# Lifetime Measurement of Cesium Atoms Using a Cold Rydberg Gas
## 2 Experimental Setup  
Experiments are performed in a standard MOT by the laser cooling and trapping technology with a temperature of \(\sim\)100 \(\upmu\)K and a density of \(\sim\)10\({}^{10}\) cm\({}^{-3}\). The MOT density is measured with the shadow imaging technique. Figure 1a shows the schematic diagram of the experiments. Two-photon scheme, see Figure 1b, is employed to excite MOT atoms to Rydberg states. The first photon, 852 nm laser (Toptica DLpro), and the second photon, 510 nm laser (Toptica DLpro + Precilasers YFL-SHG-509-1.5), are counter propagated through the MOT center. The waists of the 852 nm and 510 nm lasers at MOT center are 80 and 40 \(\upmu\)m, respectively, which forms a cylindrical excitation volume. The frequency of the 852 nm laser is locked on the \(|6S_{1/2},F=4\rangle(|g\rangle)\rightarrow|6P_{3/2},F^{\prime}=5\rangle(|e\rangle)\) transition with a polarization spectroscopy, and then \(\delta=360\) MHz blue-detuned from the intermediate \(|6P_{3/2}\rangle\) state by a double-passed acousto-optic modulator (AOM). The 510 nm laser is produced by frequency doubling of a 1020 nm laser with the frequency locked to an ultra-stable Fabry-Perot (F-P) cavity with a finesse of 15,000 employing Pound-Drever-Hall (PDH) method [17; 18; 19; 20]. The frequency, monitored by a wavelength meter (HighFinesse-Angstrom WS-U), then is tuned to the \(nS/nD\) Rydberg transition by varying the radio-frequency signal applied to the electro-optic modulator (EOM) that is used to lock the laser to the F-P cavity. Figure 1: (Color online) **(a)** The schematic diagram of the experiment. Cesium atoms are trapped in the MOT center and excited to the Rydberg state employing a two-photon excitation. The first-photon 852 nm and the second-photon 510 nm lasers are counter propagated and overlapped at the MOT center. The excited Rydberg atoms are ionized with a ramped electric field and detected with a microchannel plate (MCP) detector. Three pairs of grids are placed on either side of the MOT (the other two pairs do not show here) that can be used to apply potential for ionizing Rydberg atom or compensating a stray electric field. **(b)** The level diagram of two-photon excitation of Rydberg state. The first photon drives the lower transition \(|g\rangle\rightarrow|e\rangle\), while the second photon couples the up transition \(|e\rangle\rightarrow|r\rangle\). The single photon detuning from the intermediate state is \(\delta=360\) MHz. **(c)** A timing diagram for the excitation and the detection of Rydberg atoms. After Rydberg excitation and a variable delay time \(t_{D}\), a ramp electric field with 3 \(\upmu\)s rising time is applied for ionizing Rydberg atoms. There are three pairs of grids placed either side of the MOT in three directions, (only one pair of grids in the \(y\)-direction shown in Figure 1a), that are used to apply the potential for compensating the stray field and ionization of the Rydberg atoms. After compensating, the related stray field around the MOT is expected to be less than 30 mVcm\({}^{-1}\) measured with the Stark spectroscopy of the 70\(D_{5/2}\) state [21]. After the Rydberg excitation, we apply a ramped electric field of 3-\(\upmu\)s rise time to one grid to ionize Rydberg atoms and drive resultant ions onto a microchannel plate (MCP) detector located behind one of the grids. To obtain the evolution of Rydberg populations, we apply a variable delay time \(t_{D}\) before the ramp ionization field, see the timing of Figure 1c. The Rydberg ions are analyzed by a boxcar integrator (SRS-250) and recorded with a computer. Before the lifetime measurement, we calibrate the MCP ions detection system with two shadow images taken before and after the Rydberg excitation. The Rydberg number and the gain factor, \(G\), of our MCP detection are extracted from the difference of two shadow images.