Rotation sensing using tractor atom interferometry

AVS Quantum Sci. 6, 014407 (2024) · DOI: 10.1116/5.0175802 · arXiv: 2309.06324

Paper license: CC BY 4.0. Data: Hosted with the authors' permission; no licence granted. Ask the authors before reuse beyond citation.

Abstract

We investigate a possible realization of an ultracold-atom rotation sensor that is based on recently proposed tractor atom interferometry (TAI). An experimental design that includes generation of a Laguerre-Gaussian-beam-based "pinwheel" optical lattice and multi-loop interferometric cycles is discussed. Numerical simulations of the proposed system demonstrate TAI rotation sensitivity comparable to that of contemporary matter-wave interferometers. We analyze a regime of TAI rotation sensors in which nonadiabatic effects may hinder the system's performance. We apply quantum optimal control to devise a methodology suitable to address this nonadiabaticity. Our studies are of interest for current efforts to realize compact and robust matter-wave rotation sensors, as well as in fundamental-physics applications of TAI.

Figures

34 panels with data across 5 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

Illustrative figure, no extractable data. Shown in the paper PDF. Page 2 of the PDF.

Fig. 2

• panel (a): Optical potential $V$ (MHz) of the 8-site pinwheel lattice in the $r$-$z$ plane at $\theta = \pi/8$, against $r$ ($\mu$m) and $z$ ($\mu$m), on a logarithmic colour scale. Dashed lines mark the two radial maxima, the ring radius $R$ and $z = 0$. The $r = 0$ column, where $V$ is zero, is left empty. data.csv
• panel (b): Optical potential $V$ (MHz) in the transverse plane at the focus $z = 0$, as a polar map over $\theta$ and $r$ ($\mu$m) between the two radial maxima, on a logarithmic colour scale. The dashed spoke at $\theta = \pi/8$, the radial tick labels and the angle arrow of the print are not drawn; the panel has its own ticks. data.csv
• panel (c): Potential $V$ (MHz) along the radial direction $r$ ($\mu$m) at $z = 0$, for $\theta = \pi/8$ (solid) and $\theta = 0$ (dashed). Dashed vertical lines mark the two radial maxima and the ring radius $R$. The printed tick labels 18, $R$ and 36 and the names LG20 and LG28 are not shown; the axis is numeric. data.csv
• panel (c-inset): Inset of panel (c): the same two radial profiles, $\theta = \pi/8$ and $\theta = 0$, over a 4 $\mu$m window around the ring radius, with dashed lines at $r = R$ and $V = 4.4$ MHz. The bar marking the window width in the print is not drawn. data.csv
• panel (d): Potential $V$ (MHz) along the azimuthal direction, $\theta$ ($\pi$), at $R = 25.46$ $\mu$m and $z = 0$. data.csv

Fig. 3

• panel (a): Azimuthal displacement $\Delta\theta$ ($\pi$) of the wave packets from their initial position in the lab frame against time (ms), for the counter-rotating states $+$ and $-$. Shaded bands are the standard deviation of each wave-function density; dashed lines mark the end of the ramp-up and the start of the ramp-down. data.csv
• panel (b): Momentum expectation value $p$ ($I\pi$/s) in the lab frame against time (ms), for the counter-rotating states $+$ and $-$, with the control function $\omega(t)$ ($\pi$/s) as the dotted black curve. Shaded bands are the standard deviation of each wave-function density; dashed lines mark the end of the ramp-up and the start of the ramp-down. data.csv
• panel (c): Azimuthal-angle expectation value $\Delta\theta$ ($10^{-3}\pi$) of the wave packets in the moving frames of their lattices against time (ms), for the states $+$ and $-$, with standard-deviation bands and dashed lines at the ends of the ramps. The printed axis carries a $\times 10^{-4}$ scale factor; this one is in units of $10^{-3}\pi$. data.csv
• panel (d): Angular-momentum expectation value $p$ ($I\pi$/s) in the moving frame, relative to $\pm I\omega(t)$, against time (ms), for the states $+$ and $-$. Shaded bands are the standard deviation of each wave-function density; dashed lines mark the end of the ramp-up and the start of the ramp-down. data.csv

Fig. 4

• panel (a): Population $\vert c_- \vert^2$ in $|-\rangle$ against background rotation $\Omega$ ($10^{-2}\pi$/s) after $n = 2$ cycles with $\omega_0 = 10\pi$/s: the Sagnac curve (line) and the CN and SP points from the Crank-Nicolson and split-propagator simulations. data.csv
• panel (b): Population $\vert c_- \vert^2$ in $|-\rangle$ against background rotation $\Omega$ ($10^{-2}\pi$/s) after $n = 10$ cycles with $\omega_0 = 50\pi$/s: the Sagnac curve (line) and the SP points from the split-propagator simulations. data.csv

Fig. 5

• panel (1): Fidelity of the initial splitting, $\vert\langle \Psi(t_r) \vert \Psi_{\mathrm{tgt}}\rangle\vert^2$, against separation time (seconds, logarithmic axis) and $V_0$ (MHz). The red square marks the adiabatic point of Fig. 3, the red diamond the nonadiabatic point of Fig. 6, with a dashed line at its separation time. The print draws filled contours in steps of 0.05; this map is continuous. data.csv

Fig. 6

• panel (a): Population $\vert c_- \vert^2$ against background rotation $\Omega$ ($10^{-2}\pi$/s) under the unoptimized drive (solid), with the semiclassical Sagnac curve (dotted), for $t_r = 150$ $\mu$s and $V_0 = 0.2$ MHz. data.csv
• panel (b): Azimuthal displacement $\Delta\theta$ ($\pi$) in the lab frame against time (ms) over the whole sequence, for the states $+$ and $-$ with standard-deviation bands, at $t_r = 150$ $\mu$s and $V_0 = 0.2$ MHz under the analytic drive $\omega(t)$. data.csv
• panel (c): Lab-frame momentum $p$ ($I\pi$/s) against time (ms) for the states $+$ and $-$ with standard-deviation bands and $\omega(t)$ ($\pi$/s) dotted, under the analytic drive. The time axis is broken as printed, 0 to 1.5 and 198.65 to 200.15 ms side by side, with dashed lines at $t_r$ and $T - t_r$; the harmonic-period bar of the print is not drawn. data.csv
• panel (c-inset-1): Inset 1 of panel (c): lab-frame momentum $p$ ($I\pi$/s) for the states $+$ and $-$ with standard-deviation bands, and $\omega(t)$ ($\pi$/s) dotted, over the first 0.15 ms of the sequence. data.csv
• panel (c-inset-2): Inset 2 of panel (c): lab-frame momentum $p$ ($I\pi$/s) for the states $+$ and $-$ with standard-deviation bands, and $\omega(t)$ ($\pi$/s) dotted, over the last 0.15 ms of the sequence. data.csv
• panel (d): Moving-frame azimuthal angle $\Delta\theta$ ($10^{-3}\pi$) against time (ms) for the states $+$ and $-$ with standard-deviation bands, under the analytic drive. The time axis is broken as printed, 0 to 1.5 and 198.65 to 200.15 ms side by side, with dashed lines at $t_r$ and $T - t_r$. data.csv
• panel (d-inset-1): Inset 1 of panel (d): moving-frame azimuthal angle $\Delta\theta$ ($10^{-3}\pi$) for the states $+$ and $-$ with standard-deviation bands, over the first 0.15 ms of the sequence. data.csv
• panel (d-inset-2): Inset 2 of panel (d): moving-frame azimuthal angle $\Delta\theta$ ($10^{-3}\pi$) for the states $+$ and $-$ with standard-deviation bands, over the last 0.15 ms of the sequence. data.csv
• panel (e): Moving-frame angular momentum $p$ ($I\pi$/s), relative to $\pm I\omega(t)$, against time (ms) for the states $+$ and $-$ with standard-deviation bands, under the analytic drive. The time axis is broken as printed, 0 to 1.5 and 198.65 to 200.15 ms side by side, with dashed lines at $t_r$ and $T - t_r$. data.csv
• panel (e-inset-1): Inset 1 of panel (e): moving-frame angular momentum $p$ ($I\pi$/s) for the states $+$ and $-$ with standard-deviation bands, over the first 0.15 ms of the sequence. data.csv
• panel (e-inset-2): Inset 2 of panel (e): moving-frame angular momentum $p$ ($I\pi$/s) for the states $+$ and $-$ with standard-deviation bands, over the last 0.15 ms of the sequence. data.csv
• panel (f): Population $\vert c_- \vert^2$ against background rotation $\Omega$ ($10^{-2}\pi$/s) under the optimized drive (solid) and the unoptimized drive of panel (a) (dotted). data.csv
• panel (g): Azimuthal displacement $\Delta\theta$ ($\pi$) in the lab frame against time (ms) over the whole sequence, for the states $+$ and $-$ with standard-deviation bands, at $t_r = 150$ $\mu$s and $V_0 = 0.2$ MHz under the optimized drive $\omega_{\mathrm{opt}}(t)$. data.csv
• panel (h): Lab-frame momentum $p$ ($I\pi$/s) against time (ms) for the states $+$ and $-$ with standard-deviation bands and $\omega_{\mathrm{opt}}(t)$ ($\pi$/s) dotted, under the optimized drive. The time axis is broken as printed, 0 to 1.5 and 198.65 to 200.15 ms side by side, with dashed lines at $t_r$ and $T - t_r$. data.csv
• panel (h-inset-1): Inset 1 of panel (h): lab-frame momentum $p$ ($I\pi$/s) for the states $+$ and $-$ with standard-deviation bands, and $\omega_{\mathrm{opt}}(t)$ ($\pi$/s) dotted, over the first 0.15 ms of the sequence. data.csv
• panel (h-inset-2): Inset 2 of panel (h): lab-frame momentum $p$ ($I\pi$/s) for the states $+$ and $-$ with standard-deviation bands, and $\omega_{\mathrm{opt}}(t)$ ($\pi$/s) dotted, over the last 0.15 ms of the sequence. data.csv
• panel (i): Moving-frame azimuthal angle $\Delta\theta$ ($10^{-3}\pi$) against time (ms) for the states $+$ and $-$ with standard-deviation bands, under the optimized drive. The time axis is broken as printed, 0 to 1.5 and 198.65 to 200.15 ms side by side, with dashed lines at $t_r$ and $T - t_r$. data.csv
• panel (i-inset-1): Inset 1 of panel (i): moving-frame azimuthal angle $\Delta\theta$ ($10^{-3}\pi$) for the states $+$ and $-$ with standard-deviation bands, over the first 0.15 ms of the sequence. data.csv
• panel (i-inset-2): Inset 2 of panel (i): moving-frame azimuthal angle $\Delta\theta$ ($10^{-3}\pi$) for the states $+$ and $-$ with standard-deviation bands, over the last 0.15 ms of the sequence. data.csv
• panel (k): Moving-frame angular momentum $p$ ($I\pi$/s), relative to $\pm I\omega(t)$, against time (ms) for the states $+$ and $-$ with standard-deviation bands, under the optimized drive. The time axis is broken as printed, 0 to 1.5 and 198.65 to 200.15 ms side by side, with dashed lines at $t_r$ and $T - t_r$. data.csv
• panel (k-inset-1): Inset 1 of panel (k): moving-frame angular momentum $p$ ($I\pi$/s) for the states $+$ and $-$ with standard-deviation bands, over the first 0.15 ms of the sequence. data.csv
• panel (k-inset-2): Inset 2 of panel (k): moving-frame angular momentum $p$ ($I\pi$/s) for the states $+$ and $-$ with standard-deviation bands, over the last 0.15 ms of the sequence. data.csv

Cite

Bineet Dash, Michael H. Goerz, Alisher Duspayev, Sebastián C. Carrasco, Vladimir S. Malinovsky, Georg Raithel. Rotation sensing using tractor atom interferometry. AVS Quantum Sci. 6, 014407 (2024). https://doi.org/10.1116/5.0175802

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