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Applied Physics Letters

A Rydberg atom-based mixer: Measuring the phase of a radio frequency wave

Matthew T. Simons, Abdulaziz H. Haddab, Joshua A. Gordon, Christopher L. Holloway

Published Mar 18, 2019• 270 citations
Publisher

Abstract

Rydberg atoms have been shown to be very useful in performing absolute measurements of the magnitude of a radio frequency (RF) field using electromagnetically induced transparency. However, there has been less success in using Rydberg atoms for the measurement of the phase of an RF field. Measuring the phase of a RF field is a necessary component for many important applications, including antenna metrology, communications, and radar. We demonstrate a scheme for measuring the phase of an RF field by using Rydberg atoms as a mixer to down-convert an RF field at 20 GHz to an intermediate frequency on the order of kHz. The phase of the intermediate frequency corresponds directly to the phase of the RF field. We use this approach to measure the phase shift on an electromagnetic wave from a horn antenna as the antenna is placed at different distances from the Rydberg atom sensor. The atom-based RF phase measurements allow us to measure the propagation constant of the RF wave to within 0.1% of the theoretical value.

DOI
10.1063/1.5088821

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Rydberg atoms have been shown to be very useful in performing absolute measurements of the magnitude of a radio frequency (RF) field using electromagnetically induced transparency. However, there has been less success in using Rydberg atoms for the measurement of the phase of an RF field. Measuring the phase of a RF field is a necessary component for many important applications, including antenna metrology, communications, and radar. We demonstrate a scheme for measuring the phase of an RF field by using Rydberg atoms as a mixer to down-convert an RF field at 20 GHz to an intermediate frequency on the order of kHz. The phase of the intermediate frequency corresponds directly to the phase of the RF field. We use this approach to measure the phase shift on an electromagnetic wave from a horn antenna as the antenna is placed at different distances from the Rydberg atom sensor. The atom-based RF phase measurements allow us to measure the propagation constant of the RF wave to within 0.1% of the theoretical value.
In this work, we demonstrate the use of a Rydberg atom-based sensor for determining the angle of arrival of an incident radio frequency (RF) wave or signal. The technique uses electromagnetically induced transparency in Rydberg atomic vapor in conjunction with a heterodyne Rydberg atom-based mixer. The Rydberg atom mixer measures the phase of the incident RF wave at two different locations inside an atomic vapor cell. The phase difference at these two locations is related to the direction of arrival of the incident RF wave. To demonstrate this approach, we measure phase differences of an incident 19.18 GHz wave at two locations inside a vapor cell filled with cesium atoms for various incident angles. Comparisons of these measurements with both the full-wave simulation and the plane wave theoretical model show that these atom-based sub-wavelength phase measurements can be used to determine the angle of arrival of an RF field.
Significant progress has been made in atom-based measurements of length, time, gravity and electromagnetic fields in recently years. Rydberg atom-based microwave electric field measurement, using electromagnetically induced transparency (EIT) in room temperature alkali-metal vapors, has been extensively investigated and aroused the broad interest. This approach may establish a new standard for the measurements of microwave (MW) and radio frequency (RF) electric fields.In this review, we describe the work on a new method of measuring electric fields based on quantum interference by using either cesium or rubidium atoms contained in a dielectric vapor cell. Rydberg atoms with principal quantum number n >>1 have large direct current (DC) polarizabilities and microwave transition dipole moments, thereby making them extremely sensitive to external electric fields. Using the Rydberg three-level EIT to detect the level splitting and shift that is induced by the external field, we can realize a rapid and robust self-calibration method of measuring the electric field in a frequency range from 0.01 GHz to 1000 GHz. For the MW electric field (frequency range > 1 GHz), the MW field causes the Rydberg states to split, known as an Autler-Townes splitting (A-T) effect when the applied microwave can resonate with adjacent Rydberg states. The MW coupled A-T splitting is proportional to the applied electric field strength, from which the field strength is measured. Using the EIT window, a high sensitivity of 3 μV·cm-1·Hz-1/2 and small electric field of 1 μV/cm are expected to be achieved with a modest setup, and the limitations of the sensitivity are also addressed in the review. For the RF field at frequency mj EIT lines, and avoided crossings formed with the fine-structure levels of equal mj and different J's, which is used to calibrate and measure the RF field amplitude. On the other hand, the dependence of the EIT-line strength on the RF field polarization provides a fast and robust polarization measurement of RF fields based on matching experimental data with a theoretical simulation. The measurements of minimum strengths and sensitivity of RF fields based on Rydberg atoms are one order magnitude below the values obtained by traditional antenna methods. The atom-based field measurement paves the way for determining fields through calibration-free, invariable atomic properties and miniaturization. We also propose its various potential applications in the future.
We demonstrate a Rydberg atom-based sensor embedded in a parallel-plate waveguide (PPWG) for amplitude and phase detection of a radio-frequency (RF) electric field. This embedded atomic sensor is also capable of receiving modulated communications signals. In this configuration, the PPWG antenna serves two functions. First, the PPWG antenna acts as a source for a local oscillator (LO) field. The LO is required to use an atomic vapor cell (a glass cell containing a Rydberg atom vapor) as a Rydberg atom-based mixer, which detects the amplitude and phase of a second RF field incident from some remote location. The second function of the PPWG antenna is to capture the RF field arriving from a remote location and concentrate it at the location of the atomic vapor cell for detection. To demonstrate this, we show several examples of phase and amplitude measurements of an RF field with the embedded Rydberg-atom sensor. We also demonstrate the discrimination of the polarization of an RF field and the ability to receive phase-modulated carrier communications signals with this integrated atomic sensor. Embedding the atomic sensor in an antenna allows for the full characterization of a radio frequency field, in that the magnitude, phase, and polarization of an RF field can be measured with one compact integrated quantum-based sensor. Furthermore, the embedded sensor head allows one to easily vary the LO in order to maximize the ability to measure phase and amplitude of the field or modulated signal.
Rydberg atoms show great promise for use as self-calibrated electric field sensors for a broad range of frequencies. Their response is traceable to the international system of units making them a valuable tool for a variety of applications including traceable channel sounding. The Rydberg atom sensor is an electrically small point probe. Its detection volume is defined by the overlap of probing and coupling lasers, which can be as small as hundreds of microns. We present measurements of the beam-formed output of a horn antenna in the far field at 28 GHz. We move a Rydberg atom sensor over a synthetic aperture to obtain high angular resolution of the received signal and employ electromagnetic induced transparency with AC stark shifting and a local oscillator signal radiated onto the atoms for magnitude and phase detection at each location in the area. These results demonstrate the use of these Rydberg atom sensors in a synthetic aperture configuration and inform their eventual use for traceable channel sounding measurements.
We present a precise measurement of a weak radio frequency electric field with a frequency of ≲ 3 GHz employing a resonant atomic probe that is constituted with a Rydberg cascade three-level atom, including a cesium ground state |6S1/2⟩, an excited state |6P3/2⟩, and Rydberg state |nD5/2⟩. Two radio frequency (RF) electric fields, noted as local and signal fields, couple the nearby Rydberg transition. The two-photon resonant Rydberg electromagnetically induced transparency (Rydberg-EIT) is employed to directly read out the weak signal field having hundreds of kHz difference between the local and signal fields that is encoded in the resonant microwave-dressed Rydberg atoms. The minimum detectable signal fields of E Smin = 1.36 ± 0.04 mV/m for 2.18 GHz coupling |68D5/2⟩ → |69P3/2⟩ transition and 1.33 ± 0.02 mV/m for 1.32 GHz coupling |80D5/2⟩ → |81P3/2⟩ transition are obtained, respectively. The bandwidth dependence is also investigated by varying the signal field frequency and corresponding −3 dB bandwidth of 3 MHz is attained. This method can be employed to perform a rapid and precise measurement of the weak electric field, which is important for the atom-based microwave metrology.
Recently, a Rydberg atom-based mixer was developed to measure the phase of a radio frequency (RF) field. The phase of the signal RF (SIG RF) field is down-converted directly to the phase of a beat signal created by the presence of a local RF (LO RF) field. In this study, we propose that the Rydberg atom-based mixer can be converted to an all-optical phase detector by amplitude modulation (AM) of the LO RF field; that is, the phase of the SIG RF field is related to both the amplitude and phase of the beat signal. When the AM frequency of the LO RF field is the same as the frequency of the beat signal, the beat signal will further interfere with the AM of the LO RF field inside the atom, and then the amplitude of the beat signal is related to the phase of the SIG RF field. The amplitude of the beat signal and the phase of the SIG RF field show a linear relationship within the range of 0 to π/2 when the phase of the AM is set with a difference π/4 from the phase of the LO RF field. The minimum phase resolution can be as small as 0.6° by optimizing the experimental conditions according to a simple theoretical model. This study will expand and contribute to the development of RF measurement devices based on Rydberg atoms.