Jose Récamier

We study a two-level system coupled to two quantized electromagnetic modes within the Jaynes–Cummings framework. While the single-mode model is exactly solvable due to its conserved excitation number, yielding finite-dimensional invariant subspaces, the two-mode model extension presents a fundamental challenge: although the total excitation number remains conserved, each invariant subspace is infinite-dimensional, preventing a closed-form analytical solution. Our scheme separates the dynamics into a dominant, exactly solvable semiclassical component-the atom interacting with the mean fields of both modes-and treats the remaining quantum fluctuations through a sequence of unitary transformations that preserve essential quantum features. We validate our approach through direct comparison with numerical solutions, focusing on the non-resonant regime where multiple detunings give rise to rich interference effects and multi-timescale dynamics inaccessible to standard approximations. The method accurately reproduces atomic inversion, field observables, and fidelity over relevant timescales, while remaining computationally efficient.

We analyze the time-dependent physical spectrum of a driven Jaynes–Cummings model in which both the two-level system and the quantized cavity mode are subject to coherent classical driving. The time-dependent Hamiltonian is mapped, via well-defined unitary transformations, onto an effective stationary Jaynes–Cummings form. Within this framework, we derive closed-form expressions for the two-time correlation functions of both the atomic and field operators. These correlation functions are subsequently used to evaluate the time-dependent physical spectrum according to the Eberly–Wódkiewicz definition, which properly accounts for finite spectral resolution and transient emission dynamics. We show that the external driving leads to substantial modifications of the atomic spectral response, including controllable frequency shifts and asymmetric line shapes. Importantly, we identify a regime in which the driving parameters are chosen such that the coherent displacement induced in the cavity field exactly cancels out the initial coherent amplitude. In this limit, the system dynamics reduce to that of an effectively vacuum-initialized Jaynes–Cummings model, and the standard vacuum Rabi splitting is recovered. This behavior provides a clear and physically transparent interpretation of the spectral features as arising from coherent field displacement rather than from modifications of the underlying atom–cavity coupling.

We investigate the time-dependent physical spectrum of the driven Jaynes-Cummings model, where both the atom and the quantized field are simultaneously driven by an external classical field. By leveraging the mapping of the time-dependent Hamiltonian onto the standard stationary Jaynes-Cummings form via unitary transformations, we determine the exact two-time correlation functions for both the atomic and field subsystems. These are then employed to compute the time-dependent physical spectrum using the Eberly-Wódkiewicz formalism. Our results demonstrate that the atomic spectral features are significantly reshaped by the external driving, exhibiting tunable asymmetries and shifts. Notably, we find that the driving parameters can be tuned to exactly cancel the initial coherent field amplitude, leading to an effective vacuum limit that recovers the fundamental vacuum Rabi splitting. This provides a clear interpretation of the emission dynamics in terms of the coherent displacement of the cavity field induced by the external drive.

In this work, we make use of Lie algebraic methods to obtain the time evolution operator for an optomechanical system with linear and quadratic couplings between the field and the mechanical oscillator. Firstly, we consider the case of a non-driven system and find its exact time evolution operator, secondly we consider the case of a forced system whose time evolution operator is obtained in an approximate form. We confront our analytical results with a numerical simulation and find a good agreement between them.

In this work, we make use of Lie algebraic methods to obtain the time evolution operator for an optomechanical system with linear and quadratic couplings between the field and the mechanical oscillator. Firstly, we consider the case of a non-driven system and find its exact time evolution operator, secondly we consider the case of a forced system whose time evolution operator is obtained in an approximate form. We confront our analytical results with a numerical simulation and find a good agreement between them.

The Jaynes-Cummings quantum optics model allows us to understand the dialogue between light and matter at its most fundamental level, which is crucial for advancements in quantum science and technology. Several generalizations of the model have long been proposed, emphasizing their dynamic behavior but paying less attention to their spectroscopy. Here, we obtain analytical expressions of the time-dependent spectral response of a nonlinear Jaynes-Cummings model based on deformed field operators. We show that the long-time response of the resulting nonlinear cavity field resembles the one experimentally obtained in the strong-dispersive regime of circuit quantum electrodynamics. The spectrum is intrinsically asymmetric with the nonlinear coupling, a signature of the impossibility of getting resonant conditions for finite field excitations.

We obtain a time-evolution operator for a forced optomechanical quantum system using Lie algebraic methods when the normalized coupling between the electromagnetic field and a mechanical oscillator, G/ω _m , is not negligible compared to one, i.e., the system operates in the strong-coupling regime. Due to the forcing term, the interaction picture Hamiltonian contains the number operator in the exponents, and in order to deal with it, we approximate these exponentials by their average values taken between initial coherent states. Our approximation is justified when we compare our results with the numerical solution of the number of photons, phonons, Mandel parameter, and the Wigner function, showing an excellent agreement. In contrast to other works, our approach does not use the standard linearized description in the optomechanical interaction. Therefore, highly non-classical (non-Gaussian) states of light emerge during the time evolution.

When an electromagnetic field is confined in a cavity of variable length, real photons may be generated from vacuum fluctuations due to highly nonadiabatic boundary conditions. The corresponding effective Hamiltonian is time-dependent and contains infinite intermode interactions. Considering one of the cavity mirrors fixed and the other describing uniform motion (zero acceleration), we show that it is possible to factorize the entire temporal dependency and write its formal solution, i.e., the Hamiltonian becomes a product of a time-dependent function and a time-independent operator. With this factorization, we prove in detail that the photon production is proportional to the Planck factor involving a velocity-dependent effective temperature. This temperature significantly limits photon generation even for ultrarelativistic motion. The time-dependent unitary transformations we introduce to obtain temporal factorization help establish connections with the shortcuts to adiabaticity of quantum thermodynamics and with the quantum Arnold transformation.