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arXiv:2103.05832 · Physical Review Letters

Motional Squeezing for Trapped Ion Transport and Separation

R. T. Sutherland, S. C. Burd, D. H. Slichter, Stephen B. Libby, Dietrich G. Leibfried

Published Aug 20, 2021• 21 citations
arXivHTMLPDF

Abstract

Transport, separation, and merging of trapped ion crystals are essential operations for most large-scale quantum computing architectures. In this Letter, we develop a theoretical framework that describes the dynamics of ions in time-varying potentials with a motional squeeze operator, followed by a motional displacement operator. Using this framework, we develop a new, general protocol for trapped ion transport, separation, and merging. We show that motional squeezing can prepare an ion wave packet to enable transfer from the ground state of one trapping potential to another. The framework and protocol are applicable if the potential is harmonic over the extent of the ion wave packets at all times. As illustrations, we discuss two specific operations: changing the strength of the confining potential for a single ion and separating same-species ions with their mutual Coulomb force. Both of these operations are, ideally, free of residual motional excitation.

DOI
10.1103/physrevlett.127.083201

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Transport, separation, and merging of trapped ion crystals are essential operations for most large-scale quantum computing architectures. In this Letter, we develop a theoretical framework that describes the dynamics of ions in time-varying potentials with a motional squeeze operator, followed by a motional displacement operator. Using this framework, we develop a new, general protocol for trapped ion transport, separation, and merging. We show that motional squeezing can prepare an ion wave packet to enable transfer from the ground state of one trapping potential to another. The framework and protocol are applicable if the potential is harmonic over the extent of the ion wave packets at all times. As illustrations, we discuss two specific operations: changing the strength of the confining potential for a single ion and separating same-species ions with their mutual Coulomb force. Both of these operations are, ideally, free of residual motional excitation.
Rapid separation of linear crystals of trapped ions into different subsets is critical for realizing trapped ion quantum computing architectures where ions are rearranged in trap arrays to achieve all-to-all connectivity between qubits. We introduce a general theoretical framework that can be used to describe the separation of same-species and mixed-species crystals into smaller subsets. The framework relies on an efficient description of the evolution of Gaussian motional states under quadratic Hamiltonians that only requires a special solution of the classical equations of motion of the ions to describe their quantum evolution under the influence of a time-dependent applied potential and the ions' mutual Coulomb repulsion. We provide time-dependent applied potentials suitable for separation of a mixed-species three-ion crystal on timescales similar to that of free expansion driven by Coulomb repulsion, with all modes along the crystal axis starting and ending close to their ground states. Three separately confined mixed-species ions can be combined into a crystal held in a single well without energy gain by time-reversal of this separation process.
Qubits based on ions trapped in linear radio-frequency traps form a successful platform for quantum computing, due to their high fidelity of operations, all-to-all connectivity, and degree of local control. In principle, there is no fundamental limit to the number of ion-based qubits that can be confined in a single 1D register. However, in practice, there are two main issues associated with long trapped-ion crystals, that stem from the “softening” of their modes of motion, upon scaling up: high heating rates of the ions’ motion and a dense motional spectrum; both impede the performance of high-fidelity qubit operations. Here, we propose a holistic, scalable architecture for quantum computing with large ion crystals that overcomes these issues. Our method relies on dynamically operated optical potentials that instantaneously segment the ion crystal into cells of a manageable size. We show that these cells behave as nearly independent quantum registers, allowing for parallel entangling gates on all cells. The ability to reconfigure the optical potentials guarantees connectivity across the full ion crystal and also enables efficient midcircuit measurements. We study the implementation of large-scale parallel multiqubit entangling gates that operate simultaneously on all cells and present a protocol to compensate for crosstalk errors, enabling full-scale usage of an extensively large register. We illustrate that this architecture is advantageous both for fault-tolerant digital quantum computation and for analog quantum simulations. Published by the American Physical Society 2024
Improving coherence is a fundamental challenge in quantum simulation and sensing experiments with trapped ions. Here we discuss, experimentally demonstrate, and estimate the potential impacts of two different protocols that enhance, through motional parametric excitation, the coherent spin-motion coupling of ions obtained with a spin-dependent force. The experiments are performed on two-dimensional crystal arrays of approximately 100 9Be+{}^{9}{\mathrm{Be}}^{+}9Be+ ions confined in a Penning trap. By modulating the trapping potential at close to twice the center-of-mass mode frequency, we squeeze the motional mode and enhance the spin-motion coupling while maintaining spin coherence. With a stroboscopic protocol, we measure $5.4\ifmmode\pm\else\textpm\fi{}0.9\phantom{\rule{0.28em}{0ex}}\mathrm{dB}$ of motional squeezing below the ground-state motion, from which theory predicts a 10-dB enhancement in the sensitivity for measuring small displacements using a recently demonstrated protocol [K. A. Gilmore et al., Science 373, 673 (2021)]. With a continuous squeezing protocol, we measure and accurately calibrate the parametric coupling strength. Theory suggests this protocol can be used to improve quantum spin squeezing, limited in our system by off-resonant light scatter. We illustrate numerically the trade-offs between strong parametric amplification and motional dephasing in the form of center-of-mass frequency fluctuations for improving quantum spin squeezing in our setup.
The second-sideband Raman excitation of the motional ground state of a single ion trapped in a harmonic potential is analyzed in the strong Raman coupling regime. Appropriate Raman motional excitations driven by strong standing-wave lasers can be used to split the motional ground state to a macroscopic motional wave-packet state with spatial separation between the split parts comparable to the dimension of the involved ionic transition wavelengths. A spatial flat wave-packet with coherence persisting in a wide spatial range can also be excited. The spatial spread of such a spatial flat macroscopic motional wave-packet oscillates periodically during the free-time evolution in the harmonic trap, with a spatial flat distribution persisting at most of the oscillating times.
We have developed fast and accurate protocols for ion shuttling in a surface-electrode ion trap, which allows efficient splitting and merging of two ions. These protocols are based on innovative improvements in the driving potential field model, where voltage is introduced as a variable parameter. This enhancement specifically addresses the issue of increased control errors that occur with larger inter-ion distances. We have devised a general model-solving procedure that uses a parameterized model to describe the total potential energy of the two ions and ions oscillating eigenfrequency in a dynamical normal modes. By employing optimization techniques, we determine optimal voltage ramps for the dynamic potential field, enabling accurate control of physical quantities during the splitting process. In additionally, through simulating the classical dynamics of the theoretical scheme, we decouple the ion oscillations by employing discrete Fourier transform (DFT) and nonlinear fitting techniques. Two ions are separated into individual potential wells with a distance of 200 μ𝑚 within 50 μs. The ion position drift is only 0.01%. During the splitting process, the frequency fluctuation of the center-of-mass mode of the ions is less than 0.69%, and the minimum average excitation of a single ion is 0.02 phonon. Accurate and fast ion shuttling technology facilitates the development of large-scale trapped-ion quantum computing. Maintaining the ions oscillating eigenfrequency constant during the shuttling operation alleviates the problem of decoherence of quantum information.
We propose a new scheme for supplying voltages to the electrodes of microfabricated ion traps, enabling access to a regime in which changes to the trapping potential are made on timescales much shorter than the period of the secular oscillation frequencies of the trapped ions. This opens up possibilities for speeding up the transport of ions in segmented ion traps and also provides access to control of multiple ions in a string faster than the Coulomb interaction between them. We perform a theoretical study of ion transport using these methods in a surface-electrode trap, characterizing the precision required for a number of important control parameters. We also consider the possibilities and limitations for generating motional state squeezing using these techniques, which could be used as a basis for the investigation of Gaussian-state entanglement.