Nondestructive detection of Rydberg atoms by dispersive shift measurements on a rectangular waveguide cavity

In the last decades the interest in studying interactions of Rydberg atoms or ensembles thereof with electromagnetic fields at optical and microwave frequencies has steadily increased. The physics Nobel prize of 2012, for instance, has been partially awarded to cavity quantum electrodynamics (QED) experiments with single Rydberg atoms that allow for quantum nondemolition measurements of the photon number in a superconducting microwave cavity. These experiments detect the dispersive shift of the atomic transition frequency that results from the interaction with the photons to measure the photon number nondestructively. In this thesis, we employ the reversed effect, the dispersive shift of the resonance frequency of the TE301 mode of a rectangular microwave cavity induced an ensemble of helium Rydberg atoms, to perform nondestructive measurements of the atom number. In a first experiment, we measure the dispersive interaction between a few thousand atoms in the 36s singlet state and a copper cavity with a quality factor of about Q = 5 · 10^3. We detect the dispersive shift by continuously measuring the changes in cavity transmission with a weak coherent probe tone that injects a few hundred photons into the cavity. We model the observed time dependence of the dispersive shift, which results from the interplay between the time-dependent collective interaction strength and atom-cavity detuning. Controlling the parameters of the atom cloud, we then directly measure the dependence of the dispersive shift on the atom-cavity detuning and on the number of Rydberg atoms. The results are in good agreement with the Tavis-Cummings Hamiltonian in the dispersive regime, and indicate collective coupling strengths of gN/2pi = 1 MHz, which correspond to more than N = 3 · 10^3 Rydberg atoms. This nondestructive detection of Rydberg atoms achieves a relative precision of 4.5% and an accuracy of 20 %, which are both limited by the inhomogeneity of the atom-cavity detuning over the size of the atom cloud. In a second experiment, we reduce the inhomogeneity by decreasing the size of the atomic cloud and employing the triplet Rydberg transition at n = 42, which is less sensitive to dc electric fields. The precision of the atom number detection is further enhanced by increasing the cavity quality factor to Q = 10^5 with a superconducting niobium cavity. The combined improvements result in the nondestructive detection of a few hundred Rydberg atoms with an accuracy of 3% and a precision of 1 %, which is an order of magnitude improvement over the previous experiment. Motivated by these results obtained from averaging over about 4 × 10^4 repetitions of the experiment, we consider the nondestructive detection of the atom number in single-shot measurements with a high number of photons in the cavity. By studying the dispersive shift and the probability to excite the 42p states as functions of the photon number, we find a critical photon number ncrit = 4.4×10^4 close to the estimated value and verify that the excitation probability remains below 2.2% for all photon numbers. For optimal precision, we then use a photon number close to the critical value and perform single-shot measurements of the atom number that show a linear correlation between the results of the nondestructive detection method using the dispersive shift and the destructive detection with a microchannel plate. We achieve a single-shot uncertainty of delta N = 65 in the nondestructive atom number detection, which is close to the width of a Poissonian distribution square-root(N) = 25 for the highest atom numbers N = 600. We estimate that the precision in the single-shot measurements can be further enhanced to delta N = 5 (delta N/N = 1 %) by using quantum-limited amplifiers and increasing the single-shot integration time with Stark deceleration of the Rydberg atoms. Such precise nondestructive single-shot measurements of the number of Rydberg atoms are relevant for the quantitative evaluation of scattering cross-sections in experiments with Rydberg atoms and molecules. Moreover, the demonstrated collective coupling strengths open up the prospect for hybrid cavity QED with Rydberg atoms and superconducting quantum bits in rectangular waveguide cavities