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 foll
owing 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.
X-ray four-wave mixing signals generated in the $k_1 + k_2 - k_3$ phase-matching direction are simulated for N1s transitions in para-nitroanline and two-ring hydrocarbons disubstituted with an amine and a nitroso groups. The two-dimensional x-ray cor
relation spectra (2DXCS) provide background-free probes of couplings between core-electron transitions even for multiple core shells of the same type. Features attributed to couplings between spatially-separated core transitions connected by delocalized valence excitations provide information about molecular geometry and electronic structure unavailable from linear near-edge x-ray absorption (XANES).
We propose a three-pulse coherent ultrafast optical technique that is particularly sensitive to two-exciton correlations. Two Liouville-space pathways for the density matrix contribute to this signal which reveals double quantum coherences when displ
ayed as a two-dimensional correlation plot. Two-exciton couplings spread the cross peaks along both axes, creating a characteristic highly resolved pattern. This level of detail is not available from conventional one-dimensional four-wave mixing or other two-dimensional correlation spectroscopy signals such as the photo echo, in which two-exciton couplings show up along a single axis and are highly congested.
A compact correlation-function expansion is developed for nth order optical susceptibilities in the frequency domain using the Keldysh-Schwinger loop. By not keeping track of the relative time ordering of bra and ket interactions at the two branches
of the loop, the resulting expressions contain only n+1 basic terms, compared to the 2n terms required for a fully time-ordered density matrix description. Superoperator Greens function expressions for the nth order suscpeptibility derived using both expansions reflect different types of interferences between pathways .These are demonstrated for correlation-induced resonances in four wave mixing signals.
Nonlinear optical signals from an assembly of N noninteracting particles consist of an incoherent and a coherent component, whose magnitudes scale sim N and sim N(N-1), respectively. A unified microscopic description of both types of signals is devel
oped using a quantum electrodynamical (QED) treatment of the optical fields. Closed nonequilibrium Greens function expressions are derived that incorporate both stimulated and spontaneous processes. General (n+1)-wave mixing experiments are discussed as an example of spontaneously generated signals. When performed on a single particle, such signals cannot be expressed in terms of the nth order polarization, as predicted by the semiclassical theory. Stimulated processes are shown to be purely incoherent in nature. Within the QED framework, heterodyne-detected wave mixing signals are simply viewed as incoherent stimulated emission, whereas homodyne signals are generated by coherent spontaneous emission.
The correlated behavior of electrons determines the structure and optical properties of molecules, semiconductor and other systems. Valuable information on these correlations is provided by measuring the response to femtosecond laser pulses, which pr
obe the very short time period during which the excited particles remain correlated. The interpretation of four-wave-mixing techniques, commonly used to study the energy levels and dynamics of many-electron systems, is complicated by many competing effects and overlapping resonances. Here we propose a coherent optical technique, specifically designed to provide a background-free probe for electronic correlations in many-electron systems. The proposed signal pulse is generated only when the electrons are correlated, which gives rise to an extraordinary sensitivity. The peak pattern in two-dimensional plots, obtained by displaying the signal vs. two frequencies conjugated to two pulse delays, provides a direct visualization and specific signatures of the many-electron wavefunctions.
We propose two dimensional x-ray coherent correlation spectroscopy (2DXCS) for the study of interactions between core-electron and valence transitions. This technique might find experimental applications in the future when very high intensity x-ray s
ources become available. Spectra obtained by varying two delay periods between pulses show off-diagonal cross-peaks induced by coupling of core transitions of two different types. Calculations of the N1s and O1s signals of aminophenol isomers illustrate how novel information about many-body effects in electronic structure and excitations of molecules can be extracted from these spectra.
Frequency-domain nonlinear wave mixing processes may be described either using response functions whereby the signal is generated after all interactions with the incoming fields, or in terms of scattering amplitudes where all fields are treated symet
rically with no specific time ordering. Closed Greens function expressions derived for the two types of signals have different analytical properties. The recent controversy regarding the sign of radiative damping in the linear (Kramers Heisenberg) formula is put in a broader context.
Two-dimensional correlation spectroscopy (2DCS) based on the nonlinear optical response of excitons to sequences of ultrafast pulses, has the potential to provide some unique insights into carrier dynamics in semiconductors. The most prominent featur
e of 2DCS, cross peaks, can best be understood using a sum-over-states picture involving the many-body eigenstates. However, the optical response of semiconductors is usually calculated by solving truncated equations of motion for dynamical variables, which result in a quasiparticle picture. In this work we derive Greens function expressions for the four wave mixing signals generated in various phase-matching directions and use them to establish the connection between the two pictures. The formal connection with Frenkel excitons (hard-core bosons) and vibrational excitons (soft-core bosons) is pointed out.
