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 use direct spatial imaging of cold 85Rb Rydberg atom clouds to measure the Rydberg-Rydberg correlation function. The results are in qualitative agreement with theoretical predictions [F. Robicheaux and J. V. Hernández, Phys. Rev. A 72, 063403 (2005)]. We determine the blockade radius for states 44D(5/2), 60D(5/2), and 70D(5/2) and investigate the dependence of the correlation behavior on excitation conditions and detection delay. Experimental data hint at the existence of long-range order.

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.

In this paper we demonstrate the detection of millimeter waves via Autler-Townes splitting in 85 Rb Rydberg atoms. This method may provide an independent, atom-based, SI-traceable method for measuring mm-wave electric fields, which addresses a gap in current calibration techniques in the mm-wave regime. The electricfield amplitude within a rubidium vapor cell in the WR-10 wave guide band is measured for frequencies of 93 GHz, and 104 GHz. Relevant aspects of Autler-Townes splitting originating from a four-level electromagnetically induced transparency scheme are discussed. We measure the E-field generated by an open-ended waveguide using this technique. Experimental results are compared to a full-wave finite element simulation.

We study the repulsive van der Waals interaction of cold rubidium 70S 1/2 Rydberg atoms by analysis of time-delayed pair correlation functions. After excitation, Rydberg atoms are allowed to accelerate under the influence of the van der Waals force. Their positions are then measured using a single-atom imaging technique. From the average pair correlation function of the atom positions we obtain the initial atom-pair separation and the terminal velocity, which yield the van der Waals interaction coefficient C6. The measured C6 value agrees well with calculations. The experimental method has been validated by simulations. The data hint at anisotropy in the overall expansion, caused by the shape of the excitation volume. Our measurement implies that the interacting entities are individual Rydberg atoms, not groups of atoms that coherently share a Rydberg excitation. The van der Waals interaction is important in the description and control of interactions in few-and manybody dynamics studies. This interaction has been critical in the observation of Rydberg excitation blockades and collective excitations [1][2][3][4], Rydberg crystals [5,6], and Rydberg aggregates [7,8]. Rydberg interactions have been used in quantum information processsing [9][10][11][12]. The van der Waals interaction between two Rydberg atoms has been measured using spectroscopic methods [13,14]. Several measurements have been performed near surfaces to observe radiative Rydberg-level shifts caused by image charge interaction near metal surfaces [15,16]. The van der Waals interaction between excited cesium atoms and a dielectric surface has been measured using selective reflection spectroscopy [17].Here, we develop a method to study the van der Waals interaction between Rydberg atoms using direct spatial imaging of their trajectories [18][19][20][21]. Pairs of 70S 1/2 rubidium Rydberg atoms are prepared with a well-defined initial separation by detuning an excitation laser and utilizing the r −6 dependence of the van der Waals interaction [21,22]. After preparation, the atoms are subject to van der Waals forces (which are repulsive in this case). The effect of the forces is observed by tracking the interatomic distance between the Rydberg atoms, after they have been allowed to move for selected wait times (see Fig. 1). The atom trajectories and thereby the van der Waals interaction coefficient C 6 are extracted from the pair correlation functions of the Rydberg atom positions.The experimental setup is shown in Fig. 1(a). 85 Rb ground-state atoms are prepared in a magneto-optical trap (MOT) at a density of 10 10 cm −3 . The twophoton Rydberg excitation to 70S 1/2 is driven by simultaneous 780 nm and 480 nm laser pulses with a 5 µs duration and ≈1 GHz red-detuning from the 5P 3/2 intermediate state. Both beams propagate in the xy plane and are linearly polarized alongẑ. The 780 nm beam has a Gaussian beam parameter w 0 of 0.75 mm and the 480 nm beam is focused to w 0 = 8 µm. The Rydberg atoms are ionized by applying a high voltage to a tip imaging p...