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Physical Review A

Measuring spatially extended density profiles using atom-cavity collective strong coupling to higher-order modes

M. Niranjan, Sourav Dutta, Tridib Ray, S. A. Rangwala

Published Mar 22, 2019• 5 citations
Publisher

Abstract

The collective strong coupling of rubidium atoms in a magneto-optical trap (MOT) to the Laguerre-Gaussian (LG) modes of a Fabry-P\'erot cavity is investigated. Bright and dark $^{85}\mathrm{Rb}$ MOT atoms are prepared at the geometric center of the cavity, and the vacuum Rabi splitting (VRS) of the collectively coupled atom-cavity system is measured for ${\mathrm{LG}}_{l0}$ ($l=0,1,2,3$) modes. The atom number coupled to the cavity mode depends on the overlap of the atomic density distribution and the specific spatial mode function, which is reflected in the measured VRS spectrum. The known mode function and the measured VRS can then be used to test whether the atomic density distribution in the experiment is Gaussian or uniform. A simple theoretical model for this process is described, and the experimental measurements are found to be in close agreement with the model.

DOI
10.1103/physreva.99.033617

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The collective strong coupling of rubidium atoms in a magneto-optical trap (MOT) to the Laguerre-Gaussian (LG) modes of a Fabry-P'erot cavity is investigated. Bright and dark 85Rb^{85}\mathrm{Rb}85Rb MOT atoms are prepared at the geometric center of the cavity, and the vacuum Rabi splitting (VRS) of the collectively coupled atom-cavity system is measured for LGl0{\mathrm{LG}}_{l0}LGl0​ (l=0,1,2,3l=0,1,2,3l=0,1,2,3) modes. The atom number coupled to the cavity mode depends on the overlap of the atomic density distribution and the specific spatial mode function, which is reflected in the measured VRS spectrum. The known mode function and the measured VRS can then be used to test whether the atomic density distribution in the experiment is Gaussian or uniform. A simple theoretical model for this process is described, and the experimental measurements are found to be in close agreement with the model.
The photoassociation (PA) of a rubidium dimer in a dark magneto-optical trap (MOT) is studied using atom-cavity collective strong coupling. This allows nondestructive detection of the molecule formation process as well as rapid and repeated interrogation of the atom-molecule system. The vacuum Rabi splitting (VRS) measurements from the bright MOT are carefully calibrated against equivalent measurements with fluorescence. Further loading rates in the dark MOT are determined using VRS. This method provides a reliable, fast, and nondestructive detection scheme for detecting the PA using the free atoms coupled to a cavity when the atoms are in a nonfluorescing state.
The photoassociation (PA) of rubidium dimer (Rb2) in a dark magneto-optic trap (MOT) is studied using atom-cavity collective strong coupling. This allows non-destructive detection of the molecule formation process as well as rapid and repeated interrogation of the atom-molecule system. The vacuum Rabi splitting (VRS) measurements from the bright MOT are carefully calibrated against equivalent measurements with fluorescence. Further loading rates in dark MOT are determined using VRS. This method provides a reliable, fast, and non-destructive detection scheme for ultracold molecules when the atoms are non-fluorescing using the free atoms coupled to a cavity.
We laser cool rubidium atoms to form a magneto-optical trap, within a Fabry-Perot cavity, and demonstrate strong coupling of the cold atoms to the cavity. The coupling strength is measured using the vacuum Rabi frequency splitting (VRS) of transmitted, cavity-coupled light on atomic resonance. The VRS is measured for two- and three-level atomic systems and the atom-cavity-coupling strength for each system is determined. By allowing the laser-cooled atoms to expand for different times and measuring the corresponding VRS, we determine the number of atoms overlapped with the cavity mode as a function of time. This time-of-flight of atoms from the cavity permits the measurement of the temperature of the laser-cooled atoms. Finally, the need for this technique and its utility is discussed.
We present a technique, based on atoms coupled to an optical cavity, for nondestructive detection of trapped ions. We demonstrate the vacuum-Rabi splitting (VRS), arising from collective strong coupling of ultracold Rb atoms and a cavity, to change in the presence of trapped Rb+\mathrm{R}{\mathrm{b}}^{+}Rb+ ions. The Rb+\mathrm{R}{\mathrm{b}}^{+}Rb+ ions are optically dark and the Rb atoms are prepared in a dark magneto-optical trap. The VRS is measured on an optically open transition of the initially dark Rb atoms. The measurement itself is fast, nondestructive, and has sufficient fidelity to permit the measurement of the atomic-state-selective ion-atom collision rate. This demonstration illustrates a method based on atom-cavity coupling to measure two-particle interactions generically and nondestructively.
A coupled quantum system composed of cavity field and atoms is one of the main research contents of cavity quantum electrodynamics. It can be used to realize single atom manipulation and measurement, and has important significance for studying the interaction between light and the atom, preparing quantum states and quantum entanglement. Current research work mainly focuses on two aspects. One is to achieve the atom trapping via the feedback control of the trapping laser intensity. The other is to measure the single atomic motion in a Fabry-Perot cavity by using Hermite-Gaussian transverse modes. The detection of the atomic trajectories has been realized via the observation of transmission spectra of the strong coupling system composed of cold atoms and Hermite-Gaussian transverse modes in a Fabry-Perot cavity. In order to observe the atomic motion trajectories in the cavity, we theoretically study the transmission spectrum of a strong coupling system composed of cold atoms and Laguerre-Gaussian transverse modes in a Fabry-Perot cavity in this paper. We calculate the relationship between the coupling coefficient and the mode number of Laguerre-Gaussian transverse modes. The result shows that with the increase of Laguerre-Gaussian transverse mode number, the maximum coupling coefficient between the atoms and cavity fields is almost unchanged, so the contrast of the detected spectrum is nearly independent of the mode number. Analysis shows that Laguerre-Gaussian transverse mode provides more abundant information about atomic motion trajectory than Hermite-Gaussian transverse mode. The field distribution of Laguerre-Gaussian transverse mode is ring-shaped. Owing to the ring shape, the atoms dropped at different positions experience different electric field intensities, and the detected transmission spectra are changed. Therefore, we can implement the high precision distinguishment of the atomic trajectories by observing the features of the transmission spectra such as the number of the transmission peaks and their positions. Furthermore, a small deviation of the atomic motion trajectories, on the edges of the rings of the electric field, may induce great change in transmission spectrum, and then we can very accurately detect the atomic motion around these positions.
We experimentally demonstrate collective strong coupling, optical bi-stability (OB), and all-optical switching in a system consisting of ultracold 85Rb atoms, trapped in a dark magneto-optical trap (DMOT), and coupled to an optical Fabry-Perot cavity. The strong coupling is established by measuring the vacuum Rabi splitting (VRS) of a weak on-axis probe beam. The dependence of VRS on the probe beam power is measured, and bi-stability in the cavity transmission is observed. We demonstrate control over the transmission of the probe beam through the atom-cavity system using a free-space off-axis control beam and show that the cavity transmission can be switched on and off in micro-second timescales using micro-Watt control powers. The utility of the system as a tool for sensitive, in-situ and rapid measurements is envisaged.