Noninvasive measurement of dynamic correlations in spin systems

Uhrich, Philipp Johann (2017-12)

Thesis (MSc)--Stellenbosch University, 2017

Thesis

ENGLISH ABSTRACT : Dynamic correlations hψ| O1(t1)O2(t2)|ψi of quantum observables are useful quantities for the study of quantum dynamics. Attempts at measuring these correlations are however complicated, due to the measurement backaction (wave function collapse) incurred during measurements at the early time t1. We propose a noninvasive measurement protocol, based on a weak ancilla target coupling, which reduces this backaction at t1. We show that both real and imaginary parts of the desired correlation can be extracted through appropriate choices of the initial ancilla state and of the ancilla target coupling Hamiltonian. The protocol is applicable to arbitrary (pseudo)spin systems with arbitrary (non)equilibrium initial states. Errors arising in experimental implementations are analysed, and we show that deviations from the desired correlation can be minimised through an optimal choice of the ancilla target coupling time. Implementation in linear ion trap experiments is discussed. We derive the positive-operator-valued measure which describes the noninvasive measurement at t1. For dynamic correlations of single-site spin-1/2 observables, this operator formalism shows that measurement backaction is of no concern. Real parts can be obtained with projective measurements of the target at t1 and t2. Imaginary parts are obtained by performing a local rotation of the target at t1, followed by a projective measurement at t2. These ancilla-free protocols are theoretically simpler than the noninvasive measurement protocol, but remain experimentally challenging. Rotations and projections performed at t1 may be subject to noise, which propagates into the measured correlation. We use Lieb-Robinson theory to bound the size of the resulting error terms. An analysis of the spatio-temporal behaviour of these errors provides guidance for experimental implementation of the ancilla-free measurement protocols.

AFRIKAANSE OPSOMMING : Dinamiese korrelasies hψ| O1(t1)O2(t2)|ψi van kwantum waarneembares is nuttig in die studie van kwantum dinamika. Die meting van hierdie hoeveelhede word egter gekompliseer deur die meetingsterugreaksie (gol unksie ineenstorting), wat tydens die meting by die vroeër tyd t1 plaasvind. Ons stel 'n nie-ingrypende metingsprotokol voor, gebaseer op 'n swak ancilla teikenstelsel koppeling, wat die meetingsterugreaksie by t1 verminder. Ons toon dat die reële en imaginêre dele van die korrelasiefunksie deur geskikte keuses van die ancilla begintoestand en van die ancilla teikenstelsel koppeling bepaal kan word. Die protokol is van toepassing op (pseudo)spin stelsels met arbitrêre nie-ewewig begintoestande. Foute wat in eksperimentele implementering ontstaan word geanaliseer. Ons toon dat afwykings van die gewenste korrelasie geminimeer kan word deur 'n optimale ancilla teikenstelsel koppelingstyd. Implementering in liniêre ioonputte word bespreek. Ons herlei die positiewe operator-waardige maat wat die nie-ingrypende meting by t1 beskryf. Hierdie formalisme toon dat die meetingsterugreaksie van geen belang is vir dinamiese korrelasies van enkelpunt spin-1/2 waarneembares nie. Die reële deel kan deur projektiewe meetings by t1 en t2 bepaal word. Die imaginêre deel word verkry deur 'n lokale rotasie by t1, gevolg deur 'n projektiewe meting by t2. Hierdie ancilla-vrye protokolle is teoreties eenvoudiger as die nie-ingrypende metingsprotokol, maar eksperimentele implementering bly uitdagend. Rotasies en projeksies wat by t1 uitgevoer word kan onder steurings ly, wat dan ook die gemete korrelasies a ekteer. Ons gebruik Lieb-Robinson teorie om die grootte van die resulterende foute te begrens. 'n Analise van die foute se tyd en ruimtelike gedrag bied leiding vir die eksperimentele implementering van die ancilla-vrye metingsprotokolle

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/102742
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