Data from: Approaching the standard quantum limit of a Rydberg-atom microwave electrometer
Data files
Nov 14, 2024 version files 152.09 KB
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Dataset.zip
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README.md
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Abstract
The development of a microwave electrometer with inherent uncertainty approaching its ultimate limit carries both fundamental and technological significance. However, due to the thermal motion of atoms, the state-of-the-art Rydberg electrometer falls considerably short of the standard quantum limit by about three orders of magnitude. Here, we utilize an optically thin medium with approximately 5.2Γ105 laser-cooled atoms to implement the microwave heterodyne detection. By mitigating various noises and strategically optimizing the electrometer parameters, our study reduces the equivalent noise temperature by a factor of 20 and achieves an electric-field sensitivity of 10.0nVcm-1Hz-1/2, finally reaching a factor of 2.6 above the standard quantum limit. Our work also provides valuable insights into the inherent capabilities and limitations of Rydberg electrometers, offering superior sensitivity in detecting weak microwave signals for numerous applications.
README: Approaching the standard quantum limit of a Rydberg-atom microwave electrometer
https://doi.org/10.5061/dryad.sbcc2frgx
Description of the data and file structure
The photovoltage is recorded by a digital acquisition oscilloscope (R&S RTE1024), and the amplitude spectral density for MW sensitivity is analysed using a desktop computer. For measurements within the 3-dB bandwidth, an avalanche photodetector (Thorlabs APD130A) with a bandwidth replaces the photodetector. We conduct a discrete Fourier transform (DFT) on the photovoltage to extract the frequency and amplitude data, where a Blackman window is applied in the heterodyne time. The extracted frequency represents the intermediate frequency of the cold Rydberg-atom receiver, whilst the extracted amplitude signifies the strength of the heterodyne signal. In order to correct the amplitude of the windowed signal during the DFT, we utilize the calibration information from the balanced photodetector to determine the noise equivalent voltage (NEV). Once the amplitude correction factor is known, the photovoltage spectral density is accurately determined.
The file Fig3data.xlsx
are Microwave heterodyne detection results data. The four subtables in the file correspond to A, B, C, and D of FIG 3. A: Time traces of the continuous MWs and square-pulsed control lasers. When the signal MW is turned off (upper), a slowly rising DC signal is evident in the probe laser transmission, indicating the decreasing OD of the atomic cloud during the detection period. With the signal MW turned on (lower), the time trace similarly displays an additional oscillation, the peak-to-peak amplitude of which is double that of the heterodyne sensing signal. B: EIT (red circle) and AT-splitting (blue triangle) spectra at a moderate probe power. The profile is measured by scanning the probe frequency within 100πs (24) and the asymmetry results from the atomic heating and free expansion effects. C: Heterodyne signal amplitude versus the MW electric field πΈcal , calibrated with the standard antenna method. The dotted line is the linear fit. D: Sensitivity spectra, normalized to a 1 kHz resolution bandwidth, are measured for the photodetector noise (dark grey curve), the optical readout noise (red curve), and the overall noise when a signal MW at 10 kHz intermediate frequency is turned on (green curve) or turned off (blue curve). The red curve is measured by removing the atomic cloud and maintaining the probe laser beam in the same condition as the overall noise measurement. The black dashed line denotes the photodetector's noise floor level, which assists in calibrating the spectral density of the photovoltage during the DFT process.
The file Fig4data.xlsx
are shot-noise limited sensitivity data. The two subtables in the file correspond to A and B of FIG 4. A: Sensitivity S versus the incident power π0 of the probe beam. The black dotted line represents the PSN limited sensitivity. The inset illustrates the dependence of the measured atom number on π0. B: Sensitivity S against the number of atoms at π0=7.6 πW (the vertical dashed lines in A). The blue curve represents the theoretical prediction according to Eq. (4). The two dotted lines symbolize the single and triple SQL sensitivities, respectively, acquired from Eq. (1). The dashed green line exhibits the πeq =293 K sensitivity constraint Sπ‘β of an optimally functioning half-wave dipole antenna within the same frequency band. The dash-dotted yellow line signifies the sensitivity bound by the thermal background ( πamb =293 K ), correlating to NEFex=3.2 nVcm β1 Hzβ1/2.
The file Subfig3data.xlsx
are energy-level shift and depahsing in an interacting Rydberg ensemble data. The two subtables in the file correspond to B and C of FIG.S3. B: Interaction-induced dephasing rate πΎπ versus the probe Rabi frequency Ξ©π. The solid curve is the theoretical results, and the shaded zone represents the error band generated by the 5% uncertainty of optical depth and the anisotropy of πΆ6 interaction of the pairstate 39D5/2. The probe Rabi frequency of our experiment is indicated with the vertical dotted line. The inset depicts transmission spectrum measured at the optimal point of atomic heterodyne, and the red curve is the fit of experimental data to the approximate susceptibility. C: Dephasing rate πΎπ versus Ξ©π when the different Rydberg states nπ·5/2 are used.
The file Subfig4data.xlsx
are minimum detectable field Emin and bandwidth data. The two subtables in the file correspond to A and B of FIG.S4. A: πΈmin versus the integration time πβ². B: Normalized signal amplitude versus the MW detuning πΏs. The dotted curve is the Lorentz fit, indicating a 3βdB reduction in response at 2.3 MHz.
Methods
This is the main experimental data of this experimental work, including atomic spectral line diagrams, time-domain waveform diagrams captured by an oscilloscope, and spectral density diagrams obtained after digital Fourier transformation. It also includes indirect results such as sensitivity obtained from spectral density, with specific details detailed in the relevant papers. The theoretical simulation results provided in the paper can be calculated based on the calculation conditions and equations given in the article.