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arXiv:2007.10437 · Quantum Science and Technology

Tunable transverse spin–motion coupling for quantum information processing

Adam West, Randall Putnam, Wesley C. Campbell, Paul Hamilton

Published Nov 18, 2020• 16 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/2058-9565/abcb5d

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•Jan 1, 2014•1 citation
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.
Using a structured light beam carrying orbital angular momentum, we demonstrate excitation of the center-of-mass motion of a single atom in the transverse direction to the beam's propagation. This interaction enables quantum control of atomic motion in all axes with a single beam direction, which leads to applications in quantum computing and simulations with ion crystals. Here we demonstrate all the key features required for these applications, namely, coherent dynamics and strong carrier suppression in a configuration with the ion centered in the beam, which allows for single ion addressing and also provides robustness against pointing instabilities. To quantify transverse momentum transfer, we observe coherent dynamics on the sidebands of the S_{1/2} to D_{5/2} transition near 729 nm of a singly charged ^{40}Ca^{+} ion, cooled near the ground state of motion in the 3D harmonic potential of a Paul trap, and placed at the center of a first-order Laguerre-Gaussian beam. Exchange of quanta in the perpendicular direction to the beam's wave vector k is observed with a centered vortex shaped beam, together reduction of the parasitic carrier excitation by a factor of 40. This is in sharp contrast to the vanishing spin-motion coupling at the center of the Gaussian beam. Further, we characterize the coherent interaction by an effective transverse Lamb-Dicke factor η_{⊥}^{exp}=0.0062(5) which is in agreement with our theoretical prediction η_{⊥}^{theo}=0.0057(1).
The construction of entangling gates with individual addressing capability represents a crucial approach for implementing quantum computation in trapped-ion crystals. Conventional entangling gate schemes typically rely on laser beam wave vectors to couple the ions' spin and motional degrees of freedom. Here, we experimentally demonstrate an alternative method that employs a polarization gradient field generated by a tightly focused laser beam-an approach theoretically proposed as the Magnus effect for quantum logic gate design [Mazzanti et al., Phys. Rev. Res. 5, 033036 (2023)PPRHAI2643-156410.1103/PhysRevResearch.5.033036]. Using this technique, we perform Raman operations on hyperfine qubits encoded in ^{171}Yb^{+} ions, generating spin-dependent forces along axial motional modes in a linear trap. By utilizing an acousto-optic deflector to create arbitrary spot pairs for individual ion addressing in two-ion (four-ion) chains, we achieve Mølmer-Sørensen gates with Bell-state fidelities exceeding 98.7(1)% [and 97.2(4)%]. Further improvements in numerical aperture (NA) and laser power could reduce gate durations while enhancing fidelity by orders of magnitude. This method is compatible with-and can significantly simplify-optical tweezer gate proposals, where motional mode engineering enables scalable trapped-ion quantum computation. The technique can be readily extended to two-dimensional ion crystals, representing a key advancement toward large-scale trapped-ion quantum processors.
Spectral crowding of collective motional modes limits the fidelity of entangling interactions in trapped-ion quantum processors by inducing off-resonant coupling to spectator modes. We introduce a geometric-phase entangling interaction driven by a transverse, time-dependent structured-light force. By applying the force in a plane orthogonal to the optical propagation direction, we reduce the effects of spectral crowding while preserving single-ion addressing. The scheme is compatible with arbitrary qubit encodings, provided that the qubit states experience a differential AC Stark shift. We experimentally realise high-fidelity two-qubit gates with error rates below 5×10−35\times10^{-3}5×10−3 in ion crystals containing up to 12 ions confined within a single potential well. These results establish gradient-field light-shift gates as a scalable approach to high-fidelity entangling generation in spectrally crowded trapped-ion systems.
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.
We directly observe and spatially map an optical analog of the Magnus effect, where intrinsic spin-orbit-like coupling of light generates a spin-dependent transverse displacement of the atom-light interaction profile for a 40^{40}40Ca+^++ ion. Probed on a quadrupole transition using a tightly focused beam, we observe displacements of the maximum in the profile of the effective interaction by several 100 nm originating from intrinsic longitudinal electric field components beyond the paraxial approximation. The tight focus of the beam induces additional transverse polarization gradients, which we characterize through a phase-sensitive measurement and spatial maps for different beam configurations. The results establish the physical basis of polarization-gradient interactions relevant to optical tweezer-based quantum control.
Trapped atomic ion systems are currently the most advanced platform for quantum information processing. Their long coherence times, pristine state initialization and detection, and precisely controllable and versatile interactions make them excellent quantum systems for experiments in quantum computation and quantum simulation. One of the more promising schemes for quantum computing consists of performing single and multi-qubit quantum gates on qubits in a linear ion crystal. Some of the key challenges of scaling such a system are the individual addressing of arbitrary subsets of ions and controlling the growing complexity of motional mode interactions as the number of qubits increases or when the gates are performed faster. Traditional entangling quantum gates between ion qubits use laser pulses to couple the qubit states to the collective motion of the crystal, thereby generating a spin-spin interaction that can produce entanglement between selected qubits. The intrinsic limitations on the performance of gates using this method can be alleviated by applying optimally shaped pulses instead of pulses with constant amplitude. This thesis explains the theory behind this pulse shaping scheme and how it is implemented on a chain of Yb ions held in a linear radiofrequency `Paul' trap. Several experiments demonstrate the technique in chains of two, three, and five ions using various types of pulse shapes. A tightly focused individual addressing beam allows us to apply the entangling gates to a target pair of ions, and technical issues related to such tight focusing are discussed. Other advantages to the pulse shaping scheme include a robustness against detuning errors and the possibility of suppressing undesirable coupling due to optical spillover on neighboring ions. Combined with ion shuttling, we harness these features to perform sequential gates to different qubit pairs in order to create genuine tripartite entangled states and demonstrate the programmable quantum information processing capability of our system.