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arXiv:1601.02535 · Physical Review Applied

Optical Measurements of Strong Microwave Fields with Rydberg Atoms in a Vapor Cell

D. A. Anderson, S. A. Miller, Georg A. Raithel, J. A. Gordon, M. L. Butler, C. L. Holloway

Published Mar 4, 2016• 161 citations
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Abstract

Even in this day and age, precise absolute measurement of electric fields is not trivial. The authors extend quantum sensing via cold atoms and electromagnetically induced transparency to the strong-field regime. In this regime, existing techniques are insufficient due to the complex and highly nonlinear response of the atoms. This is an essential step toward calibration-free rf electric-field sensors for a wide range of applications that include antenna calibration, metamaterial characterization, and subwavelength imaging.

DOI
10.1103/physrevapplied.5.034003

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Even in this day and age, precise absolute measurement of electric fields is not trivial. The authors extend quantum sensing via cold atoms and electromagnetically induced transparency to the strong-field regime. In this regime, existing techniques are insufficient due to the complex and highly nonlinear response of the atoms. This is an essential step toward calibration-free rf electric-field sensors for a wide range of applications that include antenna calibration, metamaterial characterization, and subwavelength imaging.
Atoms form the basis of precise measurement for many quantities (time, acceleration, rotation, magnetic field, etc.). Measurements of microwave frequency electric fields by traditional methods (i.e. engineered antennas) have limited sensitivity and can be difficult to calibrate properly. Highly-excited (Rydberg) neutral atoms have very large electric-dipole moments and many dipole allowed transitions in the range of 1 - 500 GHz. It is possible to sensitively probe the electric field in this range using the combination of two quantum interference phenomena: electromagnetically induced transparency and the Autler-Townes effect. This technique allows for very sensitive field amplitude, polarization, and sub-wavelength imaging measurements. These quantities can be extracted by measuring properties of a probe laser beam as it passes through a warm rubidium vapor cell. Thus far, Rydberg microwave electrometry has relied upon the absorption of the probe laser. We report on our use of polarization rotation, which corresponds to the real part of the susceptibility, for measuring the properties of microwave frequency electric fields. Our simulations show that when a magnetic field is present and directed along the optical propagation direction a polarization rotation signal exists and can be used for microwave electrometry. One central advantage in using the polarization rotation signal rather than the absorption signal is that common mode laser noise is naturally eliminated leading to a potentially dramatic increase in signal-to-noise ratio.
We study Rydberg atoms modulated by strong radio-frequency (rf) fields with a frequency of 70 MHz. The Rydberg atoms are prepared in a room-temperature cesium cell, and their level structure is probed using electromagnetically induced transparency (EIT). As the rf field increases from the weak- into the strong-field regime, the range of observed rf-induced phenomena progresses from ac level shifts through increasingly pronounced and numerous rf modulation sidebands to complex state mixing and level crossings with $\mathrm{high}\ensuremath{-}l$ hydrogenlike states. Weak anharmonic admixtures in the rf field generate clearly visible modifications in the Rydberg EIT spectra. A Floquet analysis is employed to model the Rydberg spectra, and good agreement with the experimental observations is found. Our results show that all-optical spectroscopy of Rydberg atoms in vapor cells can serve as an antenna-free, atom-based, and calibration-free technique to measure rf electric fields and to analyze their higher-harmonic contents.
We have recently shown [Nat. Phys.8, 819 (2012)] that Alkali atoms contained in a vapor cell can serve as a highly accurate standard for microwave (MW) electric field strength as well as polarization. Here we show for the first time that Rydberg atom electromagnetically induced transparency can be used to image MW electric fields with unprecedented precision. The spatial resolution of the method is far into the subwavelength regime ∼λ/650 or 66 μm at 6.9 GHz. The electric field resolutions are similar to those we have already demonstrated ∼50 μV cm(-1). Our experimental results agree with finite element calculations of test electric-field patterns.
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.
An atom-based approach is presented to detect absolute microwave (MW) electric fields (E-fields). The approach uses Rydberg atoms in vapor cells at room temperature. The MW E-field measurements utilize a bright resonance prepared within an electromagnetically induced transparency (EIT) window. The large transition dipole moments between energetically adjacent Rydberg states enable this method to make traceable E-field measurements with a sensitivity that is several orders of magnitude higher than the current standard for MW E-field measurements. The method can be used to image MW E-field in the near field regime with a subwavelength resolution of mathrmlambdaMW/650\\mathrm{\\lambda_{MW}/650}mathrmlambdaMW​/650, where mathrmlambdaMW\\mathrm{\\lambda_{MW}}mathrmlambdaMW​ is the wavelength of the MW E-field. A high accuracy of $\\mathrm{1\\%}$ has been reached by minimizing the effects of the vapor cell geometry on the measured MW E-field. The dissertation also presents an alternative technique to perform the MW E-field measurement using dispersive properties of the EIT spectrum with a prism vapor cell. Recently, we applied a homodyne detection technique with a Mach Zehnder interferometer to achieve a new sensitivity limit for the MW E-field measurement, mathrmsim3 muVcm−1Hz−1/2\\mathrm{\\sim3~\\mu Vcm^{-1}Hz^{-1/2}}mathrmsim3 muVcm−1Hz−1/2. The new sensitivity is one order of magnitude better than our prior best sensitivity presented in Ref. [Nat. Phys. 8, 819 (2012)]. The Rydberg atom-based method is promising to be a new standard for MW E-field measurements and to develop into portable devices in the field of MW technologies.
We discuss a fundamentally new method for electric (E) field strength (V/m) metrology applicable to the near-field. This new approach is significantly different from currently used field measurement techniques in that it is based on the interaction of radio-frequency (RF) E-fields with Rydberg atoms (alkali atoms placed in a glass vapor cell that are excited optically to Rydberg states). The applied RF E-field alters the state of the atoms. The Rydberg atoms act like an RF-to-optical transducer, converting an RF E-field strength to an optical-frequency response. In this new approach, we employ the phenomena of electromagnetically induced transparency (EIT) and Autler-Townes splitting. The RF transition in the four-level atomic system causes a split of the EIT transmission spectrum of a probe laser into two peaks. This splitting is easily measured and is directly proportional to the applied RF E-field amplitude. The significant dipole response of Rydberg atoms enables this technique to make self-calibrating measurements over a large frequency band including 500 MHz to 500 GHz (and possibly up to 1 THz and down to 10s of megahertz). In this paper, we report on our results in the development of this metrology approach, including the first fiber-coupled vapor-cell for E-field measurements. We also discuss key applications, including self-calibrated measurements, millimeter-wave and sub-THz measurements, field mapping, and sub-wavelength and near-field imaging. We show results for mapping the fields inside vapor cells, for measuring the E-field distribution along the surface of a circuit board, and for measuring the near-field at the aperture in a cavity. We also discuss the uncertainties of this measurement technique.