Abstract We investigated the Autler–Townes (AT) splitting produced by microwave (mw) transitions between atomic Rydberg states explored by optical spectroscopy from the ground electronic state. The laser-atom Hamiltonian describing the double irradiation of such a multilevel system is analysed on the basis of the Morris–Shore transformation. The application of this transformation to the mw-dressed atomic system allows the identification of bright, dark, and spectator states associated with different configurations of atomic states and mw polarisations. We derived synthetic spectra that show the main features of Rydberg spectroscopy. Complex AT spectra are obtained in a regime of strong mw dressing, where a hybridisation of the Rydberg fine structure states is produced by the driving.
Abstract We investigated the Autler–Townes (AT) splitting produced by microwave (mw) transitions between atomic Rydberg states explored by optical spectroscopy from the ground electronic state. The laser-atom Hamiltonian describing the double irradiation of such a multilevel system is analysed on the basis of the Morris–Shore transformation. The application of this transformation to the mw-dressed atomic system allows the identification of bright, dark, and spectator states associated with different configurations of atomic states and mw polarisations. We derived synthetic spectra that show the main features of Rydberg spectroscopy. Complex AT spectra are obtained in a regime of strong mw dressing, where a hybridisation of the Rydberg fine structure states is produced by the driving.
To distinguish the contributions of electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in their applications in precision laser spectroscopy, we propose a real-imaginary spectrum decomposition method to investigate the transparency spectra in a four-level microwave (MW) dressed Rydberg system. We show that the opening transparency windows in the absorption spectra of probe field is a prominent character by EIT, EIT-ATS crossover, and ATS when the MW field is turned off and the intensity of the control field is adjusted. When the MW field is turned on and gradually increased, the EIT is destroyed and disappears. In addition, the most prominent characters that open a transparency window are the EIT-ATS crossover and the ATS. Then, if we further increase the intensity of the MW field, we find that the transparency windows open mainly due to the ATS. Compared to the previous considerations of this issue, which were limited to three-level systems, our four-level scheme reported here is useful for understanding the features of quantum interference in multilevel atomic systems, and has potential applications to study enhanced sensitivity, measurement spectroscopic, quantum processing, quantum communication, and transmission.
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 ${\mathrm{\ensuremath{\Omega}}}_{S}$. 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 3p3/2 and 4d5/2 states by the strong laser field and probed by a weak laser field on the $3{s}_{1/2}\ensuremath{-}3{p}_{3/2}$ 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 ${\mathrm{\ensuremath{\Omega}}}_{S}$, and fading from the spectrum similarly to dark states when ${\mathrm{\ensuremath{\Omega}}}_{S}$ is much larger than the HF splitting of the 3p3/2 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 ${\mathrm{\ensuremath{\Omega}}}_{S}$ and the involved quantum states, a selective excitation of otherwise unresolved hyperfine levels in excited electronic states.
We demonstrate the three-photon Autler-Townes (AT) spectroscopy in a cold cesium Rydberg four-level atom by detecting the field ionized Rydberg population. The ground state |6S1/2〉, two intermediate states |6P3/2〉 and |7S1/2〉 and Rydberg state |60P3/2〉 form a cascade four-level atomic system. The three-photon AT spectra and AT splittings are characterized by the Rabi frequency Ω852 and Ω1470 and detuning δ852 of the coupling lasers. Due to the interaction of two coupling lasers with the atoms, the AT spectrum has three peaks denoted with the letters A, B and C. Positions of the peaks and relative AT splittings, γAB and γBC, strongly depend on two coupling lasers. The dependence of the AT splitting, γAB and γBC, on the coupling laser detuning, δ852, and Rabi frequency, Ω852 and Ω1470 are investigated. It is found that the AT splitting γAB mainly comes from the first photon coupling, whereas the γBC mainly comes from the second photon coupling with the atom. The three-photon AT spectra and relevant AT splittings are simulated with the four-level density matrix equation and show good agreement with the theoretical simulations considering the spectral line broadening. Our work is of great significance both for further understanding the interaction between the laser and the atom, and for the application of the Rydberg atom based field measurement.
Abstract Polarized Autler–Townes (AT) splitting of six-wave mixing (SWM) involving Rydberg atoms is for the first time observed in a thermal vapor cell. By scanning the frequency detuning of the dressing field, AT splitting of Rydberg SWM is compared with that of non-Rydberg SWM with an elliptically polarized probe field. It is demonstrated that the AT spectra are strongly dependent on the interaction between Rydberg atoms. Moreover, AT splitting of SWM is cyclically modulated via a multi-dark state and presented by the corresponding spatial SWM AT splitting images. The theoretical calculations are in good agreement with the experimental results.
The Autler–Townes doublet and triplet spectroscopy are well known in the literature. Here, atomic systems for quartuplet, quintuplet emission spectroscopy and their linkages with the sodium atom are investigated for display of the corresponding spectra. We explore the involved fundamental processes of quantum interference in these systems by examining the Laplace transform of the corresponding state-vector subjected to steady coherent illumination in the rotating wave approximation and Weisskopf–Wigner treatment of spontaneous emission as a simplest probability loss. In the quartuplet (quintuplet), four (five) fields interact appropriately and resonantly with the five-level (six-level) atom. The spectral profile of the single decaying level, upon interaction with three (four) other levels, splits into four (five) destructively interfering dressed states generating three (four) dark lines in the spectrum. These dark lines divide the spectrum into four (five) spectral components (bright lines) whose widths are effectively controlled by the relative strength of the laser fields and the relative width of a single decaying level. The idea is also extended to higher-ordered spectroscopy. The apparent disadvantage of these schemes is the successive increase in the number of laser fields required for the strongly interactive atomic states. However, these complexities are naturally inherited and are the beauty of these atomic systems. They provide the foundations for the basic mechanisms of the quantum interference involved in the higher-ordered multiplet spectroscopy.
Electromagnetically induced transparency (EIT) and Autler–Townes splitting (ATS) are two similar yet distinct phenomena that modify the transmission of a weak probe field through an absorption medium in the presence of a coupling field, featured in a variety of three-level atomic systems. In many applications it is important to distinguish EIT from ATS splitting. We present EIT and ATS spectra in a three-level cascade system, involving cold cesium atoms in the Rydberg state. The EIT linewidth, γ EIT , defined as the full width at half maximum of the transparency window, and the ATS splitting, γ ATS , defined as the peak-to-peak distance between AT absorption peaks, are used to delineate the EIT and ATS regimes and to characterize the transition between the regimes. In the cold-atom medium, in the weak-coupler (EIT) regime γ EIT ≈ A + B ( + , where Ω c and Ω p are the coupler and probe Rabi frequencies, Γ eg is the spontaneous decay rate of the intermediate 6P 3/2 level, and parameters A and B that depend on the laser linewidth. We explore the transition into the strong-coupler (ATS) regime, which is characterized by the relation γ ATS ≈ Ω c . The experiments are in agreement with numerical solutions of the Master equation. Our analysis accounts for non-ideal conditions that exist in typical realizations of Rydberg-EIT, including laser-frequency jitter, Doppler mismatch of the utilized two-color Rydberg EIT system, and strong probe fields. The obtained criteria to distinguish cold-atom EIT from ATS are readily accessible and applicable in practical implementations.