Standing-wave Mølmer-Sørensen gates on a quadrupole transition*

Free-space standing waves (SW) are ubiquitous in atomic physics and are often employed for creating spin-dependent forces used for entangling gate operations and neutral atom trapping. Recently, there has been an interest in gaining control over the phase of the SW at the position of trapped ions [1] due to promising applications in quantum metrology, quantum information processing with continuous variables [2] and quantum simulations [3]. In our experiment, we make use of a phase-stabilised SW to coherently suppress a non-computing error source in the conventional Mølmer-Sørensen (MS) interaction.

The SW is formed by two superimposing counter-propagating beams that couple to the quadrupole qubit transition, 5S_1/2 ←→ 4D_5/2, in ⁸⁸Sr⁺. The two beams form an optical interferometer whose arm length is actively stabilised, allowing the precise control of the phase of the SW at the position of the ion. Placing the ions at the antinodes of the SW strongly suppresses the carrier coupling while maximising the motional coupling [4]. We demonstrate and characterise both single- and two-qubit gates with the SW and show how using a SW allows us to surpass the fundamental speed limit present in MS gates. 

[1] C. T. Schmiegelow et al., Phys. Rev. Lett., 116, p.033002, (2016)

[2] M. Drechsler et al., Phys. Rev. A, 101, p.052331 (2020)

[3] T. E. deLaubenfels et al. Phys. Rev. A, 92, p.061402 (2015)

[4] A. Mundt et al., Phys. Rev. Lett., 89, p.103001 (20