Atom Interferometry in a Warm Vapor

We demonstrate matter-wave interference in a warm vapor of rubidium atoms. Established approaches to light-pulse atom interferometry rely on laser cooling to concentrate a large ensemble of atoms into a velocity class resonant with the atom optical light pulse. In our experiment, we show that clear interference signals may be obtained without laser cooling. This effect relies on the Doppler selectivity of the atom interferometer resonance. This interferometer may be configured to measure accelerations, and we demonstrate that multiple interferometers may be operated simultaneously by addressing multiple velocity classes.

Figure 1

Vapor interferometer concept—not to scale. The two-dimensional mesh Gaussian represents the Maxwell-Boltzmann distribution in cylindrical coordinates $z$ and $\rho$ for room temperature atoms in $|F=1⟩$. The solid blue Sinc functions are two narrow velocity classes centered at $\pm v_z$ in $|F=2⟩$ that are selected from $|F=1⟩$ via the Raman transitions that comprise the LPAI. The arrows indicate the directions along $\widehat{z}$ of the Raman and probe lasers used to generate and detect the two narrow classes. Each Raman laser carries two frequencies separated by the hyperfine splitting, ${\nu }_{hf}$, plus an additional amount equal to $|{\mathbf{k}}_{\mathrm{eff}}|v_z/\pi$ such that a counterpropagating two-photon Raman transition is simultaneously resonant with the two velocity classes. Following the LPAI, the two velocity classes are simultaneously detected with two resonant probe lasers.

Figure 2

Schematic of the experiment showing the counterpropagating probe lasers, the off-axis application of the depump laser, and the imaging-pickoff scheme for separating the colinear probe and Raman lasers. The vapor cell sits within a heating sleeve and is surrounded by a magnetic shield. NPBSC, nonpolarizing beam splitter cube; PBSC, polarizing beam splitter cube; PMF, polarization maintaining fiber.

Figure 3

Raman detuning frequency scan revealing peaks for $\pm |{\mathbf{k}}_{\mathrm{eff}}|\widehat{z}$ at $\approx \mp 20\mathrm{MHz}$ for probe $A$ ($\mp |{\mathbf{k}}_{\mathrm{eff}}|\widehat{z}$ at $\approx \pm 20\mathrm{MHz}$ for probe $B$), which detects the velocity class centered at $\approx -7.8\mathrm{m}/\mathrm{s}$ $\widehat{z}$ ($\approx +7.8\mathrm{m}/\mathrm{s}$ $\widehat{z}$). The feature centered at $0\mathrm{m}/\mathrm{s}$ is a muted Doppler free resonance due to imperfect optical polarization. The Raman-excited velocity classes are given by ${\mathbf{v}}_c={\delta }_R/{\mathbf{k}}_{\mathrm{eff}}$ where ${\mathbf{k}}_{\mathrm{eff}}$ is simultaneously along $\pm \widehat{z}$ in our experiment. The measured widths of the four peaks are, on average, $14.6\pm 1\mathrm{MHz}$, consistent with the expected linewidth from numerical analysis of $\approx (\lambda \gamma |{\mathbf{k}}_{\mathrm{eff}}|/2\pi +1.4{\mathrm{\Omega }}_R)/2\pi =13.8\mathrm{MHz}$ for ${\mathrm{\Omega }}_R<(\lambda \gamma |{\mathbf{k}}_{\mathrm{eff}}|/2\pi )/8$.

Figure 4

(a) Timing diagram for the experimental pulse sequence with $T=15\mu \mathrm{s}$, a repetition rate of 10 kHz and $\tau =3\mu \mathrm{s}$. (b) Sample fringe in $|F=2⟩$ resulting from a Raman phase scan of a ten-point fringe at a data rate of 10 kHz. Each point is an average of 200 shots, and a $\pi$ phase shift corresponds to $88g$. The error bars for each point are below the resolution of the graphic. Inset: The normalized contrast as a function of the timing asymmetry of the interferometer pulses reveals a velocity width of $0.37(2)\mathrm{m}/\mathrm{s}\mathrm{rms}$ of the interferometer participant atoms.