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Quantum-optical spectroscopy : ウィキペディア英語版
Quantum-optical spectroscopy
Quantum-optical spectroscopy〔Kira, M.; Koch, S. (2006).
"Quantum-optical spectroscopy of semiconductors". ''Physical Review A'' 73 (1).
doi:(10.1103/PhysRevA.73.013813 ). ISSN 1050-2947.〕〔Koch, S. W.; Kira, M.; Khitrova, G.; Gibbs, H. M. (2006). "Semiconductor excitons in new light". ''Nature Materials'' 5 (7): 523–531. doi:(10.1038/nmat1658 ). ISSN 1476-1122.〕 is a quantum-optical generalization of laser spectroscopy where matter is excited and probed with a sequence of laser pulses.
Classically, such pulses are defined by their spectral and temporal shape as well as phase and amplitude of the electromagnetic field. Besides these properties of light, the phase-amplitude aspects have intrinsic quantum fluctuations that are of central interest in quantum optics. In ordinary laser spectroscopy,〔Stenholm, S. (2005). ''Foundations of laser spectroscopy''. Dover Pubn. Inc. ISBN 978-0486444987.〕〔Demtröder, W. (2008). ''Laser Spectroscopy: Vol. 1: Basic Principles''. Springer. ISBN 978-3540734154.〕〔Demtröder, W. (2008). ''Laser Spectroscopy: Vol. 2: Experimental Techniques''. Springer. ISBN 978-3540749523.〕 one utilizes only the classical aspects of laser pulses propagating through matter such as atoms or semiconductors. In quantum-optical spectroscopy, one additionally utilizes the quantum-optical fluctuations of light to enhance the spectroscopic capabilities by directly shaping and/or detecting the quantum fluctuations of light. Quantum-optical spectroscopy has applications in controlling and characterizing quantum dynamics of many-body states because one can directly access a large set of many-body states,〔Kira, M.; Koch, S. W.; Smith, R. P.; Hunter, A. E.; Cundiff, S. T. (2011). "Quantum spectroscopy with Schrödinger-cat states". ''Nature Physics''
7 (10): 799–804. doi:(10.1038/nphys2091 ). ISSN 1745-2473.〕〔Kira, M.; Koch, S. W. (2011). ''Semiconductor Quantum Optics''. Cambridge University Press. ISBN 978-0521875097.〕 which is not possible in classical spectroscopy.
==Quantum-optical state injection==
A generic electromagnetic field can always be expressed in terms of a mode expansion where individual components form a complete set of modes. Such modes can be constructed with different methods and they can, e.g., be energy eigenstate, generic spatial modes, or temporal modes. Once these light mode are chosen, their effect on the quantized electromagnetic field can be described by Boson creation and annihilation operators
\hat^\dagger
and
\hat
for photons, respectively.〔Walls, D. F.; Milburn, G. J. (2008). ''Quantum Optics''. Springer. ISBN 978-3540285731.〕 The quantum fluctuations of the light field can be uniquely defined〔Kira, M.; Koch, S. (2008). "Cluster-expansion representation in quantum optics". ''Physical Review'' A 78 (2). doi:(10.1103/PhysRevA.78.022102 ). ISSN
1050-2947.〕 by the photon correlations
\Delta\langle\left (B^ \right )^J\, B^K\rangle
that contain the pure (J+K)-particle correlations as defined with the cluster-expansion approach. Using the same second-quantization formalism for the matter being studied, typical electronic excitations in matter can be described by Fermion operators for electronic excitations and holes, i.e.~electronic vacancies left behind to the many-body ground state.〔Ashcroft, N. W.; Mermin, N. D. (1976). ''Solid state physics''. Saunders College. ISBN 978-0030839931.〕 The corresponding electron–hole excitations can be described by operators \hat^\dagger and \hat that create and annihilate an electron–hole pair, respectively.
In several relevant cases, the light–matter interaction can be described using the dipole
interaction〔

\hat_\,\hat\hat^+\mathrm\,,

where the summation is implicitly taken over all possibilities to create an electron–hole pair (the \hat^\dagger part) via a photon absorption (the \hat part); the Hamiltonian also contains the Hermitian conjugate (abbreviated as h.c.) of the terms that are explicitly written. The coupling strength between light and matter is defined by \mathcal.
When the electron–hole pairs are excited resonantly with a single-mode light \hat, the photon correlations are directly injected into the many-body correlations. More specifically, the fundamental form of the light–matter interaction inevitably leads to a correlation-transfer relation〔〔

\Delta\langle\left()^J\hat^K\rangle=\eta^}
\Delta\langle\left (B^ \right )^JB^K\rangle\,,

between photons and electron–hole excitations. Strictly speaking, this relation is valid before the onset of scattering induced by the Coulomb and phonon interactions in the solid. Therefore, it is desirable to use laser pulses that are faster than the dominant scattering processes. This regime is relatively easy to realize in present-day laser spectroscopy because lasers can already output femtosecond, or even attosecond, pulses with a high precision in controllability.

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