Intracavity Rydberg-atom electromagnetically induced transparency using a high-finesse optical cavity

We present an experimental study of cavity-assisted Rydberg-atom electromagnetically induced transparency (EIT) using a high-finesse optical cavity ($F\sim 28000$). Rydberg atoms are excited via a two-photon transition in a ladder-type EIT configuration. A three-peak structure of the cavity transmission spectrum is observed when Rydberg EIT is generated inside the cavity. The two symmetrically spaced side peaks are caused by bright-state polaritons, while the central peak corresponds to a dark-state polariton. Anticrossing phenomena and the effects of mirror adsorbate electric fields are studied under different experimental conditions. We determine a lower bound on the coherence time for the system of $7.26\pm 0.06\mu \mathrm{s}$, most likely limited by laser dephasing. The cavity-Rydberg EIT system can be useful for single-photon generation using the Rydberg blockade effect, studying many-body physics, and generating novel quantum states among many other applications.

Figure 1

(a) The energy-level diagram of ${}^{87}\mathrm{Rb}$ atoms used for Rydberg EIT. (b) Schematic of the experimental setup. The atoms are transported into the high-finesse cavity from a magneto-optical trap using a single-beam optical dipole trap controlled by a focus-tunable lens.

Figure 2

(a) Plot of the dispersion, ${\omega }_p(l/2L){\chi }^{\prime }$, and absorption, ${\omega }_p(l/2L){\chi }^{\prime \prime }$, as in Eq. (8), versus probe detuning, ${\mathrm{\Delta }}_p/2\pi$. The susceptibility is given in Eq. (7). The crossings between the dispersion curve and detuning, $-\mathrm{\Delta }$, are where peaks in the cavity transmission occur. There are five crossing points which yield transmission peaks. (b) An example cavity transmission spectrum as a function of probe detuning using Eq. (8). Only three peaks are observed because the two that would occur closest to the center peak suffer large absorption as shown in (a).

Figure 3

(a) Setup of the lens system for the dipole trap. The middle lens is a focus-tunable lens, which has a focal tuning range of 90–160 mm, controlled by an applied current. (b)–(d) Fluorescence images that show the process of the atoms moving into the cavity.

Figure 4

Measured cavity transmission versus probe laser detuning. The thick black line is the experimental data. The thin red line is the theory corresponding to Eq. (8) of the text. The data are the average of 30 traces. ${\mathrm{\Omega }}_p/2\pi =9.1$ MHz. (a) Empty cavity. (b) Two-level atoms, i.e., ${\mathrm{\Omega }}_c=0$ MHz. (c) Rydberg EIT for the $35S_{1/2}$ Rydberg state, ${\mathrm{\Omega }}_c/2\pi =4.1$ MHz. There are $\sim 25$ atoms in the interaction region in the cavity. ${\mathrm{\Gamma }}_3=53$ kHz, which is the decay rate of $35S_{1/2}$ including blackbody decay. ${\mathrm{\Gamma }}_2=6$ MHz. There are no free parameters for the fit. There is some instrumental broadening in these traces caused by the averaging and the signal integration. The trap density in the cavity is $\sim 8\times {10}^8{\mathrm{cm}}^{-3}$.

Figure 5

(a) The positions of the cavity transmission peaks as a function of cavity detuning, ${\mathrm{\Delta }}_{\text{cav}}/2\pi$, for the $35S_{1/2}$ Rydberg state. The solid lines are the peak centers calculated from Eq. (8). The error bar is the shot-to-shot peak fluctuation observed in this experiment. (b) The cavity transmission spectra for different cavity detunings as a function of probe laser detuning. ${\mathrm{\Delta }}_c=0$. The parameters are the same as in Fig. 4.

Figure 6

(a) The positions of the cavity transmission peaks as a function of coupling laser detuning, ${\mathrm{\Delta }}_c/2\pi$, for the $35S_{1/2}$ Rydberg state. The solid lines are the peak centers calculated from Eq. (8). The error bar is the shot-to-shot peak fluctuation observed in this experiment. (b) The cavity transmission spectra for different coupling detunings as a function of probe laser detuning. ${\mathrm{\Delta }}_{\text{cav}}=0$. The parameters are the same as in Fig. 4.

Figure 7

A sketch of the electric field inside our cavity as described in the text.

Figure 8

A cavity transmission peak corresponding to a dark-state polariton formed on the $5S_{1/2}(m_F=0)\to 5P_{3/2}\to 35S_{1/2}(m_F=0)$ transition. The linewidth is $138\pm 1$ kHz. The linewidth corresponds to a coherence time of $7.26\pm 0.06\mu \mathrm{s}$. The data were taken using the $35S_{1/2}$ Rydberg state. The probe and coupling Rabi frequencies were ${\mathrm{\Omega }}_p/2\pi =1.2$ MHz and ${\mathrm{\Omega }}_c/2\pi =5.2$ MHz, respectively. There were approximately 50 atoms in the interaction region of the cavity. The solid red line is a fit to a Lorentzian. The solid black line is the experimental data. A magnetic field of $\sim 3$.6 G was applied with a single coil and used for the measurement. The atomic sample was located on the symmetry axis of the coil. The trap density in the cavity is $\sim 1.5\times {10}^9{\mathrm{cm}}^{-3}$. The external, applied magnetic field was only used in obtaining this figure in the paper.