Atom Interferometry in an Optical Cavity

We propose and demonstrate a new scheme for atom interferometry, using light pulses inside an optical cavity as matter wave beam splitters. The cavity provides power enhancement, spatial filtering, and a precise beam geometry, enabling new techniques such as low power beam splitters ($<100\mu \mathrm{W}$), large momentum transfer beam splitters with modest power, or new self-aligned interferometer geometries utilizing the transverse modes of the optical cavity. As a first demonstration, we obtain Ramsey-Raman fringes with $>75\%$ contrast and measure the acceleration due to gravity, $g$, to $60\mu \mathrm{g}/\sqrt{\mathrm{Hz}}$ resolution in a Mach-Zehnder geometry. We use $>{10}^7$ cesium atoms in the compact mode volume ($600\mu \mathrm{m}$ $1/e^2$ waist) of the cavity and show trapping of atoms in higher transverse modes. This work paves the way toward compact, high sensitivity, multiaxis interferometry.

Figure 1

Left: Energy level scheme. A two-photon Raman interaction between the ground hyperfine states of cesium transfers momentum to the atoms. The laser (black arrows) is modulated at the hyperfine frequency creating sidebands (gray arrows). Two resonant pathways (solid arrows) can interfere depending on the position of the atoms and the detuning from an optical cavity resonance. Right: Mach-Zehnder interferometer. Momentum transfer from three pulses of a laser standing wave (wavy black lines) separated by a time $T$ split, redirect, and interfere a matter wave (red and blue lines).

Figure 2

Cavity and laser frequency stabilization. An external transfer cavity acts as a common reference for both the science laser and a second far-detuned laser (the “tracer” laser) which is used to stabilize the science cavity inside the vacuum chamber (gray box). The transfer cavity itself is stabilized to a reference laser. Cavity lengths and laser frequencies are stabilized via feedback using the Pound-Drever-Hall (PDH) method.

Figure 3

Top: Rabi flopping on the velocity insensitive transition after three state selection pulses with fixed intensity having pulse widths of $300\mu \mathrm{s}$ (red), $150\mu \mathrm{s}$ (blue), and $100\mu \mathrm{s}$ (green), followed by clearing pules shows improved contrast as atoms near the center of the cavity mode are preferentially selected. Bottom: Cavity suppression of velocity sensitive transitions. Changing the cavity length to be either on resonance with the carrier (red) or 2.2 MHz off resonance (blue) emphasizes one carrier-sideband pair and prevents cancellation of the transition amplitude.

Figure 4

Raman-Ramsey fringes. Two Raman $\pi /2$ pulses on the cesium clock transition are applied with a separation time $T=2\mathrm{ms}$. Each point is the average from four experimental runs. The high contrast and signal-to-noise ratio of the fringes demonstrates that, despite the small size of the optical cavity mode waist, spatial selection of the atoms gives a uniform Rabi frequency for the $2\times {10}^7$ atoms participating in the interferometer sequence.

Figure 5

Mach-Zehnder fringes of a $\pi /2-\pi -\pi /2$ pulse sequence on the cesium clock transition with pulse separation times $T=5\mathrm{ms}$ (blue) and $T=10\mathrm{ms}$ (red). The Raman frequency difference is linearly ramped to give an effective acceleration, $a_{\text{eff}}$, which compensates for the Doppler shift from the acceleration due to gravity. The phase of the interferometer is given by $k_{\text{eff}}(g-a_{\text{eff}})T^2$.

Figure 6

Left: A possible implementation of a rotation sensitive interferometer enclosing a spatial area using transverse cavity modes. Atoms enter the cavity from the side and are split by a pulsed standing wave in the Hermite-Gaussian $H_{0,10}$ cavity mode, reflected by a pulse in the fundamental $H_{0,0}$ mode, and interfered on the far side with a second pulse of the $H_{0,10}$ mode. Right: Fluorescence images of atoms in optical lattices formed by transverse modes of the optical cavity.