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arXiv:2312.13214 · Physics Letters A

A pedagogical introduction to continuously monitored quantum systems and measurement-based feedback

Francesco Albarelli, Marco G. Genoni

Published Dec 12, 2023• 26 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2023.129260

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Off-resonant optical imaging is a popular method for continuous monitoring of a Bose–Einstein condensate. However, the disturbance caused by scattered photons places a serious limitation on the lifetime of such continuously monitored condensates. In this paper, we demonstrate that a new choice of feedback control can overcome the heating effects of the measurement backaction. In particular, we show that the measurement backaction caused by off-resonant optical imaging is a multi-mode quantum-field effect, as the entire heating process is not seen in single-particle or mean-field models of the system. Simulating such continuously monitored systems is possible with the number-phase Wigner particle filter, which currently gives both the highest precision and largest timescale simulations amongst competing methods. It is a hybrid between the leading techniques for simulating non-equilibrium dynamics in condensates and particle filters for simulating high-dimensional non-Gaussian filters in the field of engineering. The new control scheme will enable long-term continuous measurement and feedback on one of the leading platforms for precision measurement and the simulation of quantum fields, allowing for the possibility of single-shot experiments, adaptive measurements and robust state-preparation and manipulation.
Quantum technology has been rapidly growing due to its potential revolutionary applications. In particular, superconducting qubits provide a strong light-matter interaction as required for quantum computation and in principle can be scaled up to a high level of complexity. However, obtaining the full benefit of quantum mechanics in superconducting circuits requires a deep understanding of quantum physics in such systems in all aspects. One of the most crucial aspects is the concept of measurement and the dynamics of the quantum systems under the measurement process. This document is intended to be a pedagogical introduction to the concept of quantum measurement from an experimental perspective. We study the dynamics of a single superconducting qubit under continuous monitoring. We demonstrate that weak measurement is a versatile tool to investigate fundamental questions in quantum dynamics and quantum thermodynamics for open quantum systems.
We present a formulation of measurement-based feedback control of a single quantum particle in one spatial dimension. An arbitrary linear combination of the position and momentum of the particle is continuously monitored, and feedback proportional to the measured signal is used to control the system. We derive a feedback master equation and discuss a general approach to computing the steady-state solutions for arbitrary potentials. For a quantum harmonic oscillator or a free particle, we show that it is possible to cool and confine the system using feedback that simultaneously damps the measured observable and its conjugate momentum, as well as compensates for noise introduced by the measurement. In addition, we demonstrate that appropriate feedback adds a quadratic term in the measured observable to the Hamiltonian of the system. For the particular case of the harmonic potential, we describe the exact dynamics of the system that can be cooled to the ground state. Moreover, we provide an argument for the possibility to cool systems with arbitrary potentials provided that the measurement is strong enough to localise the particle on an interval smaller than the characteristic length scale of the potential.