We demonstrate a continuously tunable electric field measurement based on the far off-resonant AC stark effect in a Rydberg atomic vapor cell. In this configuration, a strong far off-resonant field, denoted as a local oscillator (LO) field, acts as a gain to shift the Rydberg level to a high sensitivity region. An incident weak signal field with a few hundreds of kHz difference from the LO field is mixed with the LO field in the Rydberg system to generate an intermediate frequency signal, which is read out by Rydberg electromagnetically induced transparency (Rydberg-EIT) spectroscopy. Not like resonant EIT-Autler–Townes spectra, we realize the electric field measurement of the signal frequency from 2 to 5 GHz using a single Rydberg state. The detectable field strength is down to 2.25  μV/cm with sensitivity of the electrometry 712 nV cm−1 Hz−1/2, and a linear dynamic range is over 65 dB. The detectable field strength is comparable with a resonant microwave-dressed Rydberg heterodyne receiver using the same system, which is 0.96  μV/cm with sensitivity of 304 nV cm–1 Hz−1/2. We also show the system has an inherent polarization selectivity feature. Our method can provide high sensitivity of electric field measurement and be extended to arbitrary frequency measurements.

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.

The lifetimes of nS1/2 and nD5/2 (n = 60–83) cesium Rydberg states are measured accurately in a magneto-optical trap using the field ionization technique and analyzed with the existing theoretical model. The room temperature blackbody radiation (BBR) and interaction between Rydberg atoms can enhance the decay rate and reduce the spontaneous lifetime of the given Rydberg atom. The measured lifetime shows a good agreement with the calculation accounting a room temperature BBR at low enough Rydberg atomic density. The dependence of measured lifetime on atomic density shows that the collision and interaction between Rydberg atoms have a large effect on the lifetime at higher Rydberg atomic density. The scaling laws of n2.55±0.02 for nD5/2 state and n2.30±0.01 for nS1/2 state within n = 60–83 range are obtained and agreement with the model calculation with a relative deviation less than 3%.

Ultra-cold long-range Rydberg molecules, consisting of a Rydberg atom and a ground-state atom or another Rydberg atom or ion, have attracted considerable attention due to their exaggerated properties, such as huge size, long chemical bond, large polarization and electric dipole moment, abundant vibrational states and exotic adiabatic potentials, et al. The binding mechanism of Rydberg molecules is a low-energy scattering interaction between the Rydberg electron and the ground state atom for ground-Rydberg molecules or long-range multipole interaction for Rydberg-atom macrodimers and Rydberg-ion molecules, in contrast to covalent bonds, ionic bonds of normal and Van der Waals interaction. Owing to its huge size, the dynamic evolution become slow compared with normal diatomic molecules and the ultra-long chemical bonds allow for being imaged directly by high resolution imaging technology, which make it convenient to observe the molecular dynamics process chemical reaction process in real time. The investigation of Rydberg molecules will be significant for understanding of the mechanism of molecular collision and quantum chemical reaction.<br />In this paper, we study the ultra-cold Rydberg-ground molecule in theoretical and experimental. Theoretically, we calculate the adiabatic potential energy curve of cesium (36D_5/2+ 6S_1/2) Rydberg molecule based on the Fermi model of low energy electron scattering by numerically solving the Hamiltonian of Rydberg molecules. And also, we obtain its characteristic parameters, such as the potential depth, binding energy and equilibrium nuclear distance of Rydberg molecule. Experimentally, the Rydberg-ground molecules are investigated by a photoassociation spectroscopy, where two laser pulses are used to achieve a two-photon transition, and their spectra is obtained by ion detection technology. We successfully observe the Rydberg-ground molecules spectra that correspond to a scattering triplet and a scattering single-triplet mixture (^{S, T}Σ). The measured binding energy of Rydberg-ground molecules is in good agreement with the theoretical results. In addition, taking the Rydberg-ground molecules formed by scattering triplet (^TΣ) as an example, we demonstrate the spectrum broadening of Rydberg molecules in a weak electric field, from which we obtain the permanent electric dipole moments |<span style="text-decoration:overline"><em>d</em></span>| of polar Rydberg-ground molecules about 12.10±1.65 Debye (4.76±0.65 <em>ea</em>₀). The results are consistent with the theoretical calculations. Our study provides a feasible scheme for the experimental preparation of D-type Rydberg-ground molecules, which is of great significance for the study of binding mechanism and the spectral characteristics of polar Rydberg molecules.

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