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arXiv:2411.03566 · Materials Today Quantum

Programming an optical lattice interferometer

Lennart Maximilian Seifert, V. E. Colussi, Michael A. Perlin, Pranav Gokhale, Frederic T. Chong

Published Feb 26, 2025• 3 citations
arXivHTMLPDF

Abstract

Programming a quantum device describes the usage of quantum logic gates, agnostic of hardware specifics, to perform a sequence of operations with (typically) a computing or sensing task in mind. Such programs have been executed on gate-based quantum computers, which despite their noisy character, have shown the ability to optimize metrological functions, for example in the generation of spin squeezing and optimization of quantum Fisher information for signals manifesting as spin rotations in a quantum register. However, the qubits of these programmable quantum sensors are tightly spatially confined and therefore suboptimal for enclosing the kinds of large spacetime areas required for performing inertial sensing. In this work, we derive a set of quantum logic gates for a cold atom optical lattice interferometer that manipulates the momentum of atoms. Here, the operations are framed in terms of single qubit operations and mappings between qubit subspaces with internal levels given by the Bloch (crystal) eigenstates of the lattice. We describe how the quantum optimal control method of direct collocation is well suited for obtaining modulation waveforms of an optical lattice to achieve these operations in existing experimental setups.

DOI
10.1016/j.mtquan.2025.100026

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Programming a quantum device describes the usage of quantum logic gates, agnostic of hardware specifics, to perform a sequence of operations with (typically) a computing or sensing task in mind. Such programs have been executed on gate-based quantum computers, which despite their noisy character, have shown the ability to optimize metrological functions, for example in the generation of spin squeezing and optimization of quantum Fisher information for signals manifesting as spin rotations in a quantum register. However, the qubits of these programmable quantum sensors are tightly spatially confined and therefore suboptimal for enclosing the kinds of large spacetime areas required for performing inertial sensing. In this work, we derive a set of quantum logic gates for a cold atom optical lattice interferometer that manipulates the momentum of atoms. Here, the operations are framed in terms of single qubit operations and mappings between qubit subspaces with internal levels given by the Bloch (crystal) eigenstates of the lattice. We describe how the quantum optimal control method of direct collocation is well suited for obtaining modulation waveforms of an optical lattice to achieve these operations in existing experimental setups.
In this paper, we propose a paradigm for atom interferometry and demonstrate that there exists a universal set of atom optic components for inertial sensing. These components constitute gates with which we carry out quantum operations and represent input-output matter wave transformations between lattice eigenstates. Each gate is associated with a modulation pattern of the position of the optical lattice according to machine-designed protocols. In this methodology, a sensor can be reprogramed to respond to an evolving set of design priorities without modifying the hardware. We assert that such a gate set is metrologically universal, in analogy to universal gate sets for quantum computing. Experimental confirmation of the designed operation is demonstrated via imaging of the spatial evolution of a Bose-Einstein condensate in an optical lattice and by measurement of the momentum probabilities following time-of-flight expansion. The representation of several basic quantum sensing circuits is presented for the measurement of inertial forces, rotating reference frames, and gravity gradients.
Performing interferometry in an optical lattice formed by standing waves of light offers potential advantages over its free-space equivalents since the atoms can be confined and manipulated by the optical potential. We demonstrate such an interferometer in a one-dimensional lattice and show the ability to control the atoms by imaging and reconstructing the wave function at many stages during its cycle. An acceleration signal is applied, and the resulting performance is seen to be close to the optimum possible for the time-space area enclosed according to quantum theory. Our methodology of machine design enables the sensor to be reconfigurable on the fly, and when scaled up, offers the potential to make state-of-the art inertial and gravitational sensors that will have a wide range of potential applications. Published by the American Physical Society 2024
We present theoretical and experimental progress on developing and demonstrating a novel atom interferometer. Our work is based on formulating a universal set of atom optic components for inertial sensing. These components constitute matterwave gates with which we build sensing circuits by cascading protocols in sequence. Unlike quantum computation, here our gates represent input-output matterwave transformations between lattice eigenstates. Each gate is associated with a modulation function of the position of an optical lattice according to machine-designed patterns. In this methodology, a sensor is not fixed in hardware but can be programmed and reprogrammed to respond to an evolving set of design priorities. The gates we provide are metrologically universal, in analogy to universal gate sets for quantum computing, and can therefore sense any signal. Experimental confirmation of the designed operation is demonstrated via in situ imaging of the spatial evolution of a Bose-Einstein condensate in an optical lattice, and by measurement of the momentum probabilities following time-of-flight expansion. The application to several basic quantum sensing circuits is presented for the measurement of inertial forces, rotating reference frames, and gravity gradients.
We introduce shaken lattice interferometry with atoms trapped in a one-dimensional optical lattice. By phase modulating (shaking) the lattice, we control the momentum state of the atoms. Through a sequence of shaking functions, the atoms undergo an interferometer sequence of splitting, propagation, reflection, reverse propagation, and recombination. Each shaking function in the sequence is optimized with a genetic algorithm to achieve the desired momentum state transitions. As with conventional atom interferometers, the sensitivity of the shaken lattice interferometer increases with interrogation time. The shaken lattice interferometer may also be optimized to sense signals of interest while rejecting others, such as the measurement of an ac inertial signal in the presence of an unwanted dc signal.
Neutral atoms offer a promising platform for single- and many-body quantum control, as required for quantum information processing. This includes excellent isolation from the decohering influence of the environment, and the existence of well developed techniques for atom trapping and coherent manipulation. We present a review of our work to implement quantum control and measurement for ultra-cold atoms in far-off-resonance optical lattice traps. In recent experiments we have demonstrated coherent behavior of mesoscopic atomic spinor wavepackets in optical double-well potentials, and carried out quantum state tomography to reconstruct the full density matrix for the atomic spin degrees of freedom. This model system shares a number of important features with proposals to implement quantum logic and quantum computing in optical lattices. We present a theoretical analysis of a protocol for universal quantum logic via single qubit operations and an entangling gate based on electric dipole-dipole interactions. Detailed calculations including the full atomic hyperfine structure suggests that high-fidelity quantum gates are possible under realistic experimental conditions.
The creation of a 1D matter-wave interferometer can be achieved by utilizing ultracold atoms loaded into an optical lattice. By shaking the lattice via either phase or frequency modulation, the traditional steps of interferometry- effectively splitting, propagating, reflecting, again propagating and then recombining the atomic wavefunction- can be implemented, allowing for the sensing of inertial signals. This approach is interesting, since the atoms can be supported against external forces and perturbations, and the system can be completely reconfigurable on-the-fly for a new design goal. We report on experimental results in which atoms are cooled into a dipole trap and subsequently loaded into an optical lattice. Shaking protocols for obtaining interferometry steps are derived via machine learning and quantum optimal control methods. We report experimental progress in realizing a shaken lattice interferometer and its sensitivity to an applied acceleration signal along with the possibility of tailoring the signal to specific scenarios. Additionally, closed loop learning from the experiment to improve signal sensitivity is explored and demonstrated.