Realization of near-deterministic arithmetic operations and quantum state engineering

TL;DR

This paper demonstrates near-deterministic, robust quantum addition and subtraction of phonons in a trapped ion system, enabling classical arithmetic operations and quantum state engineering through hybrid quantum-classical computation.

Contribution

It introduces a method to perform conventional phonon addition and subtraction in a trapped ion, bridging classical arithmetic with quantum state manipulation.

Findings

Operations are nearly deterministic and robust against parameter variations.

Able to transform classical states into nonclassical states with sub-Poissonian statistics.

Demonstrates non-commutativity of Susskind-Glogower phase operators.

Abstract

Quantum theory is based on a mathematical structure totally different from conventional arithmetic. Due to the symmetric nature of bosonic particles, annihilation or creation of single particles translates a quantum state depending on how many bosons are already in the given quantum system. This proportionality results in a variety of non-classical features of quantum mechanics including the bosonic commutation relation. The annihilation and creation operations have recently been implemented in photonic systems. However, this feature of quantum mechanics does not preclude the possibility of realizing conventional arithmetic in quantum systems. We implement conventional addition and subtraction of single phonons for a trapped \Yb ion in a harmonic potential. In order to realize such operations, we apply the transitionless adiabatic passage scheme on the anti-Jaynes-Cummings coupling between the internal energy states and external motion states of the ion. By performing the operations on superpositions of Fock states, we realize the hybrid computation of classical arithmetic in quantum parallelism, and show that our operations are useful to engineer quantum states. Our single-phonon operations are nearly deterministic and robust against parameter changes, enabling handy repetition of the operations independently from the initial state of the atomic motion. We demonstrate the transform of a classical state to a nonclassical one of highly sub-Poissonian phonon statistics and a Gaussian state to a non-Gaussian state, by applying a sequence of the operations. The operations implemented here are the Susskind-Glogower phase operators, whose non-commutativity is also demonstrated.