We develop interferometry-based atomic inertial sensors robust to Doppler-type inhomogeneities by using quantum optimal control methods. Theoretical results show optimized phase profiles of Raman and Bragg optical π-pulses enabling maximization of the fidelity.
Abstract We present the theoretical design and experimental implementation of mirror and beamsplitter pulses that improve the fidelity of atom interferometry and increase its tolerance of systematic inhomogeneities. These pulses are designed using the GRAPE optimal control algorithm and demonstrated experimentally with a cold thermal sample of 85Rb atoms. We first show a stimulated Raman inversion pulse design that achieves a ground hyperfine state transfer efficiency of 99.8(3)%, compared with a conventional π pulse efficiency of 75(3)%. This inversion pulse is robust to variations in laser intensity and detuning, maintaining a transfer efficiency of 90% at detunings for which the π pulse fidelity is below 20%, and is thus suitable for large momentum transfer interferometers using thermal atoms or operating in non-ideal environments. We then extend our optimization to all components of a Mach–Zehnder atom interferometer sequence and show that with a highly inhomogeneous atomic sample the fringe visibility is increased threefold over that using conventional π and π/2 pulses.
The mirrors and beamsplitters of atom interferometers often suffer from inhomogeneities in coupling strength and effective detuning because different atoms see different laser intensities, Zeeman and Doppler shifts and are in different Zeeman sub-states. This limits the fringe visibility for a simple interferometer, which falls off rapidly if extra mirrors are added, for example to increase the interferometer area. In practice, one usually therefore filters the atomic velocities/sub-states, thus losing signal, and/or restricting operation to small-area interferometers with low sensitivity. The problem is familiar in the field of NMR, where, instead of using simple pi or pi/2 pulses, the phase and potentially amplitude are modulated during the pulse so as to make the result robust to the inhomogeneities encountered. Despite the similarities with NMR systems, the numbers, correlations and performance measures for atom interferometry are different. We have used optimal control theory to obtain robust high fidelity mirror pulses for atom interferometry. Importantly, while the designs are found by computational simulation, we can validate them experimentally, with remarkably good agreement. We have addressed the optimization of individual mirror pulses, but the eventual aim is to optimize the interferometer as a whole: errors introduced in one pulse can be compensated at a later stage, for example. Our pulses yield high contrast without the need to filter the atomic sample and maintain this even in the case of extended pulse sequences, thus making it possible to achieve significantly larger interferometer areas than with simple pi pulses.
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.
Bragg diffraction of matter waves is an established technique used in the most accurate quantum sensors. It is also the method of choice to operate large-momentum-transfer, high-sensitivity atom interferometers. It suffers, however, from an intrinsic multi-path character. Optimal control theory (OCT) has recently led to an improved robustness of atom interferometers to a range of challenging environmental effects such as vibrations or platform accelerations. In this theoretical work, we apply OCT protocols to control the Bragg diffraction phase shifts, thereby enhancing the metrological accuracy of the interferometer. We show a minimization of the diffraction phase for realistic conditions of finite temperature of the incoming wavepacket in a multi-path, high-order Bragg interferometer in a Mach–Zehnder configuration. We study input states with different momentum widths and find that our approach mitigates diffraction phases below the microradian level in the case of 1% of the photon recoil, thereby eliminating one of the leading systematic effects in atom interferometry.
We present an analysis of the robustness of existing analytic schemes for the implementation of an atomic fountain interferometer, and develop concepts for improving this robustness through the use of optimal control theory. For an interferometer operating in the Raman regime, we consider an implementation that manipulates the atomic momentum states with a series of Rabi pulses, and analyze how robust the population dynamics are with respect to variations in the effective pulse amplitude seen by the atoms in the atomic clouds, and variations in the initial velocity of the atoms relative to the rest frame. We then show that using rapid adiabatic passage to implement momentum transfer can significantly improve this robustness. Finally, we formulate the most general control conditions for an atomic fountain interferometer and design a functional that can be used for an ensemble optimization over the robustness landscape. We show preliminary results of optimizing the system using Krotov's method, suggesting that optimal control may be able to significantly enhance the robustness of atom interferometers.
We formulate a robust optimal control algorithm to synthesize minimum energy pulses that can transfer a cold atom system into various momentum states. The algorithm uses adaptive linearization of the evolution operator and sequential quadratic programming to iterate the control towards a minimum energy pulse that achieves optimal target state fidelity. Robustness to parameter variation is achieved using Legendre polynomial approximation over the domain of variation. The method is applied to optimize the Bragg beamsplitting operation in ultra-cold atom interferometry. Even in the presence of 10-40% variability in the initial momentum dispersion of the atomic cloud and the intensity of the optical pulse, the algorithm reliably converges to a control protocol that robustly achieves unprecedented momentum levels with high fidelity for a single-frequency multi-photon Bragg diffraction scheme (e.g. ∣±40ℏk⟩). We show the advantages of our method by comparison to stochastic optimization using sampled parameter values, provide detailed sensitivity analyses, and performance of the designed pulses is verified in laboratory experiments.