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arXiv:0905.0225 · Physical Review Letters

Entanglement and Tunable Spin-Spin Couplings between Trapped Ions Using Multiple Transverse Modes

Kihwan Kim, M.-S. Chang, Rajibul Islam, S. É. Korenblit, L.-M. Duan, Christopher R. Monroe

Published Sep 16, 2009• 324 citations
arXivHTMLPDF

Abstract

We demonstrate tunable spin-spin couplings between trapped atomic ions, mediated by laser forces on multiple transverse collective modes of motion. A sigma_{x}sigma_{x}-type Ising interaction is realized between quantum bits stored in the ground hyperfine clock states of ;{171}Yb;{+} ions. We demonstrate entangling gates and tailor the spin-spin couplings with two and three trapped ions. The use of closely spaced transverse modes provides a new class of interactions relevant to quantum computing and simulation with large collections of ions in a single crystal.

DOI
10.1103/physrevlett.103.120502

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We demonstrate tunable spin-spin couplings between trapped atomic ions, mediated by laser forces on multiple transverse collective modes of motion. A sigma_{x}sigma_{x}-type Ising interaction is realized between quantum bits stored in the ground hyperfine clock states of ;{171}Yb;{+} ions. We demonstrate entangling gates and tailor the spin-spin couplings with two and three trapped ions. The use of closely spaced transverse modes provides a new class of interactions relevant to quantum computing and simulation with large collections of ions in a single crystal.
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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.
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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.
Abstract Laser-controlled entanglement between atomic qubits (‘spins’) and collective motion in trapped ion Coulomb crystals requires conditional momentum transfer from the laser. Since the spin-dependent force is derived from a spatial gradient in the spin–light interaction, this force is typically longitudinal—parallel and proportional to the average laser k -vector (or two beams’ k -vector difference), which constrains both the direction and relative magnitude of the accessible spin–motion coupling. Here, we show how momentum can also be transferred perpendicular to a single laser beam due to the gradient in its transverse profile. By controlling the transverse gradient at the position of the ion through beam shaping, the relative strength of the sidebands and carrier can be tuned to optimize the desired interaction and suppress undesired, off-resonant effects that can degrade gate fidelity. We also discuss how this effect may already be playing an unappreciated role in recent experiments.
We present a scheme of quantum simulation of many-body interactions with trapped ions via the exchange of virtual phonons, where the motion from both the longitudinal and the transverse directions is considered. By tuning the detunings of Raman lasers, the long-range and locally tunable interaction is easily obtained between different spins. We show that the competing spin-spin couplings mediated by all motion modes can give rise to higher levels of frustration and richer phase transitions than the conventional approaches based on the longitudinal or the transverse phonon modes alone.