Time-dependent Hamiltonian estimation for Doppler velocimetry of trapped ions

TL;DR

This paper presents an experimental method to estimate a time-dependent Hamiltonian of a single qubit in a trapped ion system, enabling better control and understanding of quantum dynamics.

Contribution

The authors develop and demonstrate a novel technique for estimating time-dependent Hamiltonians using measurements of a single trapped ion's evolution.

Findings

Successfully estimated the spatial dependence of laser intensity.

Determined the ion's velocity as a function of time.

Enhanced control in ion transport and quantum gate operations.

Abstract

The time evolution of a closed quantum system is connected to its Hamiltonian through Schroedinger's equation. The ability to estimate the Hamiltonian is critical to our understanding of quantum systems, and allows optimization of control. Though spectroscopic methods allow time-independent Hamiltonians to be recovered, for time-dependent Hamiltonians this task is more challenging. Here, using a single trapped ion, we experimentally demonstrate a method for estimating a time-dependent Hamiltonian of a single qubit. The method involves measuring the time evolution of the qubit in a fixed basis as a function of a time-independent offset term added to the Hamiltonian. In our system the initially unknown Hamiltonian arises from transporting an ion through a static, near-resonant laser beam. Hamiltonian estimation allows us to estimate the spatial dependence of the laser beam intensity and the ion's velocity as a function of time. This work is of direct value in optimizing transport operations and transport-based gates in scalable trapped ion quantum information processing, while the estimation technique is general enough that it can be applied to other quantum systems, aiding the pursuit of high operational fidelities in quantum control.