Dual-Axis High-Data-Rate Atom Interferometer via Cold Ensemble Exchange

We demonstrate a dual-axis accelerometer and gyroscope atom interferometer, which can form the building blocks of a six-axis inertial measurement unit. By recapturing the atoms after the interferometer sequence, we maintain a large atom number at high data rates of 50 to 100 measurements per second. Two cold ensembles are formed in trap zones located a few centimeters apart and are launched toward one another. During their ballistic trajectory, they are interrogated with a stimulated Raman sequence, detected, and recaptured in the opposing trap zone. We achieve sensitivities at $\mu \mathit{g}/\sqrt{\mathrm{Hz}}$ and $(\mu \mathrm{rad}/\mathrm{s})/\sqrt{\mathrm{Hz}}$ levels, making this a compelling prospect for expanding the use of atom interferometer inertial sensors beyond benign laboratory environments.

Figure 1

Diagram of the apparatus implementing the cold ensemble exchange and dual-axis high-data-rate atom interferometer. (a) Front view: Two MOTs are loaded 36 mm apart. Cooling beams are shown in blue, probe beams in pink, and Raman beams in yellow. The trap is turned off, and the outer and inner cooling beams are blue and red detuned, respectively, which launches the ensembles towards each other. After the experiment, atoms are recaptured in the opposite trap to facilitate loading. (b) Side view: The design allows for four planes of optical access, enabling a compact apparatus. The vector $\mathbf{g}$ shows the direction of gravity, while $\mathbf{a}$ and $\mathbf{\Omega }$ are the directions of acceleration and rotation measurement, respectively.

Figure 2

Frames from a movie [16] demonstrating the ensemble exchange with a cycle time of 20 ms. The ensembles are launched towards each other over 2 ms to a velocity of $2.5\mathrm{m}/\mathrm{s}$, with simultaneous sub-Doppler cooling. The interferometer takes place during their ballistic trajectory with an interrogation time $T\approx 4\mathrm{ms}$. Imaging beams are off during the interferometer to reduce photon scatter which would otherwise cause decoherence. Dashed circles represent the approximate positions of the ensembles during this stage. Atoms are then recaptured in the opposite trapping region, with additional atoms loaded from vapor for 7 ms. This cycle represents a high atom number, low-bandwidth cycle to optimize the image contrast. Images are taken with a Lumenera CCD camera (Lm075) using a 0.2-ms exposure.

Figure 3

Recapture process during steady-state ensemble exchange. Black dots show the atom number calculated from an avalanche photodiode (APD) signal as atoms are being recaptured and loaded into the trap. The red dashed line indicates the total steady-state atom number $N_s$, while the red dotted line is the vapor-loading rate contribution. Many atoms are loaded via recapture over a few milliseconds, followed by vapor loading to replenish the lost atoms. By subtracting out the vapor-loading contribution, we determine the net recapture efficiency to be $r=85\%$. This includes losses due to background collisions during the cycle.

Figure 4

Inset: Loading of the exchange MOT after starting with the traps off, at $\beta =3.3$ $1/\mathrm{s}$. Each data point represents a single shot of the experiment. Fitting the data to Eq. (2) gives values for $r$ and $N_s$ at any given vapor pressure. Figure: Recapture efficiency $r$ and steady-state atom number $N_s$ as a function of loss rate $\beta$. Circles represent observed data during ensemble exchange. Solid lines are calculated from MOT loading parameters $\alpha$ and $\beta$, using the base recapture efficiency $r_0$ as a free parameter. The data show that sacrificing a moderate amount of recapture efficiency optimizes the atom number in the cycle due to a higher loading rate from vapor while the trap is active. The dashed circles show typical operating regimes, as well as the parameters for Fig. 3.

Figure 5

(a) Transition probability as a function of the two-photon Raman detuning with respect to the hyperfine transition. The 10° projection of the Raman beam axis along the launch trajectory results in a Doppler shift, causing the resonance conditions of the two ${\mathbf{k}}_e$ vectors to be separated by 2.2 MHz. For a given choice of resonance, one interferometer is operated at $+{\mathbf{k}}_e$ while the other is at $-{\mathbf{k}}_e$. (b) Gravitational acceleration causes the resonance conditions to shift oppositely for each interferometer, resulting in the second and third pulses being driven off resonance. Technical limitations in Raman beam alignment give rise to an asymmetry in pulse efficiencies. (c) Sample fringes from the interferometer generated by scanning the electro-optical phase of the third pulse. The interferometer uses an interrogation time of $T=4.1\mathrm{ms}$, and data are taken at $60\mathrm{shots}/\mathrm{s}$. We set a $\pi$ phase difference between the interferometers by appropriate choice of $T$ to suppress detection noise in favor of the rotation measurement.

Figure 6

Immunity of the atom interferometer to a range of tilt. The tilt direction corresponds to ${\theta }_y$, thus, changing the projection of gravity on the Raman beam axis, as well as the launch axis. Error bars represent the long-term drift seen in the apparatus over 1 h when the interferometer is flat on the table. The fringe contrast and steady-state atom number are largely unaffected by the orientation.

Figure 7

Recapture efficiency over a range of ensemble positions relative to the trap center, at the onset of ballistic recapture. Dashed lines represent the $1/e^2$ diameter of the trapping volume. For early onset (negative position), the ensemble’s momentum still carries it into the trap. Recapture is still efficient over a large fraction of the trap volume.

Figure 8

Contrast loss under high rotation rate. The black points are the observed fringe contrast as the apparatus is rotated in the $\pm \widehat{\mathbf{g}}$ direction, up to $\pm 1.5\mathrm{rad}/\mathrm{s}$. The red line is a Gaussian fit, with a width of $\sigma =0.60(1)\mathrm{rad}/\mathrm{s}$.