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arXiv:1609.05602 · Physical Review A

Emergence of singularities from decoherence: Quantum catastrophes

Aaron Z. Goldberg, Asma Al-Qasimi, J. Mumford, Duncan H J O’Dell

Published Dec 16, 2019• 11 citations
arXivHTMLPDF

Abstract

Dynamics of two coupled macroscopic quantum systems subject to a weak continuous measurement is studied using a master equation approach and compared with classical and quantum solutions for the equivalent closed systems. Decoherence in such systems can lead to singularities in the form of caustics. The authors show that continuous weak measurements do not lead to the closed classical result and instead measurement backaction introduces noise that softens the singularities.

DOI
10.1103/physreva.100.063628

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Dynamics of two coupled macroscopic quantum systems subject to a weak continuous measurement is studied using a master equation approach and compared with classical and quantum solutions for the equivalent closed systems. Decoherence in such systems can lead to singularities in the form of caustics. The authors show that continuous weak measurements do not lead to the closed classical result and instead measurement backaction introduces noise that softens the singularities.
We study the effect of decoherence on a weak value measurement in a paradigm system consisting of a double quantum dot continuously measured by a quantum point contact. Fluctuations of the parameters controlling the dot state induce decoherence. We find that, for measurements longer than the decoherence time, weak values are always reduced within the range of the eigenvalues of the measured observable. For measurements at shorter time scales, the measured weak value strongly depends on the interplay between the decoherence dynamics of the system and the detector backaction. In particular, depending on the postselected state and the strength of the decoherence, a more frequent classical readout of the detector might lead to an enhancement of weak values.
We derive a stochastic master equation (SME) which describes the decoherence dynamics of a system in spin environments conditioned on the measurement record. Markovian and non-Markovian nature of environment can be revealed by a spectroscopy method based on weak continuous quantum measurement. On account of that correlated environments can lead to a non-local open system which exhibits strong non-Markovian effects although the local dynamics are Markovian, the spectroscopy method can be used to demonstrate that there is correlation between two environments.
Mesoscopic physics considers systems of appropriate size and at time scales of the order of decoherence time, which allows us to analyse the transformation of information from a quantum state to a classical signal, occurring in a process of quantum measurement. We concentrate on the limiting cases of weak and strong coupling between a mesoscopic source of noise and a subsystem functioning as a detector. In the ``weak coupling'' part we elaborate on the idea of cross-correlation measurements for quantum noise detection and develop a set of original methods to tackle the perturbation theory up to fourth order. In the ``strong coupling'' part we provide an exact solution for one-dimensional system out of equilibrium, strongly interacting with a localized state and predict some remarkable experimentally verifiable features, such as Fermi-edge singularity in the noise induced transition rates and unusually pronounced manifestation of non-Gaussian noise effects.
Abstract All quantum systems are subject to noise and imperfections due to stray fields, inhomogeneities or drifting experimental controls. An understanding of the effects of noise and decoherence is critical to the progress towards fully functional quantum devices. In this perspective, we focus on noise in quantum systems which are modelled by a dynamic stochastic parameter in the Hamiltonian. We will outline exact evolution equations describing the ensemble average dynamics for a variety of common noise types and their connections. We will also highlight an approximate evolution equation valid in the weak noise limit for an arbitrary classical stochastic field. This framework should serve as a starting point for identifying signatures of differing noise types and optimisation of robust control protocols.
We develop a new master equation as a unified description of the effects of both quantum noise (system-bath interaction) and classical noise on a system's dynamics, using a two-dimensional series expansion method. When quantum and classical noises are both present, their combined effect on a system's dynamics is not necessarily a simple sum of the two individual effects. Thus previous master equations for open systems and those for classical noise, even when jointly used, may not capture the full physics. Our formalism can determine whether there is interference between quantum and classical noises and will be able to capture and describe such interference if there is any (in a perturbative manner). We find that, interestingly, second-order interference between quantum and classical noises vanishes identically. This work thus also serves to justify simple additive treatments of quantum and classical noises, especially in the weak coupling regime. For a Zeeman-splitted atom in a stochastic magnetic field interacting with an optical cavity, we use the formalism developed herein to find the overall decoherence rate between the atom's energy levels.