The strong coupling of atoms and molecules to radiation field modes in optical cavities creates dressed matter/field states known as polaritons with controllable dynamical and energy transfer properties. We propose a multidimensional optical spectroscopy technique for monitoring polariton dynamics. The response of a two-level atom to the time-dependent coupling to a single-cavity mode is monitored through time-and-frequency-resolved single-photon coincidence measurements of spontaneous emission. Polariton population and coherence dynamics and its variation with cavity photon number and controlled by gating parameters are predicted by solving the Jaynes-Cummings model.

Multidimensional optical signals are commonly recorded by varying the delays between time ordered pulses. These control the evolution of the density matrix and are described by ladder diagrams. We propose a new non-time-ordered protocol based on following the time evolution of the wavefunction and described by loop diagrams. The time variables in this protocol allow to observe different types of resonances and reveal information about intraband dephasing not readily available by time ordered techniques. The time variables involved in this protocol become coupled when using entangled light, which provides high selectivity and background free measurement of the various resonances. Entangled light can resolve certain states even when strong background due to fast dephasing suppresses the resonant features when probed by classical light.

Photon-based quantum information processing is based on manipulating multi photon interference. We focus on the Hong-Ou-Mandel (HOM) dip in the photon coincidence rate which provides a direct measure of interference of indistinguishable photons linked to their Bose statistics. The effect has been first observed with entangled photons generated by parametric down conversion and then extended to independent emitters. Fluctuations caused by coupling between emitters and a bath can erode the interference which causes the dip. Here we show how the magnitude and shape of the HOM dip is affected by spectral diffusion induced by coupling to a brownian oscillator bath. Conditions for maintaining and controlling the interference are specified.

Quantum optical fields offer numerous control knobs which are not available with classical light and may be used for monitoring the properties of matter by novel types of spectroscopy. It has been recently argued that such quantum spectroscopy signals can be obtained by a simple averaging of their classical spectroscopy counterparts over the Glauber-Sudarshan quasiprobability distribution of the quantum field; the quantum light thus merely provides a novel gating window for the classical response functions. We show that this argument only applies to the linear response and breaks down in the nonlinear regime. The quantum response carries additional valuable information about response and spontaneous fluctuations of matter that may not be retrieved from the classical response by simple data processing. This is connected to the lack of a nonlinear fluctuation-dissipation relation.

The strong coupling of atoms and molecules to radiation field modes in optical cavities creates dressed matter/field states known as polaritons with controllable dynamical and energy transfer properties. We propose a multidimensional optical spectroscopy technique for monitoring polariton dynamics. The response of a two-level atom to the time-dependent coupling to a single-cavity mode is monitored through time-and-frequency-resolved single-photon coincidence measurements of spontaneous emission. Polariton population and coherence dynamics and its variation with cavity photon number and controlled by gating parameters are predicted by solving the Jaynes-Cummings model.

Coherent multidimensional optical spectroscopy is broadly applied across the electromagnetic spectrum ranging from NMR to UV. These techniques reveal the properties of matter through the correlation plots of signal fields generated in response to sequences of short pulses with variable delays. Here we discuss a new class of multidimensional techniques obtained by the time-and-frequency-resolved photon coincidence counting measurements of N photons, which constitute a dimensional spectrum. A compact description of these signals is developed based on time-ordered superoperators rather than the normally ordered ordinary operators used in Glauber's photon counting formalism. The independent control of the time and frequency gate parameters reveals fine details of matter dynamics not available otherwise. These signal are illustrated for application to an anharmonic oscillator model with fluctuating energy and anharmonicity.

Excited-state vibrational dynamics in molecules can be studied by an electronically off-resonant Raman process induced by a probe pulse with variable delay with respect to an actinic pulse. We establish the connection between several variants of the technique that involve either spontaneous or stimulated Raman detection and different pulse configurations. By using loop diagrams in the frequency domain, we show that all signals can be described as six wave mixing which depend on the same four point molecular correlation functions involving two transition dipoles and two polarizabilities and accompanied by a different gating. Simulations for the stochastic two-state-jump model illustrate the origin of the absorptive and dispersive features observed experimentally.

Nonstationary molecular states which contain electronic coherences can be impulsively created and manipulated by using recently developed ultrashort optical and x-ray pulses via photoexcitation, photoionization, and Auger processes. We propose several stimulated-Raman detection schemes that can monitor the subsequent phase-sensitive electronic and nuclear dynamics. Three detection protocols of an x-ray broadband probe are compared: frequency-dispersed transmission, integrated photon number change, and total pulse energy change. In addition, each can be either linear or quadratic in the x-ray probe intensity. These various signals offer different gating windows into the molecular response, which is described by correlation functions of electronic polarizabilities. Off-resonant and resonant signals are compared.