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arXiv:2207.11193 · Physical Review A

Synthesizing a σz spin-dependent force for optical, metastable, and ground-state trapped-ion qubits

O. Băzăvan, Sebastian Saner, Mariella Minder, A. C. Hughes, R. T. Sutherland, D. M. Lucas, R. Srinivas, Christopher J. Ballance

Published Feb 22, 2023• 18 citations
arXivHTMLPDF

Abstract

A single bichromatic field near resonant to a qubit transition is typically used for ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$ or ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{y}$ M\o{}lmer-S\o{}rensen-type interactions in trapped-ion systems. Using this field configuration, it is also possible to synthesize a ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{z}$ spin-dependent force by merely adjusting the beat-note frequency. Here, we expand on previous work and present a comprehensive theoretical and experimental investigation of this scheme with a laser near resonant to a quadrupole transition in $^{88}\mathrm{Sr}^{+}$. Further, we characterize its robustness to optical phase and qubit frequency offsets, and demonstrate its versatility by entangling optical, metastable, and ground-state qubits.

DOI
10.1103/physreva.107.022617

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A single bichromatic field near resonant to a qubit transition is typically used for \ensuremathσ\ifmmode^\elseˆ\fix{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}\ensuremathσ\ifmmode^\elseˆ\fi​x​ or \ensuremathσ\ifmmode^\elseˆ\fiy{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{y}\ensuremathσ\ifmmode^\elseˆ\fi​y​ M\o{}lmer-S\o{}rensen-type interactions in trapped-ion systems. Using this field configuration, it is also possible to synthesize a \ensuremathσ\ifmmode^\elseˆ\fiz{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{z}\ensuremathσ\ifmmode^\elseˆ\fi​z​ spin-dependent force by merely adjusting the beat-note frequency. Here, we expand on previous work and present a comprehensive theoretical and experimental investigation of this scheme with a laser near resonant to a quadrupole transition in 88Sr+^{88}\mathrm{Sr}^{+}88Sr+. Further, we characterize its robustness to optical phase and qubit frequency offsets, and demonstrate its versatility by entangling optical, metastable, and ground-state qubits.
Favored schemes for trapped-ion quantum logic gates use bichromatic laser fields to couple internal qubit states with external motion through a "spin-dependent force." We introduce a new degree of freedom in this coupling that reduces its sensitivity to phase decoherence. We demonstrate bichromatic spin-dependent forces on a single trapped 111Cd+ ion, and show that phase coherence of the resulting entangled states of spin and motion depends critically upon the spectral arrangement of the optical fields. This applies directly to the operation of entangling gates on multiple ions.
In ion traps, entangling gate operations can be realized by a bichromatic pair of laser beams that collectively interact with the ions. In this paper, a new method of modelling the laser–ion interaction is introduced that turns out to be superior to standard techniques for the description of gate operations on optical qubits. The treatment allows for a comparison of the performance of gates based on σ z ⊗σ z and σ ϕ ⊗σ ϕ interactions on optical transitions where the bichromatic laser field can be realized by an amplitude-modulated laser resonant with the qubit transition. Shaping the amplitude of the bichromatic laser pulse is shown to make the gates more robust against experimental imperfections.
Trapped atomic ion qubits or effective spins are a powerful quantum platform for quantum computation and simulation, featuring densely connected and efficiently programmable interactions between the spins. While native interactions between trapped ion spins are typically pairwise, many quantum algorithms and quantum spin models naturally feature couplings between triplets, quartets or higher orders of spins. Here we formulate and analyze a mechanism that extends the standard Mølmer-Sørensen pairwise entangling gate and generates a controllable and programmable coupling between NNN spins of trapped ions. We show that spin-dependent optical forces applied at twice the motional frequency generate a coordinate-transformation of the collective ion motion in phase-space, rendering displacement forces that are nonlinear in the spin operators. We formulate a simple framework that enables a systematic and faithful construction of high-order spin Hamiltonians and gates, including the effect of multiple modes of motion, and characterize the performance of such operations under realistic conditions.
Trapped ions offer a controlled and versatile platform for the simulation of spin and spin-boson quantum systems. The Coulomb interaction between ions trapped in a harmonic potential can be used to mediate interactions between effective spins in the ion chain. Generally, coherent operations on ions are performed on ground-state qubits encoded in magnetically insensitive hyperfine sublevels. In this thesis, we extend this toolbox with the aim of simultaneously manipulating both ground-state and optical qubits, with the latter encoded in metastable optically excited states. The optical qubit provides another set of coherent and dissipative operations that can be performed on the ions, opening new avenues for quantum computing and simulation. In our experiment, we use 171Yb+ and 172Yb+ ions to encode ground-state and optical qubits. We discuss the laser setup needed to address the narrow quadrupole transition from 2S1/2 →2 D3/2 of 3.02 Hz linewidth, and we describe spectroscopy techniques to study this transition in both the isotopes. We describe how the low linewidth allows resolved sideband cooling on the shared motional modes in an ion chain, enabling sympathetic cooling with one ion, 172Yb+ , while simultaneously performing coherent operations on the 171Yb+ ion. Finally, we discuss the prospects of using this tool for light-shift entangling gates, showing the flexibility of this trapped-ion system for simulating coherent as well as dissipative quantum systems.
Trapped ions are a leading technology for quantum computing, but their reliance on bespoke tabletop laser and optical systems remains a major obstacle to scaling and robustness. Integrated silicon nitride lasers, compatible with future monolithic integration with surface electrode ion traps, have recently demonstrated frequency-selective qubit state preparation and measurement as well as interrogation of an optical clock transition. However, coherent qubit gates impose even more stringent requirements on laser phase noise, and their implementation with integrated laser sources has remained an outstanding challenge. Here, we use a visible-wavelength integrated Brillouin laser stabilized to an integrated coil resonator to drive coherent single- and two-qubit gates with \Sr optical qubits. We measure an average single-qubit fidelity of 99.61%±0.03%99.61\%\pm 0.03\%99.61%±0.03% per Clifford gate with randomized benchmarking and use a two-qubit Mølmer-Sørensen interaction to generate an entangled Bell state with a fidelity of 92.35%±1.50%92.35\% \pm 1.50\%92.35%±1.50%. The qubit exhibits a bare Ramsey coherence time of 659±9 μ659 \pm 9~μ659±9 μs, more than a tenfold improvement over our previous implementation, which extends to 1.750±0.0331.750 \pm 0.0331.750±0.033~ms with an echo. These results demonstrate, for the first time, that integrated visible-wavelength narrow-linewidth photonic lasers can meet the phase-noise requirements for coherent quantum logic with trapped ion optical qubits, providing a path for scalable optical systems integrated within trapped ion quantum processors.
Trapped atomic ion qubits or effective spins are a powerful quantum platform for quantum computation and simulation, featuring densely connected and efficiently programmable interactions between the spins.While native interactions between trapped-ion spins are typically pairwise, many quantum algorithms and quantum spin models naturally feature couplings between triplets, quartets, or higher orders of spins.Here, we formulate and analyze a mechanism that extends the standard Mølmer-Sørensen pairwise entangling gate and generates a controllable and programmable coupling between N spins of trapped ions.We show that spin-dependent optical parametric drives applied at twice the motional frequency generate a coordinate transformation of the collective ion motion in phase space, rendering displacement forces that are nonlinear in the spin operators.We formulate a simple framework that enables a systematic and faithful construction of high-order spin Hamiltonians and gates, including the effect of multiple modes of motion, and characterize the performance of such operations under realistic conditions.