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Physica Scripta

Hosting of exceptional points in an atom-field interaction Hamiltonian and manipulation of light states

Anubhav Paul, Arnab Laha, Somnath Ghosh

Published Apr 14, 2021• 0 citations
Publisher

Abstract

Abstract We report an analytical model to investigate an atom-cavity interaction phenomenon with the consideration of a two-level atom and a quantized mode of the cavity field in the form of harmonic oscillation. Accordingly, we consider the matrix form of a special type of two-level Hamiltonian consisting of three units, explaining a two-level atom, a quantum harmonic oscillator to be equivalent to a quantized cavity-mode field, and an interaction matrix between them, which are connected by some iteration parameters. The iteration parameters of the proposed Hamiltonian have judiciously been modulated to encounter an exceptional point (EP). A specific closed parameter space encircling the embedded EP has been considered to study the dynamics of the coupled states in the context of a flip-of-state phenomenon. We also incorporate a deliberate phase difference between the two unperturbed levels associated with the atomic system and study the phase induced interaction between them in the context of state-flipping around the identified EP. The proposed analytical model indeed opens up a fertile platform to explore a range of interesting applications associated with the atom-cavity interaction.

DOI
10.1088/1402-4896/abf7ff

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Abstract We report an analytical model to investigate an atom-cavity interaction phenomenon with the consideration of a two-level atom and a quantized mode of the cavity field in the form of harmonic oscillation. Accordingly, we consider the matrix form of a special type of two-level Hamiltonian consisting of three units, explaining a two-level atom, a quantum harmonic oscillator to be equivalent to a quantized cavity-mode field, and an interaction matrix between them, which are connected by some iteration parameters. The iteration parameters of the proposed Hamiltonian have judiciously been modulated to encounter an exceptional point (EP). A specific closed parameter space encircling the embedded EP has been considered to study the dynamics of the coupled states in the context of a flip-of-state phenomenon. We also incorporate a deliberate phase difference between the two unperturbed levels associated with the atomic system and study the phase induced interaction between them in the context of state-flipping around the identified EP. The proposed analytical model indeed opens up a fertile platform to explore a range of interesting applications associated with the atom-cavity interaction.
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Abstract The dynamics of an atom of three levels in Λ configuration interacting with a quantized field of two modes in a cavity is studied within the rotating wave approximation by considering experimental values of accessible hyperfine levels of alkali atoms. The Hamiltonian model is constructed on the basis of the direct product of the atomic states with Fock states of light. This simplified basis allows us to generalize the state of light to any quantum field. The interaction term of the Hamiltonian restricts the system to a 3D Hilbert space. The system’s time evolution results show some similarities with the effective two-level system, such as the presence of collapses and revivals and the atom-field entanglement. By an analysis of the statistics of the photons, we show that when the three-level atom is interacting with a coherent field of two modes, it is possible to control experimentally the statistics of the field to be super-Poissonian or sub-Poissonian by the choice of the initial atomic state.
The dynamics of an ensemble of two-level atoms moving through a single-mode lossless cavity is investigated in the semiclassical and rotating-wave approximations. The dynamical system for the expectation values of the atomic and field observables is considered as a perturbation to one of the following integrable versions: (i) a model with atoms moving through a spatially inhomogeneous resonant field, and (ii) a model with atoms interacting with a nonresonant eigenmode which is assumed to be homogeneous on the cavity size. We find the general exact solutions for both the models and show that they contain special solutions describing a coherent effect of population and radiation trapping. Using the Melnikov method, we prove analytically transverse intersections of stable and unstable manifolds of a hyperbolic fixed point under a small modulation of the vacuum Rabi frequency. These intersections are believed to provide the Smale horseshoe mechanism of Hamiltonian chaos. The analytical results are accompanied with direct computation of topographical maps of maximal Lyapunov exponents that give a representative image of regularity and chaos in the atom-field system in different ranges of its control parameters--the frequency detuning, the number, and the velocity of atoms.
An exceptional point is a special point in parameter space at which two (or more) eigenvalues and eigenvectors coincide. The discovery of exceptional points within mechanical and optical systems has uncovered peculiar effects in their vicinity. Here, we consider perhaps the simplest quantum model that exhibits an exceptional point and allows for an analytical treatment. In particular, we reexamine a two-level atom driven by a laser and suffering from losses. The same exceptional point arises in several non-Hermitian matrices, which determine various aspects of the dynamics of the system. There are consequences for some important observables, for example, the spectrum evolves from being a Lorentzian-like singlet to a Mollow triplet upon passing through the exceptional point. Our analysis supports the perspective that viewing certain quantum systems through the lens of exceptional points offers some desirable explanatory advantages.
We consider a generalization of the non-Hermitian PT{\mathcal PT}PT symmetric Jaynes-Cummings {Hamiltonian, recently introduced for studying optical phenomena with time-dependent physical parameters, that includes environment-induced decay}. In particular, we investigate the interaction of a two-level fermionic system (such as a two-level atom) with a single bosonic field mode in a cavity. The states of {the} two-level system are allowed to decay because of the interaction with the environment, {and this is included phenomenologically in our non-Hermitian Hamiltonian by introducing complex energies for the fermion system. We focus our attention} on the occurrence of exceptional points in the spectrum of the Hamiltonian, clarifying its mathematical and physical meaning.
We theoretically investigate quantum Rabi oscillations in a system consisting of a two-level atom (qubit) strongly coupled to a one-dimensional open waveguide. In contrast to conventional cavity quantum electrodynamics, the qubit interacts with a continuum of propagating modes, which gives rise to fundamentally different dynamical behavior. Within the rotating-wave approximation, we express the multimode Jaynes-Cummings Hamiltonian in terms of collective bosonic operators and show that the system possesses two integrals of motion, enabling an exact diagonalization of the Hamiltonian in the single-excitation subspace. We show that for a strongly interacting qubit-photon system, the dynamics are captured by a reduced two-level model. In this framework, each level is defined as the product of the atomic excited state and a specific field mode, which takes the form of a multiphoton Fock-like state. In this picture, the Rabi oscillations represent a collective phenomenon corresponding to oscillations between multiphoton states differing by a single photon. We then extend our analysis to multiphoton processes in which the initial field is a coherent state with a continuous spectrum. In this case, the Rabi frequency is shown to be sensitive to the spectral profile of the function that generates the coherent state.