Applications of Spin-Dependent Generalized Squeezing in Trapped Ions

Spin-dependent generalized squeezing interactions have recently come under experimental control in trapped ion systems, expanding the trapped-ion toolbox from spin-dependent squeezing to spin-dependent tri-squeezing, quad-squeezing, and arbitary superpositions [1,2]. These interactions represent a new resource for hybrid spin-oscillator quantum computing. In this work, we explore four distinct applications enabled by this resource: (i) fast, squeezing-mediated geometric phase gates between two spins coupled to a single oscillator; (ii) squeezing-mediated thermometry of an oscillator via spin readout; (iii) preparation of high-purity oscillator Fock states via spin-dependent generalized squeezing and projective spin measurements; and (iv) N-body spin interactions mediated by individually addressed spin-dependent generalized squeezing. These applications contribute to the advancement of fast, high-fidelity discrete- and continuous-variable quantum computation and sensing.

[1] O. Băzăvan, S. Saner, et al., arXiv:2403.05471 (2024).

[2] S. Saner, O. Băzăvan, et al., arXiv:2409.03482 (2024).