Efficient Adiabatic Spin-Dependent Kicks in an Atom Interferometer

We present an atom interferometry technique in which the beam splitter is split into two separate operations. A microwave pulse first creates a spin-state superposition, before optical adiabatic passage spatially separates the arms of that superposition. Despite using a thermal atom sample in a small ($600\mu \mathrm{m}$) interferometry beam, this procedure delivers an efficiency of 99% per $\hslash k$ of momentum separation. Utilizing this efficiency, we first demonstrate interferometry with up to $16\hslash k$ momentum splitting and free-fall limited interrogation times. We then realize a single-source gradiometer, in which two interferometers measuring a relative phase originate from the same atomic wave function. Finally, we demonstrate a resonant interferometer with over 100 adiabatic passages, and thus over $400\hslash k$ total momentum transferred.

Figure 1

SDK interferometry. (a) SDK beam splitter. A microwave ($\pi /2$) pulse ${\widehat{\mu }}_{\pi /2}$ puts the atom into a superposition of hyperfine states. A Raman adiabatic passage ${\widehat{O}}_{+}$ then delivers a spin-dependent kick to each arm of the superposition. The energy level diagrams at right show the transitions for both arms. (b) Basic SDK interferometer. During the wave packet separation time $T$ the arms have $4\hslash k$ momentum separation, while $\tau$ denotes the time between halves of the SDK mirror pulse sequence, where the arms are at rest relative to each other. (c) Large momentum transfer. Inverting the laser wave vectors kicks the arms in opposite directions, ${\widehat{O}}_{-}$. Since both laser frequencies travel in both directions, either operation can be chosen (a large enough Doppler shift breaks the degeneracy).

Figure 2

Top: SDK interferometer contrast as a function of gravity phase $\mathrm{\Delta }\varphi$, measured for various orders of momentum transfer at wave packet separation times $T=5$, 15, 25, and 44 ms. The gravity phase $\mathrm{\Delta }\varphi (g)$ is due to the acceleration from Earth’s gravity, $g\approx 9.8\mathrm{m}/{\mathrm{s}}^2$. High visibility fringes are observed for $\mathrm{\Delta }\varphi \lesssim 0.5\mathrm{Mrad}$, above which vibration noise dominates. Contrast is therefore determined by fitting histograms of $\sim 200$ interferometer outputs to an arcsine probability distribution function [33]. Error bars represent the $1\sigma$ statistical uncertainty in the contrast fit parameter. The blue dotted line provides a comparison to traditional $2\hslash k$ Raman Mach-Zehnder interferometers in our apparatus with $T=22$, 55, and 65 ms. Bottom: The fringe for a $4\hslash k$ interferometer with $T=1\mathrm{ms}$, $\tau =26\mathrm{ms}$ is shown, along with its contrast histogram. Each point in the top panel of this figure comes from such a fitted histogram.

Figure 3

Single-source gradiometer. A schematic of the arm trajectories is shown in the inset. The first half of an $8\hslash k$ SDK interferometer separates two arms. Once brought back to relative rest, the actual interferometer sequence begins, simultaneously addressing both arms. The phases of the two interferometers can then be read out using the four output ports. The main plot shows gradiometer data. The two interferometers have a fixed phase difference independent of common mode phase noise. When plotted parametrically, the interferometer outputs form an ellipse whose shape is determined by this relative phase difference. Ellipses are plotted both with (red, hollow) and without (blue, filled) a transverse laser beam applied to phase shift the lower interferometer by ${\varphi }_{\mathrm{ac}}$. For this data, the atoms separated for 63 ms, giving 1.764 mm of separation to the gradiometer. $T=\tau =0.3\mathrm{ms}$ was then used for the interferometers.

Figure 4

Resonant atom interferometer. Top: Interference fringes for different number of loops $m$, as the phase per loop is varied. Bottom: Contrast decay is shown as both a function of the number of loops $m$, and corresponding number of optical pulses $n$. Resonant interferometer geometry for $m=3$ loops is illustrated in the lower left. The dotted line represents a model with no free parameters, using only the independently measured Ramsey contrast (88%) and ARP pulse efficiency (96%), and the calculated single photon scattering (1% per pulse). Agreement with the data indicates negligible sources of additional contrast loss. A stable fringe is observed even after 51 loops.