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Optimal control of cold atoms for ultra-precise quantum sensors

Jack Saywell

Published Dec 1, 2020• 1 citation
OpenAlex

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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We present designs for the augmentation ``mirror'' pulses of large-momentum-transfer atom interferometers that maintain their fidelity as the wave-packet momentum difference is increased. These biselective pulses, tailored using optimal control methods to the evolving bimodal momentum distribution, should allow greater interferometer areas and hence increased inertial measurement sensitivity, without requiring elevated Rabi frequencies or extended frequency chirps. Using an experimentally validated model, we have simulated the application of our pulse designs to large-momentum-transfer atom interferometry using stimulated Raman transitions in a laser-cooled atomic sample of $^{85}\mathrm{Rb}$ at 1 $\ensuremath{\mu}\mathrm{K}$. After the wave packets have separated by 42 photon recoil momenta, our pulses maintain a fringe contrast of 90%, whereas, for adiabatic rapid passage and conventional $\ensuremath{\pi}$ pulses, the contrast is less than 10%. Furthermore, we show how these pulses may be adapted to be robust to laser intensity variations between pulses and to suppress the detrimental off-resonant excitation that limits other broadband pulse schemes.

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Optimized Raman pulses for atom interferometry

Jack Saywell, Max Carey, Mohammad Belal +2 more

We present mirror and beamsplitter pulse designs that improve the fidelity of atom interferometry and increase its tolerance of systematic inhomogeneities. These designs are demonstrated experimentally with a cold thermal sample of $^{85}$Rb 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.

arXiv:1911.08789•Nov 20, 2019•0 citations
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.
We present designs for the augmentation ``mirror'' pulses of large-momentum-transfer atom interferometers that maintain their fidelity as the wave-packet momentum difference is increased. These biselective pulses, tailored using optimal control methods to the evolving bimodal momentum distribution, should allow greater interferometer areas and hence increased inertial measurement sensitivity, without requiring elevated Rabi frequencies or extended frequency chirps. Using an experimentally validated model, we have simulated the application of our pulse designs to large-momentum-transfer atom interferometry using stimulated Raman transitions in a laser-cooled atomic sample of 85Rb^{85}\mathrm{Rb}85Rb at 1 $\ensuremath{\mu}\mathrm{K}$. After the wave packets have separated by 42 photon recoil momenta, our pulses maintain a fringe contrast of 90%, whereas, for adiabatic rapid passage and conventional $\ensuremath{\pi}$ pulses, the contrast is less than 10%. Furthermore, we show how these pulses may be adapted to be robust to laser intensity variations between pulses and to suppress the detrimental off-resonant excitation that limits other broadband pulse schemes.
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.
Developments in the precise control of quantum systems have led to advances in both fundamental research and emerging technologies in areas including quantum sensing and computation. One particularly useful application is atom interferometry, which uses laser pulses to split, redirect, and recombine atomic wavepackets, enabling precision measurements of inertial effects. This thesis presents the construction and characterisation of a compact cold atom interferometer, to meet the longer-term aim of developing an atomic gyroscope. We detail the setup of a rubidium-85 Magneto-Optical Trap (MOT) and the development of a laser to perform Raman transitions across the hyperfine Rb-85 levels. We then demonstrate and characterise the coherent manipulation of the atomic state of the rubidium as well as atom-interferometric fringes, in a Doppler-insensitive configuration. Systematic errors can degrade the performance of laser pulse interactions with cold atoms by reducing the fidelity of the atom–light interactions. In this thesis, we investigate the implementation of composite pulses and optimal control pulses, which use pulses with varying phase sequences and durations to mitigate against experimental inhomogeneities. We also show that phase modulators can introduce distortions in both the applied laser phase and the Raman modulation amplitude, which can in turn degrade pulse performance. To address this, we develop a compensation protocol that corrects for these non-linearities and demonstrate that it leads to a further improvement in pulse fidelity, for the Waltz and Knill composite pulses. Applying this protocol to the rotary echo sequence led to Rabi oscillations that could last 4 times longer, compared to the uncalibrated IQ modulator. Although an optimal control inversion pulse showed more resilience to the IQ modulator distortions, the Mach-Zehnder interferometer sequence was more susceptible to them. It was demonstrated that compensating for IQ modulator non-linearities improved the optimised fringe signal-to-noise ratio, and reduced the phase-offset error by a factor of 2.4.
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 sensitivity of atom interferometers depends on the fidelity of the light pulses used as beamsplitters and mirrors. Atom interferometers typically employ pulses that affect π/2 and π fractional Rabi oscillations, the fidelities of which are reduced when there are variations in atomic velocity and laser intensity. We have previously demonstrated the application of optimal control theory to design pulses more robust to such errors; however, if these variations exhibit a time dependence over periods on the order of the interferometer duration then phase shifts can be introduced in the final fringe that potentially reduce the sensitivity. In this paper, we explain why care must be taken when optimising interferometer pulse sequences to ensure that phase shifts arising from inter-pulse variations are not significantly increased. We show that these phase shifts can in fact be minimised by choosing an appropriate measure of individual pulse fidelity.
We present mirror and beamsplitter pulse designs that improve the fidelity of atom interferometry and increase its tolerance of systematic inhomogeneities. These designs are demonstrated experimentally with a cold thermal sample of 85^{85}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 πππ 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 πππ 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 πππ and π/2π/2π/2 pulses.