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arXiv:2404.13794 · Journal of the Optical Society of America B

Effects of classical drivings on the power broadening of atomic lineshapes

Leonardi Hernández-Sánchez, Ivan A. Bocanegra-Garay, I. Ramos-Prieto, Francisco Soto, H. M. Moya-Cessa

Published May 6, 2024• 5 citations
arXivHTMLPDF

Abstract

In the framework of the Jaynes–Cummings model, we investigate how atomic lineshapes are affected by coherently driving the atom–field interaction. We pay particular attention to the two-level atom interaction with a thermal cavity field when both are influenced by external classical fields. Adopting a density matrix formalism, we calculate the average atomic inversion and demonstrate how the corresponding lineshapes vary as a function of the average number of thermal photons and the atom–field classical coupling. Furthermore, we compare these results with those obtained from the standard Jaynes–Cummings model and validate our findings through numerical calculations.

DOI
10.1364/josab.522587

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In the framework of the Jaynes–Cummings model, we investigate how atomic lineshapes are affected by coherently driving the atom–field interaction. We pay particular attention to the two-level atom interaction with a thermal cavity field when both are influenced by external classical fields. Adopting a density matrix formalism, we calculate the average atomic inversion and demonstrate how the corresponding lineshapes vary as a function of the average number of thermal photons and the atom–field classical coupling. Furthermore, we compare these results with those obtained from the standard Jaynes–Cummings model and validate our findings through numerical calculations.
We study the properties of atoms and cavity field in the two-atom Tavis–Cummings model where the two atoms interact with each other and are also driven by an external classical field. We consider the special case that the cavity is initially in a coherent state. The atomic inversion, the average photons number and the Mandel parameter in the driven Tavis–Cummings model are given and analysed numerically. We pay special attention to the dynamical behaviour of the atoms and the cavity field modified by the external field.
The dynamics of the driven Jaynes-Cummings model where a two-level atom is coupled to a single mode of cavity fields and is driven by an external coherent field is investigated. We find that in this model quantum collapse and revivals of the atomic population inversion and squeezing of the cavity field can be generated from a thermal photon state. We also notice that the squeezing is very sensitive to the mean number of thermal photons initially in the cavity, but the quantum collapse and revivals are not. The influence of the amplitude of the driving field and various detuning parameters on the nonclassical effects is discussed. The result shows that one can use the external field to control nonclassical effects in the Jaynes-Cummings model.
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.
The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of a radiation field prepared in a Glauber-Lachs state is investigated to study the development of seemingly chaotic oscillations of the atomic inversion from a regular collapse-and-revival phenomenon, as the field statistics is changed from the coherent state to the thermal state. The effect of thermal photons on the coherent light is shown to be striking: Both the photon distribution as well as the atomic inversion are highly sensitive to even a very small addition of thermal photons to an initially coherent radiation field. We also compare the collapse and revival occurring in the micromaser case with the Glauber-Lachs version of the Jaynes-Cummings model.
We extend the standard Jaynes-Cummings model to include transient effects due to a modulation of the atom-field coupling. The exact solution for such a generalized model is found in terms of Bessel functions for the atom-cavity mode interaction modulated by the exponential function. This function is incorporated into the basic Hamiltonian phenomenologically for modelling the processes of adiabatic switching on or switching off the interaction of a two-level atom (at rest) with a quantized mode. The dynamical behaviour of the atomic inversion for such processes is plotted and compared with the atomic dynamics for the standard model. If we take into account that, in micromaser experiments, Rydberg atoms move through a cavity with a spatially inhomogenous field, we deal with the Jaynes-Cummings model with a spatial modulation the form of which is defined by the mode-shape function depending, in turn, on the geometrical form of resonator. In the cases of a rectangular and a spherical cavity the analytical solutions for atomic inversion are found in the explicit form in the weak-coupling limit. We consider in detail the time evolution of the atomic inversion while the atom passes through a rectangular cavity. Contrary to the standard model the initial inversion can be exactly restored during the atomic transit depending on the relation between the detuning, the atomic velocity and the number of half-wavelengths of the chosen mode. The numerical solutions of the basic equations are also obtained and plotted for rectangular and spherical resonators.
We calculate the quasienergies and steady states of a coupled two-level atom and quantized electromagnetic cavity mode with the cavity mode driven by a periodic classical field. The atom, the cavity mode, and the classical field are all on resonance. The quasienergies give shifted Jaynes-Cummings level splittings. These splittings are reduced by the interaction with the driving field and vanish at a threshold value of the driving field strength. Above the threshold, discrete quasienergies and normalizable steady states do not exist. Below the threshold, for weak driving fields, the steady states are squeezed and displaced Jaynes-Cummings eigenstates. We discuss the relevance of these results to work in cavity quantum electrodynamics.