Noninvasive measurement of dynamic correlations in spin systems

[摘要] ENGLISH ABSTRACT : Dynamic correlations hψ| O1(t1)O2(t2)|ψi of quantum observables are useful quantitiesfor the study of quantum dynamics. Attempts at measuring these correlationsare however complicated, due to the measurement backaction (wave function collapse)incurred during measurements at the early time t1. We propose a noninvasivemeasurement protocol, based on a weak ancilla target coupling, which reduces thisbackaction at t1. We show that both real and imaginary parts of the desired correlationcan be extracted through appropriate choices of the initial ancilla state andof the ancilla target coupling Hamiltonian. The protocol is applicable to arbitrary(pseudo)spin systems with arbitrary (non)equilibrium initial states. Errors arisingin experimental implementations are analysed, and we show that deviations fromthe 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 noninvasivemeasurement at t1. For dynamic correlations of single-site spin-1/2 observables, thisoperator formalism shows that measurement backaction is of no concern. Real partscan be obtained with projective measurements of the target at t1 and t2. Imaginaryparts are obtained by performing a local rotation of the target at t1, followedby a projective measurement at t2. These ancilla-free protocols are theoreticallysimpler than the noninvasive measurement protocol, but remain experimentallychallenging. Rotations and projections performed at t1 may be subject to noise,which propagates into the measured correlation. We use Lieb-Robinson theory tobound the size of the resulting error terms. An analysis of the spatio-temporalbehaviour of these errors provides guidance for experimental implementation of theancilla-free measurement protocols.

[发布机构] Stellenbosch University