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arXiv:1712.08671 · Journal of Applied Physics

Electromagnetically Induced Transparency (EIT) and Autler-Townes (AT) splitting in the presence of band-limited white Gaussian noise

Matthew T. Simons, Marcus D. Kautz, Christopher L. Holloway, David A. Anderson, Georg A. Raithel, Daniel Stack, Marc C. St. John, Wansheng Su

Published May 28, 2018• 50 citations
arXivHTMLPDF

Abstract

We investigate the effect of band-limited white Gaussian noise (BLWGN) on electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting, when performing atom-based continuous-wave (CW) radio-frequency (RF) electric (E) field strength measurements with Rydberg atoms in an atomic vapor. This EIT/AT-based E-field measurement approach is currently being investigated by several groups around the world as a means to develop a new International System of Units traceable RF E-field measurement technique. For this to be a useful technique, it is important to understand the influence of BLWGN. We perform EIT/AT based E-field experiments with BLWGN centered on the RF transition frequency and for the BLWGN blue-shifted and red-shifted relative to the RF transition frequency. The EIT signal can be severely distorted for certain noise conditions (bandwidth, center frequency, and noise power), hence altering the ability to accurately measure a CW RF E-field strength. We present a model to predict the line shifts and broadenings in the EIT signal in the presence of noise. This model includes AC Stark shifts and on resonance transitions associated with the noise source. The results of this model are compared to the experimental data, and we find very good agreement between the two.

DOI
10.1063/1.5020173

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We investigate the relationship between the Rabi frequency (ΩRF, 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 cold- to 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 ΩRF.
In this work, we demonstrate an approach for improved sensitivity in weak radio frequency (RF) electric-field strength measurements using Rydberg electromagnetically induced transparency (EIT) in an atomic vapor. This is accomplished by varying the RF frequency around a resonant atomic transition and extrapolating the weak on-resonant field strength from the resulting off-resonant Autler-Townes (AT) splittings. This measurement remains directly traceable to SI compared to previous techniques, precluding any knowledge of experimental parameters such as optical beam powers as is the case when using the curvature of the EIT line shape to measure weak fields. We use this approach to measure weak RF fields at 182 GHz and 208 GHz demonstrating improvement greater than a factor of 2 in the measurement sensitivity compared to on-resonant AT splitting RF electric field measurements.
Abstract We utilize an electromagnetically induced transparency (EIT) of a three-level cascade system involving Rydberg state in a room-temperature cell, formed with a cesium 6S1/2–6P3/2–66S1/2 scheme, to investigate the Autler–Townes (AT) splitting resulting from a 15.21-GHz radio-frequency (RF) field that couples the | 66 S 1 / 2 〉 → | 65 P 1 / 2 〉 Rydberg transition. The radio-frequency electric field induced AT splitting, γ AT, is defined as the peak-to-peak distance of an EIT-AT spectrum. The dependence of AT splitting γ AT on the probe and coupling Rabi frequency, Ωp and Ωc, is investigated. It is found that the EIT-AT splitting strongly depends on the EIT linewidth that is related to the probe and coupling Rabi frequency in a weak RF-field regime. Using a narrow linewidth EIT spectrum would decrease the uncertainty of the RF field measurements. This work provides new experimental evidence for the theoretical framework in [J. Appl. Phys. 121, 233106 (2017)].
Magnetic-field-induced splitting of Rydberg Electromagnetically Induced Transparency (EIT) and Autler-Townes (AT) spectra in 87^{87}87Rb vapor cell
We theoretically and experimentally investigate the Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting of 87^{87}87Rb vapor under the combined influence of a magnetic field and a microwave field. In the presence of static magnetic field, the effect of the microwave field leads to the dressing and splitting of each mFm_FmF​ state, resulting in multiple spectral peaks in the EIT-AT spectrum. A simplified analytical formula was developed to explain the EIT-AT spectrum in a static magnetic field, and the calculations are in excellent agreement with experimental results.We further studied the enhancement of the Rydberg atom microwave electric field sensor performance by making use of the splitting interval between the two maximum absolute mFm_FmF​ states under static magnetic field. The traceable measurement limit of weak electric field by EIT-AT splitting method was extended by an order of magnitude, which is promising for precise microwave electric field measurement.
We present a technique for measuring radio-frequency (RF) electric field strengths with sub-wavelength 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-terahertz regime.
We investigate the effects of spatially non-uniform radio-frequency electric (E) field amplitudes on the spectral line shapes of electromagnetically induced transparency (EIT) signals in Rydberg atomic systems used in electrometry (i.e., the metrology of E-field strengths). Spatially non-uniform fields distort the EIT spectra from that of an ideal case, and understanding this distortion is important in the development of Rydberg atom-based sensors, as these distortions can limit accuracy and sensitivity. To characterize this distortion, we present a model that approximates the atom vapor as multi-layered media and then uses Beer’s law to combine the absorption through its many discrete thin segments. We present a set of expected line distortions caused by various RF electric-field distributions found in practice. This provides an intuitive diagnostic tool for experiments. We compare this model to measured experimental atomic spectra in both two-photon and three-photon excitation schemes in the presence of non-uniform radio-frequency fields. We show that we can accurately model and reproduce the EIT lineshape distortion observed in these experimental data.