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Atom Interferometer Gates Realization: An Optimal Quantum Control Method

Javad Sharifi

Published Jan 1, 2022• 0 citations
Publisher

Abstract

Abstract Atom Interferometer has two quantum unitary gates that must be realized for quantum sensing purposes such as atomic gravimeter and atomic interferometer gyroscope. An optimal cost function which defines the distance between two unitary operators is defined and based on it, general adaptive (GADA) algorithms for optimization based quantum control are innovated to realize the atomic mirror and atomic beam-splitter gates. For the realization of those atom interferometer gates, we used optimal quantum control. We obtained gate fidelities of 0.9980 and 0.9998 for the mirror and the beam-splitter gates, respectively. In this research, a two-level atom system with clock transitions 1S0 ↔ 3P0 of strontium(87Sr) atom was employed.

DOI
10.21203/rs.3.rs-1526996/v1

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Abstract Atom Interferometer has two quantum unitary gates that must be realized for quantum sensing purposes such as atomic gravimeter and atomic interferometer gyroscope. An optimal cost function which defines the distance between two unitary operators is defined and based on it, general adaptive (GADA) algorithms for optimization based quantum control are innovated to realize the atomic mirror and atomic beam-splitter gates. For the realization of those atom interferometer gates, we used optimal quantum control. We obtained gate fidelities of 0.9980 and 0.9998 for the mirror and the beam-splitter gates, respectively. In this research, a two-level atom system with clock transitions 1S0 ↔ 3P0 of strontium(87Sr) atom was employed.
Atomic Interferometer has two quantum unitary gates that must be realized for quantum sensing purposes from atomic gravimeter and atomic interferometer gyroscope. An optimal cost function which define the distance between two unitary operator is defines and based on it a pulse based stochastic gradient descent algorithm is derived for implementation of atomic mirror and atomic beam-splitter gates. By using numerical optimal control for those gate realization, we achieved to gate fidelity of 0.995 and 0.998 for mirror and beam-splitter gates, respectively. For this research, a two-level atomic clock transitions are employed.
Strontium clock atom interferometry is a promising new technology, with multiple experiments under development around the world to explore its potential for dark matter and gravitational wave detection. In these detectors, large momentum transfer using sequences of many laser pulses is necessary, and thus high-fidelity pulses are important since small errors become magnified. Quantum optimal control (QOC) is a framework for developing control pulse waveforms that achieve high fidelity and are robust against experimental imperfections. Resonant single-photon transitions using the narrow clock transition of strontium involve significantly different quantum dynamics than more established atom interferometry methods based on far-detuned two-photon Raman or Bragg transitions, which leads to new opportunities and challenges when applying QOC. Here, we study in simulation QOC pulses for strontium clock interferometry and demonstrate their advantage over basic square pulses (primitive pulses) and composite pulses in terms of robustness against multiple noise channels. This could improve the scale of large momentum transfer in Sr clock interferometers, paving the way to achieving these scientific goals.
Methods of optimal control are applied to a model system of interacting two-level particles (e.g., spin-half atomic nuclei or electrons or two-level atoms) to produce high-fidelity quantum gates while simultaneously negating the detrimental effect of decoherence. One set of particles functions as the quantum information processor, whose evolution is controlled by a time-dependent external field. The other particles are not directly controlled and serve as an effective environment, coupling to which is the source of decoherence. The control objective is to generate target one- and two-qubit unitary gates in the presence of strong environmentally-induced decoherence and under physically motivated restrictions on the control field. The quantum-gate fidelity, expressed in terms of a novel state-independent distance measure, is maximized with respect to the control field using combined genetic and gradient algorithms. The resulting high-fidelity gates demonstrate the feasibility of precisely guiding the quantum evolution via optimal control, even when the system complexity is exacerbated by environmental coupling. It is found that the gate duration has an important effect on the control mechanism and resulting fidelity. An analysis of the sensitivity of the gate performance to random variations in the system parameters reveals a significant degree of robustness attained by the optimal control solutions.
Methods of optimal control are applied to a model system of interacting two-level particles (e.g., spin-half atomic nuclei or electrons or two-level atoms) to produce high-fidelity quantum gates while simultaneously negating the detrimental effect of decoherence. One set of particles functions as the quantum information processor, whose evolution is controlled by a time-dependent external field. The other particles are not directly controlled and serve as an effective environment, coupling to which is the source of decoherence. The control objective is to generate target one- and two-qubit unitary gates in the presence of strong environmentally-induced decoherence and under physically motivated restrictions on the control field. The quantum-gate fidelity, expressed in terms of a novel state-independent distance measure, is maximized with respect to the control field using combined genetic and gradient algorithms. The resulting high-fidelity gates demonstrate the feasibility of precisely guiding the quantum evolution via the optimal control, even when the system complexity is exacerbated by environmental coupling. It is found that the gate duration has an important effect on the control mechanism and resulting fidelity. An analysis of the sensitivity of the gate performance to random variations in the system parameters reveals a significant degree of robustness attained by the optimal control solutions.
Atom interferometers require both high efficiency and robust performance in their mirror pulses under experimental inhomogeneities. In this work, we demonstrated that quantum optimal control designed mirror pulse significantly enhance interferometer performance by using novel adaptive sliced structure. Using gradient ascent pulse engineering (GRAPE), optimized mirror pulse for a Mach-Zehnder light-pulse atom interferometer was designed by discretizing the control into non-uniform phase slices. This design broadened the tolerence to experimentally relevant variations in detuning [−Ω0,Ω0][-Ω_0,Ω_0][−Ω0​,Ω0​] and Rabi frequency [0.1×Ω0,1.9×Ω0][0.1\timesΩ_0,1.9\timesΩ_0][0.1×Ω0​,1.9×Ω0​] (Ω0=2π×25Ω_0=2π\times25Ω0​=2π×25 kHz), while maintaining high transfer efficiency even when the response-time delays up to 1.6 μs\rm{μs}μs. The optimized pulse was found to be robust to coupling inhomogeneity and velocity spread, offering a significant improvement in robustness over conventional pulse. The adaptive pulse slicing method provides a minimalist strategy that reduces experimental complexity while enhancing robustness and scalability, offering an innovative scheme for quantum optimal control in high precision atom interferometry.