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The high-fidelity analysis of many-body quantum states of indistinguishable atoms requires the accurate counting of atoms. Here we report the tomographic reconstruction of an atom-number-resolving detector. The tomography is performed with an ultracold rubidium ensemble that is prepared in a coherent spin state by driving a Rabi coupling between the two hyperfine clock levels. The coupling is followed by counting the occupation number in one level. We characterize the fidelity of our detector and show that a negative-valued Wigner function is associated with it. Our results offer an exciting perspective for the high-fidelity reconstruction of entangled states and can be applied for a future demonstration of Heisenberg-limited atom interferometry.

Frequency stabilized light sources with narrow linewidth are mandatory for atom interferometry based experiments. For compact experiment designs used on space platforms, tunable DFB diode lasers are often used. These lasers combine low energy consumption with small sizes, but lack long-term frequency stability. This paper presents an FPGA based laser frequency stabilization system for highly variable target frequencies using frequency modulated Rb-spectroscopy achieving latencies below 100 μs. The system consists of a DFB laser, a Rb-spectroscopy cell, a laser current controller and an FPGA board with an analog-digital conversion board. The digital part of the frequency stabilization system is a SoC mapped on an FPGA. The SoC consists of a processor, enabling user interaction via network connection, and the dedicated frequency stabilization module. This module consists of a demodulation stage, digital filters, a frequency estimator and a controller. To estimate the frequency, small ramps of the laser frequency are generated using a high-speed DAC connected to the laser current controller. The absorption spectroscopy output of this beam is sampled using a photodiode and a high-speed ADC. After signal conditioning with digital filters, the frequency estimator extracts the present mid-frequency of the laser applying pattern matching with a prerecorded reference spectrum. The frequency controller adjusts the mean laser current based on this estimation. The performance as well as the accuracy of the proposed laser stabilization system and its FPGA resource and power consumption are evaluated.

We report on the sub-kilohertz optical spectroscopy on the 1S0-3P1 intercombination transition in magnesium at 457 nm. The spectroscopic signal is probed by a time domain atom interferometer. The realization of this time domain atom interferometer with laser cooled and trapped atoms allows extremely long interaction times and leads to resolutions down to 491 Hz (FWHM). This corresponds to a high line Q factor of 1.3×1012. Because of the high accuracy in the determination of the line center, applications with respect to an optical frequency standard are possible. © 1998 The American Physical Society.

We report on a frequency measurement of the $(3s^2)^1S_0\to(3s3p)^3P_1$ clock transition of $^{24}$Mg on a thermal atomic beam. The intercombination transition has been referenced to a portable primary Cs frequency standard with the help of a femtosecond fiber laser frequency comb. The achieved uncertainty is $2.5\times10^{-12}$ which corresponds to an increase in accuracy of six orders of magnitude compared to previous results. The measured frequency value permits the calculation of several other optical transitions from $^1S_0$ to the $^3P_J$-level system for $^{24}$Mg, $^{25}$Mg and $^{26}$Mg. We describe in detail the components of our optical frequency standard like the stabilized spectroscopy laser, the atomic beam apparatus used for Ramsey-Bord\'e interferometry and the frequency comb generator and discuss the uncertainty contributions to our measurement including the first and second order Doppler effect. An upper limit of $3\times10^{-13}$ in one second for the short term instability of our optical frequency standard was determined by comparison with a GPS disciplined quartz oscillator., Comment: 8 pages, 8 figures