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arXiv:2407.20369 · Physical Review Applied

Complete three-dimensional vector polarimetry with a Rydberg-atom rf electrometer

Peter K. Elgee, Kevin C. Cox, Joshua C. Hill, Paul D. Kunz, David H. Meyer

Published Dec 3, 2024• 20 citations
arXivHTMLPDF

Abstract

Radio-frequency (rf) receivers using Rydberg atoms offer appealing features over classical sensors, such as their size, frequency tuning range, and lack of field absorption. In this work, we extend the application space by demonstrating a Rydberg atom rf polarimeter. Using rf heterodyne with three independent and orthogonal local oscillators, we are able to extract the polarization ellipse of the field in three dimensions, in addition to the total amplitude of the field. We use the relative phases and amplitudes of the three generated heterodyne signals to measure the field amplitudes and phases along three cardinal axes giving the full three-dimensional polarization. We demonstrate this polarization measurement for incoming fields at different angles around the sensor. Lastly, we investigate the reception of data symbols encoded in the horizontal and vertical signal field polarizations and the phase between them. Our measurements yield an amplitude noise of $57\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{V}/\mathrm{m}/\sqrt{\text{Hz}}$ for horizontal polarization, $66\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{V}/\mathrm{m}/\sqrt{\text{Hz}}$ for vertical polarization, and a standard deviation of 0.094 rad in the phase between the field components.

DOI
10.1103/physrevapplied.22.064012

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Radio-frequency (rf) receivers using Rydberg atoms offer appealing features over classical sensors, such as their size, frequency tuning range, and lack of field absorption. In this work, we extend the application space by demonstrating a Rydberg atom rf polarimeter. Using rf heterodyne with three independent and orthogonal local oscillators, we are able to extract the polarization ellipse of the field in three dimensions, in addition to the total amplitude of the field. We use the relative phases and amplitudes of the three generated heterodyne signals to measure the field amplitudes and phases along three cardinal axes giving the full three-dimensional polarization. We demonstrate this polarization measurement for incoming fields at different angles around the sensor. Lastly, we investigate the reception of data symbols encoded in the horizontal and vertical signal field polarizations and the phase between them. Our measurements yield an amplitude noise of 57\ensuremath\muV/m/Hz57\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{V}/\mathrm{m}/\sqrt{\text{Hz}}57\ensuremath\muV/m/Hz​ for horizontal polarization, 66\ensuremath\muV/m/Hz66\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}\mathrm{V}/\mathrm{m}/\sqrt{\text{Hz}}66\ensuremath\muV/m/Hz​ for vertical polarization, and a standard deviation of 0.094 rad in the phase between the field components.
We present an electrically small Rydberg atom electric field sensor with the ability to extract the three-dimensional k -vector of an elliptically polarized radio-frequency field. In most mediums, the k -vector (or wave vector) provides the direction of propagation of an electromagnetic wave. Our method uses a field vector measurement at a single point in space and is thus compatible with a sensor volume that is arbitrarily small compared with the carrier wavelength. We measure the k -vector of a circularly polarized signal field with average absolute errors in the polar and azimuthal angles of 33 and 43 mrad, respectively, and statistical noise of 1.3 and 1.5 mrad/ Hz , respectively. Additionally, we characterize the performance of the sensor as a function of the ellipticity of the input field and the size of the sensing region. We find that the sensor works over a broad range of ellipticities, and validate that an electrically small sensing region is optimal.
Rydberg atom radio-frequency sensors are a unique platform for precision electromagnetic field measurement; e.g., they have extraordinary carrier bandwidth spanning MHz to THz and can be self-calibrated. These photonic sensors use lasers to prepare and read out the atomic response to a radio-frequency electromagnetic field. Most work on Rydberg atom sensors centers on radio-frequency electric field strength because the sensor functions as a square law detector, unless an external radio-frequency heterodyning field is used. A heterodyning field acts as a local oscillator and enables phase readout at the expense of the radio-frequency equipment necessary to generate it. In order to overcome the disadvantages of a radio-frequency local oscillator, we investigate all-optical phase-sensitive detection using a five-level closed-loop excitation scheme. We show that under finite detuning of the loop fields, the atomic response oscillates at the frequency of the detuning. The oscillation is transferred to a probe laser absorption signal. The phase, frequency, and amplitude of the radio-frequency signal are imprinted on the oscillatory dynamics and can be determined using demodulation and matched filter techniques applied to the probe laser transmission signal.
We present enhanced sensing of radio frequency (RF) electric fields (E-fields) by the combined polarizability of Rydberg atoms and the optimized local oscillator (LO) fields of supergheterodyne receiving. Our modified theoretical model reveals the dependencies of sensitivity of E-field amplitude measurement on the polarizability of Rydberg states and the strength of the LO RF field. The enhanced sensitivity of megahertz(MHz) E-field are demonstrated at an optimal LO field for three different Rydberg states 43D5/2\rm 43D_{5/2}43D5/2​, 60S1/2\rm 60S_{1/2}60S1/2​, and 90S1/2\rm 90S_{1/2}90S1/2​. The sensitivity of 63 MHz for the 90S1/2\rm 90S_{1/2}90S1/2​ state reaches 0.96 μV/cm/Hzμ\rm V/cm/\sqrt{Hz}μV/cm/Hz​ that is about an order of magnitude higher than those already published. This result closely approaches the theoretical sensitivity limit of RF dipole antennas, and indicates the potential for breaking the limit in measuring sub-MHz E-fields. This atomic sensor based on Rydberg Stark effect with heterodyne technique is expected to boost an alternative solution to electric dipole antennas.
We present enhanced sensing of a radio frequency (RF) electric field (E-field) by the combined polarizability of Rydberg atoms and the optimized local oscillator (LO) field of a superheterodyne receiver. Our modified theoretical model reveals the dependencies of the sensitivity of E-field amplitude measurement on the polarizability of Rydberg states and the strength of the LO field. The enhanced sensitivities of the megahertz (MHz) E-field are demonstrated at the optimal LO field for three different Rydberg states 43D5/2{\rm 43D}_{5/2}43D5/2​, 60S1/2{\rm 60S}_{1/2}60S1/2​, and 90S1/2{\rm 90S}_{1/2}90S1/2​. The sensitivity of 63 MHz for the 90S1/2{\rm 90S}_{1/2}90S1/2​ state reaches 9.6 ×10−5 V/m/Hz\times 10^{-5}\rm \,V/m/\sqrt {Hz}×10−5V/m/Hz​, which is approximately an order of magnitude higher than those already published. This result closely approaches the sensitivity limit of a 1 cm passive dipole antenna without using an impedance matching network. This atomic sensor based on the Rydberg Stark effect with heterodyne technique is expected to boost an alternative solution to electric dipole antennas.
We present a method for simultaneously measuring the phase fronts of three or more RF fields using thermal Rydberg atoms. We demonstrate this method using an all-dielectric atomic electrometer acting in a heterodyne configuration to detect three single tone continuous-wave microwave signals propagating in free space. We show that this method can be used to measure the angle of arrival of each source. This method requires no calibration of the incident fields and assumes only far-field distance and phase stability of the incident phase fronts. Because the sensor is minimally perturbing, it provides a direct probe of signal phase even in complex environments, such as the near field of an antenna source or a scattering surface. The measurements presented here are performed using a single scanned sensor, but this technique can trivially be extended to an array of sensors, which would enable phase-sensitive imaging and related applications.
When internal states of atoms are manipulated using coherent optical or radio-frequency (rf) radiation, it is essential to know the polarization of the radiation with respect to the quantization axis of the atom. We first present a measurement of the two-dimensional spatial distribution of the electric-field amplitude of a linearly polarized pulsed rf electric field at $\ensuremath{\sim}25.6\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}$ and its angle with respect to a static electric field. The measurements exploit coherent population transfer between the 35s35s35s and 35p35p35p Rydberg states of helium atoms in a pulsed supersonic beam. Based on this experimental result, we develop a general framework in the form of a set of equations relating the five independent polarization parameters of a coherently oscillating field in a fixed laboratory frame to Rabi rates of transitions between a ground and three excited states of an atom with arbitrary quantization axis. We then explain how these equations can be used to fully characterize the polarization in a minimum of five Rabi-rate measurements by rotation of an external bias field, or, knowing the polarization of the driving field, to determine the orientation of the static field using two measurements. The presented technique is not limited to Rydberg atoms and rf fields but can also be applied to characterize optical fields. The technique has the potential for sensing the spatiotemporal properties of electromagnetic fields, e.g., in metrology devices or in hybrid experiments involving atoms close to surfaces.