Quantum-optical spectroscopy

Quantum-optical spectroscopy 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, 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, which is not possible in classical spectroscopy.

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 ${\displaystyle {\hat {B}}^{\dagger }}$ and ${\displaystyle {\hat {B}}}$ for photons, respectively. The quantum fluctuations of the light field can be uniquely defined by the photon correlations ${\displaystyle \Delta \langle \left[B^{\dagger }\right]^{J}\,B^{K}\rangle }$ that contain the pure ${\displaystyle (J+K)}$-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. The corresponding electron–hole excitations can be described by operators ${\displaystyle {\hat {X}}^{\dagger }}$ and ${\displaystyle {\hat {X}}}$ that create and annihilate an electron–hole pair, respectively.

...
Wikipedia