Optimal control of cold atoms for ultra-precise quantum sensors

Abstract

Atom interferometric sensors can enable extremely precise measurements of inertial motion and external fields by manipulating and interfering atomic states using pulses of laser light. However, like many experiments that require the coherent control of a quantum system, the interaction fidelity is limited by inhomogeneities in the control fields. Variations in atomic velocity and laser intensity lead different atoms to experience different interactions under the same pulse, reducing the interference fringe contrast, introducing bias, and limiting the sensitivity. We present the theoretical design and experimental demonstration of pulses for atom interferometry which compensate inhomogeneities in atomic velocity and laser intensity. By varying the laser phase throughout a pulse and choosing an appropriate fidelity measure to be maximised, pulses are optimised by adapting optimal control techniques originally designed for nuclear magnetic resonance applications. We show using simulations that optimised pulses significantly improve the fidelity of interferometer operations and verify this experimentally using Raman transitions within a cold sample of 85Rb atoms. We demonstrate a robust state-transfer pulse that achieves a fidelity of 99.8(3)% in a ∼ 35 µK sample and obtain a threefold increase in the fringe contrast using a full sequence of optimised pulses. Many of the pulse shapes found by optimal control are simple and symmetrical, and we show that certain symmetries are integral to error compensation. By systematically exploring the dependence of these solutions on the model and optimisation parameters, we demonstrate a stability which underlines the general applicability of optimised pulses to a range of interferometer configurations. Finally, we introduce and computationally analyse a novel theoretical approach to improve the sensitivity of large-momentum-transfer (LMT) interferometers, whereby “biselective” pulses are optimised to track the changing resonance conditions encountered in extended pulse sequences that are designed to increase the measurement sensitivity. When conventional pulses of steady phase are used, the interference contrast decays rapidly as extra pulses are added because of the change in resonance. Using numerical simulations, we show that bi-selective pulses maintain interaction fidelity throughout extended pulse sequences, allowing significant increases in the sensitivity that may be obtained using LMT.

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Identifiers

ORCID for Timothy Freegarde: orcid.org/0000-0002-0680-1330

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