Classically, such pulses are defined by their spectral and temporal shape as well as phase and amplitude of the electromagnetic field.
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,[6][7] which is not possible in classical spectroscopy .
Once these light mode are chosen, their effect on the quantized electromagnetic field can be described by Boson creation and annihilation operators
[8] The quantum fluctuations of the light field can be uniquely defined[9] by the photon correlations
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.
part); the Hamiltonian also contains the Hermitian conjugate (abbreviated as h.c.) of the terms that are explicitly written.
More specifically, the fundamental form of the light–matter interaction inevitably leads to a correlation-transfer relation[1][7]
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.
Physically, the correlation-transfer relation means that one can directly inject desired many-body states simply by adjusting the quantum fluctuations of the light pulse, as long as the light pulse is short enough.
This opens a new possibility for studying properties of distinct many-body states, once the quantum-optical spectroscopy is realized through controlling the quantum fluctuations of light sources.
To directly excite bound electron–hole pairs, i.e., excitons, described by a two-particle correlation
To realize quantum-optical spectroscopy, high-intensity light sources with freely adjustable quantum statistics are needed which are currently not available.
However, one can apply projective methods[6][11][12] to access the quantum–optical response of matter from a set of classical measurements.
Especially, the method presented by Kira, M. et al[6] is robust in projecting quantum-optical responses of genuine many-body systems.
This work has shown that one can indeed reveal and access many–body properties that remain hidden in classical spectroscopy.
Therefore, the quantum-optical spectroscopy is ideally suited for characterizing and controlling complicated many-body states in several different systems, ranging from molecules to semiconductors.
Quantum-optical spectroscopy is an important approach in general semiconductor quantum optics.
The capability to discriminate and control many-body states is certainly interesting in extended semiconductors such as quantum wells because a typical classical excitation indiscriminately detects contributions from multiple many-body configurations; With quantum-optical spectroscopy one can access and control a desired many-body state within an extended semiconductor.
[7] At the same time, the ideas of quantum-optical spectroscopy can also be useful when studying simpler systems such as quantum dots.
Quantum dots are a semiconductor equivalent to simple atomic systems where most of the first quantum-optical demonstrations have been measured.
[8] Since quantum dots are man-made, one can possibly customize them to produce new quantum-optical components for information technology.
Such sources have already been demonstrated with quantum dots by controlling their photon emission with various schemes.
[17] Quantum-dot microcavity investigations have progressed rapidly ever since the experimental demonstration[18][19] of vacuum Rabi splitting between a single dot and a cavity resonance.
This regime can be understood on the basis of the Jaynes–Cummings model while the semiconductor aspects provide many new physical effects[20][21] due to the electronic coupling with the lattice vibrations.
Nevertheless, the quantum Rabi splitting—stemming directly from the quantized light levels—remained elusive because many experiments were monitoring only the intensity of photoluminescence.
[22] predicted that quantum-Rabi splitting could be resolved in photon-correlation measurement even when it becomes smeared out in photoluminescence spectrum.
This was experimentally demonstrated[23] by measuring the so-called g2 correlations that quantify how regularly the photons are emitted by the quantum dot inside a microcavity.