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In this work, we demonstrate a microwave magnetic field imaging technique based on Rabi resonance with a cesium atom vapor cell. Rabi resonance signals are generated when atoms interact with a phase-modulated microwave (MW) field and are detected by a photodiode and camera. A low noise, high quantum efficiency camera is used to capture a series of frames for different phase modulation frequencies. Rabi frequencies of each spatial point in the field can be measured by scanning the frames. Thus, the strength of the MW magnetic field distribution is obtained by combing the Rabi frequencies, measured with camera pixels in the range of the probe laser beam. The simple architecture of this imaging setup holds great potential for the construction of compact/miniature MW field sensors for material testing, field imaging of MW components, and biomedical imaging., Comment: 11 pages, 6 figures

High-sensitive measurement of radio-frequency (RF) electric field is available via the electromagnetically induced transparency (EIT) effect of Rydberg atom at room-temperature, which has been developed to be a promising atomic RF receiver. In this Letter, we investigate the credibility of the digital communication via this quantum-based antenna over the entire continuously tunable RF-carrier. Our experiment shows that digital communication at a rate of 500 kbps performs reliably within a tunable bandwidth of 200 MHz at carrier 10.22 GHz and a bit error rate (BER) appears out of this range, for example, the BER runs up to 15 % at RF-detuning $\pm150$ MHz. In the measurement, the time-variant RF field is retrieved by detecting the density of the probe laser at the center frequency of RF-induced symmetric or asymmetric Autler-Townes splitting in EIT. Prior to the digital test, we have studied the RF-receiving quality versus the physical ambiance and found that a choice of linear gain response to the RF-amplitude can suppress the signal distortion and the modulating signal is able to be decoded as fast as up to 500 kHz in the tunable bandwidth. Our checkout consolidates the physical foundation for a reliable communication and spectrum sensing over the broadband RF-carrier., Comment: 5 pages, 5 figures

We experimentally investigated Rabi resonance-based continuously frequency-tunable microwave (MW) magnetic field detection using a single hybrid vapor cell filled with cesium and rubidium atoms. The multispecies atomic systems, with their tunable abilities in transition frequencies, enabled this atomic sensing head to cover a broader detectable MW field scope compared to the use of a single metal atom. Here, we demonstrated the simultaneous observation of atomic Rabi resonance signals with 85Rb, 87Rb, and 133Cs in the same vapor cell. Using an experimentally feasible static magnetic field (DC field) below 500 Gauss, we realized a MW magnetic field strength detection with bandwidths of 4.8 GHz around 8.1 GHz. The use of these three atomic systems confined in a single vapor cell also enabled the establishment of an identical MW field with the help of DC field, allowing us to perform a perfect comparison for different applications that require the same electromagnetic environment. The results may be useful for the realization and application of many atomic detectors based on different physical principles., Comment: 10 pages, 7 figures

In the electronic measurement of the Boltzmann constant based on Johnson noise thermometry, the ratio of the power spectral densities of thermal noise across a resistor at the triple point of water, and pseudo-random noise synthetically generated by a quantum-accurate voltage-noise source is constant to within 1 part in a billion for frequencies up to 1 GHz. Given this ratio, and the values of other known or measured parameters, one can determine the Boltzmann constant. Due, in part, to mismatch between transmission lines, the experimental ratio spectrum varies with frequency. We model this spectrum as an even polynomial function of frequency where the constant term in the polynomial determines the Boltzmann constant. When determining this constant (offset) from experimental data, the assumed complexity of the ratio spectrum model and the maximum frequency analyzed (fitting bandwidth) dramatically affects results. We select the complexity of the model by cross-validation. For each of many fitting bandwidths, we determine the component of uncertainty of the offset term that accounts for random and systematic effects associated with imperfect knowledge of model complexity. We select the fitting bandwidth that minimizes this uncertainty. In the most recent measurement of the Boltzmann constant, results were determined, in part, by application of an earlier version of the method described here. Here, we extend the earlier analysis by considering a broader range of fitting bandwidths and quantify an additional component of uncertainty that accounts for imperfect performance of our fitting bandwidth selection method. For idealized simulated data our method correctly selects the true complexity of the ratio spectrum model for all cases considered. A new analysis of data from the recent experiment yields evidence for a temporal trend in the offset parameters., Comment: 25 pages, 8 figures. New version has a modified abstract, added text in Introduction, new entries in Table 5, additional references, and a new title. The main technical results are unchanged

The unit of thermodynamic temperature, the kelvin, will be redefined in 2018 by fixing the value of the Boltzmann constant, k. The present CODATA recommended value of k is determined predominantly by acoustic gas-thermometry results. To provide a value of k based on different physical principles, purely electronic measurements of k were performed by using a Johnson noise thermometer to compare the thermal noise power of a 200 Ohm sensing resistor immersed in a triple-point-of-water cell to the noise power of a quantum-accurate pseudo-random noise waveform of nominally equal noise power. Measurements integrated over a bandwidth of 550 kHz and a total integration time of 33 days gave a measured value of k = 1.3806514(48)x10^-23 J/K, for which the relative standard uncertainty is 3.5x10^-6 and the relative offset from the CODATA 2010 value is +1.9x10^-6., Comment: 20 pages, 9 figures

The Boltzmann constant was measured by comparing the Johnson noise of a resistor at the triple point of water with a quantum-based voltage reference signal generated with a superconducting Josephson-junction waveform synthesizer. The measured value of k = 1.380651(18) \times 10^-23 J/K is consistent with the current CODATA value and the combined uncertainties. This is our first measurement of k with this electronic technique, and the first noise thermometry measurement to achieve a relative combined uncertainty of 13 parts in 10^6. We describe the most recent improvements to our Johnson Noise Thermometer that enabled the statistical uncertainty contribution to be reduced to seven parts in 10^6, as well as the further reduction of spurious systematic errors and EMI effects. The uncertainty budget for this measurement is discussed in detail., Comment: 23 pages, 7 figures