Nonlinear Spectroscopy of Trapped Ions

TL;DR

This paper develops a diagrammatic nonlinear spectroscopy method for trapped ions, enabling scalable analysis of excitation dynamics, steady state currents, and quantum chaos signatures in large many-body quantum systems.

Contribution

It introduces a novel diagrammatic approach for nonlinear measurement protocols applicable to controlled quantum systems like trapped ions, overcoming size limitations of traditional methods.

Findings

Protocols can probe steady state currents

Detect influence of anharmonicities on phonon transport

Identify signatures of chaotic dynamics near quantum phase transitions

Abstract

Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and has become a highly successful method for experiments in chemical physics. Current quantum optical experiments approach system sizes and levels of complexity which require the development of efficient techniques to assess spectral and dynamical features with scalable experimental overhead. However, established methods from optical spectroscopy of macroscopic ensembles cannot be applied straightforwardly to few-atom systems. Based on the ideas proposed in [M. Gessner et al. New J. Phys. 16 092001 (2014)], we develop a diagrammatic approach to construct nonlinear measurement protocols for controlled quantum systems and discuss experimental implementations with trapped ion technology in detail. These methods in combination with distinct features of ultra-cold matter systems allow us to monitor and analyze excitation dynamics in both the electronic and vibrational degrees of freedom. They are independent of system size, and can therefore reliably probe systems where, e.g., quantum state tomography becomes prohibitively expensive. We propose signals that can probe steady state currents, detect the influence of anharmonicities on phonon transport, and identify signatures of chaotic dynamics near a quantum phase transition in an Ising-type spin chain.