Trapped-Ion Spin-Motion Coupling with Microwaves and a Near-Motional Oscillating Magnetic Field Gradient

Abstract

We present a new method of spin-motion coupling for trapped ions using microwaves and a magnetic field gradient oscillating close to the ions' motional frequency. We demonstrate and characterize this coupling experimentally using a single ion in a surface-electrode trap that incorporates current-carrying electrodes to generate the microwave field and the oscillating magnetic field gradient. Using this method, we perform resolved-sideband cooling of a single motional mode to its ground state.

Microwaves in Quantum Computing

“…For magnetic-field-sensitive qubits, an applied magnetic field gradient along the ion string causes each ion to have a separate qubit frequency, so that frequency domain addressing is possible [ 57 ]. Alternatively, focused laser beams, or microwave field gradients from near-field electrodes, can be used for individual addressing by creating differential Rabi frequencies or differential qubit frequencies on multiple ions, among other techniques [ 58 ]–[ 61 ]. These latter methods can be used on both field-sensitive and field-insensitive (clock) qubits.…”

“…Therefore, physical Z rotations are typically implemented by compiling them to XY gates, applying ac Stark shifts to the ions using detuned laser beams, or applying ac Zeeman shifts to the ions using detuned microwave or rf magnetic fields. Individually addressed Z rotations can be applied using focused laser beams to shift only specific ions, or by using a gradient of an rf/microwave magnetic field [ 60 ], [ 64 ]. These techniques have the added benefit that they can be applied to hyperfine clock qubits as well.…”

“…The magnetic field gradient of free-space microwaves near ω 01 (usually a few GHz) is very small over this length scale. However, microwave magnetic fields with negligible gradient strength can be combined with additional static [ 71 ], [ 72 ] or few-MHz [ 64 ], [ 73 ] magnetic field gradients to produce the desired spin-motion coupling. Magnetic field gradients at microwave frequencies near ω 01 , or near resonance with the ion motional frequency, can also be used for spin-motion coupling and entangling gates [ 10 ], [ 74 ].…”

“…A number of experimental demonstrations of high-fidelity microwave-based entangling gates between ions have been carried out [ 61 ], [ 77 ]–[ 80 ]. In general, these gates are slower (~ ms duration) than laser-based entangling gates, which can be performed in tens or hundreds of μ s (and some as fast as a few μ s [ 81 ]).…”

Universal hybrid quantum computing in trapped ions

“…Such phase-gate interactions are typically used in trapped-ion experiments to generate entanglement with or without lasers. We also show that this scheme can be implemented in a laser-free experiment with a single radiofrequency gradient [20,38,39]. We consider a single spin, with states |↓ and |↑ , whose interaction is represented by Pauli operators σα , where α ∈ {x, y, z}.…”