We have obtained Nth-order response functions for a two-level system described by displaced anharmonic potential surfaces coupled to a heat bath. The anharmonicity of the potentials has been taken into account as a perturbation of harmonic potentials. The heat-bath was assumed to be an ensemble of harmonic oscillators. Coupling between the two-level system and the bath was assumed to be bilinear. The calculations were done analytically using the Liouville-space generating functional, which had been obtained by way of the path-integral approach. The response functions have been defined in terms of line-shape functions with these line-shape functions being expressed in terms of the bath spectral density and the temperature. We have carried out model calculations of the first-, third-, and fifth-order optical processes for various parameters of anharmonicity to show that anharmonicity plays a minor role in linear absorption, impulsive pump–probe, and photon echo experiments, but plays a major role, in some cases, in fifth-order two-dimensional resonant spectroscopy which is proposed in this paper.
The Doppler-broadened steady state and transient response of a thermal ensemble of anharmonic oscillators to incident laser radiation is investigated. Non-linear polarization of this classical system is obtained by analytically solving the dynamical equations up to third order in the electric field. Except for the sign of the third-order transient polarization, the results are in striking contrast to those obtained in semi-classical theory. In particular, the classical response at resonance is unsaturated up to this order. The Doppler-integrated third-order free induction decay (FID) signal vanishes in the usual approximation of the homogeneous width being smaller than the Doppler width. The physical conclusion of the paper is negative: resonant non-linear and coherent effects such as saturation and nutation typical of the quantum mechanical two-level atoms do not arise for classical anharmonic oscillators.
The quantum Fokker-Planck equation is derived for a system nonlinearly coupled to a harmonic oscillator bath. The system-bath interaction is assumed to be linear in the bath coordinates but quadratic in the system coordinate. The relaxation induced dynamics of a harmonic system are investigated by simulating the higher-order correlation functions of the Raman polarizability and the dipole moment, which represent the nonlinear optical responses of Raman or infrared spectroscopy. The 5th-order Raman response shows that, in addition to the frequency fluctuations induced by the bath, higher-order energy transfer between the system and bath plays a role. The nonlinearity of the system-bath interaction yields also an interesting feature in the 7th-order Raman echo or the 3rd-order infrared photon echo response: The calculations predict a finite signal for the case of a harmonic potential and a linear coordinate dependence of the polarizability or dipole while for linear system-bath coupling this response vanishes completely due to destructive interference of different Liouville space pathways.
Multidimensional optical spectroscopies are powerful techniques to investigate energy transfer pathways in natural and artificial systems. Because of the high information content of the spectra, numerical simulations of the optical response are of primary importance to assist the interpretation of spectral features. However, the increasing complexity of the investigated systems and their quantum dynamics call for the development of novel simulation strategies. In this work, we consider using digital quantum computers. By combining quantum dynamical simulation and nonlinear response theory, we present a quantum algorithm for computing the optical response of molecular systems. The quantum advantage stems from the efficient quantum simulation of the dynamics governed by the molecular Hamiltonian, and it is demonstrated by explicitly considering exciton-vibrational coupling. The protocol is tested on a near-term quantum device, providing the digital quantum simulation of the linear and nonlinear response of simple molecular models.
Conventional weak-coupling perturbation theory suffers from problems that arise from the resonant coupling of successive orders in the perturbation series. Multiple-scale perturbation theory avoids such problems by implicitly performing an infinite reordering and resummation of the conventional perturbation series. Multiple-scale analysis provides a good description of the classical anharmonic oscillator. Here, it is extended to study the Heisenberg operator equations of motion for the quantum anharmonic oscillator. The analysis yields a system of nonlinear operator differential equations, which is solved exactly. The solution provides an operator mass renormalization of the theory.
Multidimensional spectroscopy has become an established tool for disentangling microscopic processes that remain unresolved in conventional linear spectroscopy. Its extension to the terahertz regime now enables analogous questions to be addressed for low-energy collective excitations in quantum materials and synthetic many-body systems. Unlike isolated few-level systems, however, these collective modes generally cannot be described within the standard framework of nonlinear spectroscopy based on a few-level description. Their response is instead governed by their extended nature, interplay of interactions, fluctuations, disorder, dissipation, and coupling to additional degrees of freedom. This thesis develops a theoretical framework for computing and interpreting multidimensional nonlinear spectroscopy in quantum many-body systems. Using real-time nonequilibrium field theory, we formulate nonlinear susceptibilities diagrammatically in terms of propagators, interaction vertices, and self-energies, with particular emphasis on the third-order susceptibility relevant to infrared-active collective excitations. This approach places the established concepts and capabilities of multidimensional spectroscopy within a systematic many-body field-theoretical framework. Furthermore, this formulation makes it possible to move beyond the established probing capabilities, extending multidimensional spectroscopy beyond few-level descriptions and revealing new signatures and functionalities specific to interacting many-body systems. At the same time, it provides a controlled framework for constructing approximations that preserve the underlying symmetries and conservation laws of the system while remaining amenable to both analytical and numerical calculations. By incorporating quantum and thermal fluctuations within the random-phase approximation, we demonstrate that two-dimensional spectra can reveal the growth of fluctuations, identify field-theoretical bound states, and characterize their coupling to many-body continua. We further develop a diagrammatic description of rephasing in extended bosonic systems in the presence of static disorder. We identify the disorder vertex corrections responsible for echo formation and show how echo spectroscopy separates disorder-induced broadening from intrinsic relaxation. This framework is extended to coupled modes and strongly interacting regimes, where interactions can either enhance or suppress rephasing. A further result is the identification of a nonrephasing four-wave-mixing signal that is critically enhanced near a phase transition, in contrast to simpler nonlinear protocols like third-harmonic generation. We apply this framework to electromagnons in NiI
2, Josephson plasmons in La
2−xSr
xCuO
4, and the low-energy collective excitations in coupled one-dimensional Bose-Einstein condensates. Across these systems, we show how multidimensional spectroscopy can disentangle disorder from intrinsic relaxation, reveal the effects of interactions and fluctuations, identify coupling between collective modes and continua, and extract microscopic information that remains obscured in conventional spectroscopy. Taken together, the results of this thesis provide a diagrammatic framework for calculating and interpreting multidimensional nonlinear spectroscopic signals in many-body systems, while establishing this technique as a selective probe of collective dynamics across a broad range of quantum materials and synthetic platforms.