Collective light shifts of many longitudinal cavity modes induced by coupling to a cold-atom ensemble

Abstract

We experimentally study the interaction between a cold atom cloud and many longitudinal modes of a high quality Fabry-Perot cavity, by measuring signatures of collective light shifts in the cavity transmission spectrum of an optical frequency comb probe. Using a resonator coupled to more than $10^5$ intracavity atoms, we detect significant shifts of $\sim 100$ cavity modes simultaneously, which is a direct manifestation of physics beyond the hitherto explored regime of cavity-cold atom interaction with only single or few longitudinal modes at a time. For the cavity mode closest to the atomic resonance, we demonstrate a bistability in the transmission spectrum, arising due to a combined coupling of the cloud to an external pump laser and a cavity mode probed by the optical frequency comb. These results establish a platform for deeper exploration of multifrequency cavity quantum electrodynamics, where ultrashort pulsed sources can be used for optical manipulation, cooling and entanglement of cold atoms in a resonator.

Figures (8)

• Figure 1: Detecting collective light shifts of many cavity modes using an optical frequency comb (OFC). (a) Illustration of the experimental setup with cold atoms inside a linear cavity. Cavity transmission of an OFC beam is measured using an optical spectrum analyzer. (b) Measurement results for an empty cavity (golden dashed line) and with atoms present (red solid line), under the condition of the $\nu_1$ comb line shifted by $\Delta f_0=-200$ kHz from its nearest bare-cavity mode $\nu_c^{(1)}$. The dispersive atom-cavity interaction detunes the bare cavity mode frequencies by the collective atomic light shift $u_{m}$ (see text), enhancing transmission on the red side and suppressing it on the blue side of the atomic resonance. Inset: sketch of the frequencies and resonances in the system, for the cavity frequencies nearest to the atomic resonance $\nu_a$ for an empty cavity (dashed lines, $\nu_c^{(m)}$) and with atoms present (blue curves), with OFC modes at frequencies (solid lines, $\nu_m$).
• Figure 2: Atom number dependence of the OFC cavity transmission spectrum. (a) Experimental and (b) numerical data for empty cavity (black), partially loaded MOT (blue) and fully loaded MOT (magenta). Lines are guide to the eyes. Insets: Atom number scans of (a) experimental and (b) theoretical number of cavity modes significantly shifted due to the presence of atoms. The cutoff for the modes to count as significantly shifted is estimated as roughly $5\%$ of the maximum transmission value. (c) Experimental and (d) simulated difference in the transmission value with respect to empty cavity for the highest number of atoms. Experimental parameters: MOT atom number $N_{MOT}=(0,1.2,5.3)\times10^6$ for black, blue and pink, $\Delta f_0=-200$ kHz. Simulation parameters: $\hbox{FSR}=1.93$ GHz, $g_0=2\pi\times 140$ kHz, $\Delta_a^{(1)}=2\pi\times 495$ MHz, $\epsilon=18$ Hz, mirror transmission coefficient $t=0.0125$, $N=(0,0.06,\:1.2)\times 10^5$ for black, blue and magenta and $\Delta f_0=-220$ kHz.
• Figure 3: Cavity transmission spectra for OFC tuned resonantly and to the blue of the empty cavity modes. Frequency schematics of the first several modes for (a) $\Delta f_0=0$ and (b) $\Delta f_0=200$ kHz. (c, d) Experimental and (e, f) simulation data for the resonant and blue-detuned cases, respectively. Thick lines - cavity with atoms loaded, semitransparent lines - no atoms in the cavity. Experimental parameters: see text. Simulation parameters: $\hbox{FSR}=1.93$ GHz, $g_0=2\pi\times 140$ kHz, $\Delta_a^{(1)}=2\pi\times 495$ MHz, $\epsilon=18$ Hz, mirror transmission coefficient $t=0.0125$, $N=1.2\times 10^5$ and $\Delta f_0=0,\: 160$ kHz for (e,f) respectively.
• Figure 4: Cavity transmission of individual comb lines in the single comb mode coupling regime. (a) Experimental measurements of transmission curves for modes with $m=1$ (red), $m=-1$ (purple), $m=2$ (green), $m=-2$ (blue) and for an empty cavity mode (black). (b) Simulated difference in cavity photon number when the comb beam is turned on and off (see text), normalized to the empty cavity value. For comparison, the curve for the $m=1$ mode with $\Omega_M=0$ is shown. Experimental parameters: see text. Simulation parameters: $N=3.7\times 10^5$, $\kappa=2\pi\times 0.24$ MHz, $g_0=2\pi\times 140$ kHz, $\Omega_M=2\pi\times 1.7$ MHz, $\eta/\sqrt{N}=2\pi\times 0.06$ MHz, $\Gamma=2\pi\times 6.066$ MHz, $(\Delta_a^{(1)},\Delta_a^{(-1)},\Delta_a^{(2)},\Delta_a^{(-2)})=2\pi\times( 495,-1437,2427,-3369)$ MHz and $\Delta_M^{(m)}=\Delta_a^{(m)}+2.1\Gamma$.
• Figure S1: (a) Experimental setup. A cloud of cold $^{87}Rb$ atoms is loaded into MOT from background vapor in a stainless-steel vacuum chamber. The center of the MOT is spatially overlapped with the waist of the optical cavity. The cavity is driven by the OFC, and the transmitted light is detected using a photodiode, an optical spectrum analyzer (OSA), and via heterodyne spectroscopy. $\lambda/2$ – half wave plate, $\lambda$/4 – quarter wave plate, BS – beam splitter, DM – dichroic mirror, GR – grating, L – lens. (b) Locking scheme. The 852 nm laser is locked to the optical cavity using the Pound–Drever–Hall (PDH) technique, while the cavity itself is stabilized to the 852 nm laser via frequency modulated saturation absorption spectroscopy (FM SAS) in warm cesium vapor. Both the cooling laser and the repumper laser use a warm rubidium vapor cell in their locking setup. The cooling laser is stabilized to the cooling transition via modulation transfer spectroscopy (MTS), while the repumper laser is stabilized using SAS. The OFC is stabilized by locking two degrees of freedom: $f_n$ is stabilized to the cooling laser, and $f_{rep}$ is stabilized to a cesium frequency standard-referenced low-noise synthesizer (DDS). (c) Heterodyne measurement scheme. After amplification, the photodiode signal is split into a monitoring branch (RF spectrum analyzer) and a measurement branch. The measurement branch signal is mixed with a signal generator output and then analyzed using an oscilloscope. LPF – low pass filter, SA – spectrum analyzer, LO – local oscillator.