and the system is assumed and treated as a perturbation interaction. Time evolution of the density operator is calculated using the second-order perturbation approximation.
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Notes
- 1.
- 2.
\(\alpha ^2\) is the Huang–Rhys factor, which is considered to be small (\(\alpha ^2 <1 \)) in a bulk solid.
- 3.
When we set \(\hat{B} = |e\rangle \langle e|\), the exponential \(\exp (\hat{H}_e \hat{B} t)\) is expressed by \(\exp (\hat{H}_e \hat{B} t) = \sum _n (\hat{A} t)^n \hat{B}^n\). Since \(\hat{B}^2 = (|e\rangle \langle e|)(|e\rangle \langle e|)= |e\rangle \langle e| = \hat{B}\), then \(\hat{B}^n = \hat{B} \) for \(n \ge 1\). Finally, we get \(\exp (\hat{H}_e |e\rangle \langle e| t) |e\rangle \langle g| = \exp (\hat{H}_e t) |e\rangle \langle g|\).
- 4.
The harmonic potential can be deformed under a long-range external field such as the surface-charge field. Supposing a uniform electric field (\(F(x)=-\mathrm{d}x\)) acting along the phonon coordinate (x), the effective charge field can be treated as uniform in such a short scale. When the external field potential is applied to a harmonic potential \(U(x)= kx^2/2\), the potential changes to \(U'(x)=U(x)+F(x) = k(x-\mathrm{d}/k)^2/2 -\mathrm{d}^2/(2k)\). Then, the potential minimum position and energy shift are \(\mathrm{d}/k\) and \(-\mathrm{d}^2/(2k)\), respectively. The slope d of the external fields in the electronic excited state is lower than that in the ground state, because the surface screening is suppressed by a electron–hole pair or electronic polarization. Then, the effective harmonic potential in the excited state is displaced from that in the ground state.
References
Scholz, R., Pfeifer, T., Kurz, H.: Density-matrix theory of coherent phonon oscillations in germanium. Phys. Rev. B 24, 16229–16236 (1993)
Kuznetsov, A.V., Stanton, C.J.: Theory of coherent phonon oscillations in semiconductors. Phys. Rev. Lett. 43, 3243–3246 (1994)
Hu, X., Nori, F.: Quantum phonon optics: coherent and squeezed atomic displacement. Phys. Rev. B 53, 2419–2424 (1996)
Merlin, R.: Generating coherent THz phonons with light pulses. Solid State Commun. 102, 107–220 (1997)
Stevens, T.E., Kuhl, J., Merlin, R.: Coherent phonon generation and two stimulated Raman tensors. Phys. Rev. B 65, 144304 (2002)
Nakamura, K.G., Shikano, Y., Kayanuma, Y.: Influence of pulse width and detuning on coherent phonon generation. Phys. Rev. B92, 144304 (2015)
Pollard, W.T., Fragnito, H.L., Bigot, J.-Y., Shank, C.V., Mathies, R.A.: Quantum-mechanical theory for 6 fs dynamic absorption spectroscopy. Chem. Phys. Lett. 168, 239–245 (1990)
Banin, U., Bartana, A., Ruthman, S., Kosloff, R.: Impulsive excitation of coherent vibrational motion ground surface dynamics induced by intense short pulse. J. Chem. Phys. 101, 8461–8481 (1994)
Cerullo, G., Manzoni, C.: Time domain vibrational spectroscopy: principle and experimental tools. In: De Silvestri, S., Cerullo, G., Lanzani, G. (eds.) Coherent Vibration Dynamics. CRC Press, Boca Raton (2008)
Mukamel, S.: Principles of Nonlinear Optical Spectroscopy. Oxford University Press, New York (1995)
Nakamura, K.G., Ohya, K., Takahashi, H., Tsuruta, T., Sasaki, H., Uozumi, S., Norimatsu, K., Kitajima, M., Shikano, Y., Kayanuma, Y.: Spectrally resolved detection in transient-reflectivity measurements of coherent optical phonons. Phys. Rev. B94, 024303 (2016)
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Nakamura, K. (2019). Coherent Phonons: Quantum Theory. In: Quantum Phononics. Springer Tracts in Modern Physics, vol 282. Springer, Cham. https://doi.org/10.1007/978-3-030-11924-9_6
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DOI: https://doi.org/10.1007/978-3-030-11924-9_6
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