Hyperfine interaction in the Autler-Townes effect: The formation of bright, dark, and chameleon states

Abstract

This paper is devoted to clarifying the implications of hyperfine (HF) interaction in the formation of adiabatic (i.e., "laser-dressed") states and their expression in the Autler-Townes (AT) spectra. We first use the Morris-Shore model [J. R. Morris and B. W. Shore, Phys. Rev. A 27, 906 (1983)] to illustrate how bright and dark states are formed in a simple reference system where closely spaced energy levels are coupled to a single state with a strong laser field with the respective Rabi frequency S . We then expand the simulations to realistic hyperfine level systems in Na atoms for a more general case when non-negligible HF interaction can be treated as a perturbation in the total system Hamiltonian. A numerical analysis of the adiabatic states that are formed by coupling of the 3p 3/2 and 4d 5/2 states by the strong laser field and probed by a weak laser field on the 3s 1/2 − 3p 3/2 transition yielded two important conclusions. Firstly, the perturbation introduced by the HF interaction leads to the observation of what we term "chameleon" states-states that change their appearance in the AT spectrum, behaving as bright states at small to moderate S , and fading from the spectrum similarly to dark states when S is much larger than the HF splitting of the 3p 3/2 state. Secondly, excitation by the probe field from two different HF levels of the ground state allows one to address orthogonal sets of adiabatic states; this enables, with appropriate choice of S and the involved quantum states, a selective excitation of otherwise unresolved hyperfine levels in excited electronic states.

Expressions of “fast” and “slow” chameleon dressed states in Autler–Townes spectra of alkali‐metal atoms

“…The ground basis vectors are specially chosen as a set of eigenvectors of the HF operator, |g ⟩ F ′′ M = ketg, F ′′ M. The effect of HF interaction is then reduced to the well-documented HF energy shifts of g-substates |g ⟩ 𝜂 , depicted in Figure 2. The f -subspace Λ f corresponds to nd states, for which the HF energy shifts are essentially negligible, less than 0.3 MHz even for n = 4 (Kirova et al 2017).…”

“…In obtaining the AT spectra, we use the same algorithm as in our previous works (Kirova et al 2017;Porfido et al 2015), where we solve the modified optical Bloch…”

“…On the other hand, it is impossible to excite | | i 𝜇M ⟩ or | | f 𝜇M ⟩ directly from the ground state (Figure 2), so they should be classified as dark states (Morris & Shore 1983). To summarize, the basis vectors | | i 𝜇M ⟩, | | f 𝜇M ⟩ share the features of both bright and dark states, which gave the reason to assign them the name "chameleons" (Kirova et al 2017) and to associate the manifolds Λ f ,3∕2 = V(S) Λ i,3∕2 with subspaces Λ CS i,f of chameleon states.…”

Autoionization widths of cold Rydberg atomic complexes

“…Analysis of phenomena with strong path stochastization requires the use of reliable tools for numerical computation of particle parameters. Such tools include symplectic integrators of motion equations (Hairer, 1999) for various physical problems, including complex integro-differential tasks related to the radiation energy transfer processes in optically dense media (Kazansky et al, 2001) with a multi-level structure of atomic quantum states (Sydoryk et al, 2008;Kirova et al, 2017). A numeric algorithm of advanced stability for analyzing stochastic migration effects was suggested in publication Efimov et al (2014).…”

Dynamic Instability of Rydberg Atomic Complexes

“…The experimental methods existing in atomic and molecular physics make it possible to compare the ionization parameters that were calculated in the frame of stochastic dynamics with the results of direct measurements performed in atomic beams of different types [59]. Atomic/molecular beams have been widely implemented in practice as convenient sources of particles that are used for investigations in the physics of collisions [60], spectroscopy [61], and the analysis of the interaction of light and matter [62]. In recent decades, a new type of beams, known as "cold beams" [63], has been added to the two classical types of beams, i.e., diffusion [14,64] and supersonic [59] ones.…”