Abstract-We discuss a fundamentally new approach for the measurement of electric (E) fields that will lead to the development of a broadband, direct SI-traceable, compact, selfcalibrating E-field probe (sensor). This approach is based on the interaction of radio frequency (RF) fields with alkali atoms excited to Rydberg states. The RF field causes an energy splitting of the Rydberg states via the Autler-Townes effect and we detect the splitting via electromagnetically induced transparency (EIT). In effect, alkali atoms placed in a vapor cell act like an RFto-optical transducer, converting an RF E-field strength measurement to an optical frequency measurement. We demonstrate the broadband nature of this approach by showing that one small vapor cell can be used to measure E-field strengths over a wide range of frequencies: 1 GHz to 500 GHz. The technique is validated by comparing experimental data to both numerical simulations and far-field calculations for various frequencies. We also discuss various applications, including: a direct traceable measurement, the ability to measure both weak and strong field strengths, compact form factors of the probe, and sub-wavelength imaging and field mapping.Keywords: atom based metrology, Autler-Townes splitting, broadband sensor and probe, electrical field measurements and sensor, EIT, sub-wavelength imaging, Rydberg atoms

We investigate the relationship between the Rabi frequency (X RF , related to the applied electric field) and Autler-Townes (AT) splitting, when performing atom-based radio-frequency (RF) electric (E) field strength measurements using Rydberg states and electromagnetically induced transparency (EIT) in an atomic vapor. The AT splitting satisfies, under certain conditions, a well-defined linear relationship with the applied RF field amplitude. The EIT/AT-based E-field measurement approach derived from these principles is currently being investigated by several groups around the world as a means to develop a new SI-traceable RF E-field measurement technique. We establish conditions under which the measured AT-splitting is an approximately linear function of the RF electric field. A quantitative description of systematic deviations from the linear relationship is key to exploiting EIT/AT-based atomic-vapor spectroscopy for SI-traceable field measurement. We show that the linear relationship is valid and can be used to determine the E-field strength, with minimal error, as long as the EIT linewidth is small compared to the AT-splitting. We also discuss interesting aspects of the thermal dependence (i.e., hot-versus cold-atom) of this EIT-AT technique. An analysis of the transition from coldto hot-atom EIT in a Doppler-mismatched cascade system reveals a significant change of the dependence of the EIT linewidth on the optical Rabi frequencies and of the AT-splitting on X RF .

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We observe long-range homonuclear diatomic nD Rydberg molecules photoassociated out of an ultracold gas of 87 Rb atoms for 34≤ n ≤40. The measured ground-state binding energies of 87 Rb(nD − 5S 1/2 ) molecular states are larger than those of their 87 Rb(nS − 5S 1/2 ) counterparts, showing the dependence of the molecular bond on the angular momentum of the Rydberg atom. We exhibit the transition of 87 Rb(nD − 5S 1/2 ) molecules from a molecular-binding-dominant regime at low n to a fine-structure-dominant regime at high n [akin to Hund's cases (a) and (c), respectively]. In the analysis the fine structure of the nD Rydberg atom and the hyperfine structure of the 5S 1/2 atom are included.PACS numbers: 34.50. Cx,34.20.Cf,33.80.Rv,31.10.+z, Cold atomic systems have opened new frontiers at the interface of atomic and molecular physics. Of particular interest are a recently discovered class of long-range, homonuclear Rydberg molecules [1,2]. Formed via an attractive interaction between a Rydberg electron and a ground-state atom [1], these molecules are among the largest ever observed with internuclear separations of several thousand Bohr radii. Their distinctive binding mechanism, which is unlike conventional covalent, ionic, and van der Waals bonds between ground-state atoms, results in loosely bound molecules whose properties closely mimic those of their constituent Rydberg atoms. The discovery of these molecular bonds has been likened to a new ultracold chemistry [3], and has spurred a significant amount of theoretical [4,5] and experimental interest [6][7][8][9]. Non-degenerate, low angular momentum Rydberg states (orbital angular momentum ℓ ≤ 2 in rubidium) produce molecules with a few tens of MHz binding energies and permanent electric dipole moments of a few Debye. The ℓ = 0 molecules were first observed by photoassociation [10] The relevant interaction was first described by Fermi [11] to help explain pressure-induced energy shifts of Rydberg absorption lines in a gas [12]. The deBroglie wavelength of the Rydberg electron (position r) is much larger than that of a heavy ground-state atom (position R) that lies within the Rydberg atom's volume, and their interaction can be approximated as a low-energy s-wave scattering process (scattering length a s ). The interaction is described with a Fermi-type pseudopotential [1,13], V pseudo (r) = 2πa s δ 3 (r − R), where p-wave and higherorder scattering [4] are neglected. For negative a s the interaction can lead to bound molecular states [1,13].In the present work we focus on long-range 87 Rb 2 molecules formed by an nD Rydberg and a 5S 1/2 ground state atom. The binding energies generally increase with ℓ, due to the √ 2ℓ + 1-scaling of the Y m=0 l (θ = 0). Among the low-ℓ variety of these molecules the nD ones have the highest binding energies. The angular-momentum coupling spans three Hund's cases when varying ℓ from 0 to 2. The nS 1/2 − 5S 1/2 molecules are akin to Hund's case (b), because they have L = 0 and total electron spin S = 1. The nP j − 5S 1/2 molecules a...

We present a technique for measuring radio-frequency (RF) electric field strengths with subwavelength resolution. We use Rydberg states of rubidium atoms to probe the RF field. The RF field causes an energy splitting of the Rydberg states via the Autler-Townes effect, and we detect the splitting via electromagnetically induced transparency (EIT). We use this technique to measure the electric field distribution inside a glass cylinder with applied RF fields at 17.04 GHz and 104.77 GHz. We achieve a spatial resolution of ≈100 µm, limited by the widths of the laser beams utilized for the EIT spectroscopy. We numerically simulate the fields in the glass cylinder and find good agreement with the measured fields. Our results suggest that this technique could be applied to image fields on a small spatial scale over a large range of frequencies, up into the sub-THz regime.