Easy as XYZ: exploring non-commuting coherent interactions in trapped ions

Thesis

Developing coherent control operations to precisely achieve desired unitary evolutions is central to various fields of quantum science. For example, these operations are crucial for creating multi-qubit entangling operations and designing tailored, tunable Hamiltonians for analogue quantum simulations. This challenge is compounded by the fact that the systems in question are neither ideal nor isolated, and they frequently suffer from unavoidable spurious interactions.

A common source of errors in coherent operations typically stems from incoherent processes, where the system interacts with the environment. However, as interaction durations decrease, these become negligible and coherent errors begin to dominate the behaviour of the system. Among these, the most challenging to deal with are errors that do not commute with the main interaction. We investigate such errors within the spin-oscillator system of a trapped ion. For example, in the Mølmer-Sørensen entangling gate operation, the travelling wave fields that generate the essential spin-motion coupling also induce an off-resonant non-commuting carrier term. This term introduces errors in the entanglement operation. To address this, we introduce control over the optical phase of the laser field by using a standing wave, whose position we stabilise to λ/100 with respect to the ion. This allows us to gain control over the phase degree of freedom of the laser-ion interaction, enabling us to circumvent the non-commutativity and suppress the strength of the problematic carrier term by a factor of 18.

Conversely, non-commuting interactions can also be advantageous, enabling the creation of novel, effective interactions when the appropriate control is employed. By combining two spin-dependent forces that do not commute, we demonstrate a method to generate nonlinear interactions in the motion of an ion with favourable scaling. Unlike conventional methods that rely on higher orders of the Lamb-Dicke parameter expansion, our approach achieves linear scaling with the increase in interaction order. Specifically, we focus on generalised squeezing interactions and experimentally demonstrate squeezing (second order), trisqueezing (third order), and quadsqueezing (fourth order). The quadsqueezing achieved is over 100 times stronger than that possible with conventional methods and, to the best of our knowledge, represents the first implementation of fourth-order generalised squeezing across any platform. Our method does not impose a fundamental limit on the interaction order and is universally applicable to any platform that supports spin-dependent linear interactions.

Authors: Băzăvan, O

• DOI: 10.5287/ora-mzgkqerrx
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: non-commuting interactions; squeezing; nonlinear interactions; trapped ions; standing waves; coherent control
• Subjects: Quantum computing; Trapped ions