Classical versus quantum mechanical description of nuclear magnetic resonance

J. Grunzweig-Genossar

R. Lenk

E. Conte

J. Jeener, Françoise Hénin

We show that there is excellent quantitative agreement between the usual semiclassical predictions for nuclear magnetic resonance experiments (quantized spins interacting with a classical radio frequency magnetic field, including radiation damping), and the predictions of a fully quantized description of the same experiment. We also propose a pictorial description of the relevant dynamical quantum states, which helps to lead the intuition towards the same conclusion. Our model ignores spin relaxation, and simulates the equivalent damping resistor of the sample circuit by a very long piece of lossless coaxial cable. The classical rf field (pulses and free induction decay) is described quantum mechanically by means of Glauber’s “coherent” or “quasiclassical” states.

Bogdan A. Rodin, Daniel Abergel

Spin relaxation has been at the core of many studies since the early days of nuclear magnetic resonance (NMR) and the underlying theory worked out by its founding fathers. This Bloch-Redfield-Abraham relaxation theory has been recently reinvestigated () in the perspective of Lindblad theory of quantum Markovian master equations in order to account for situations where the widely used semi-classical relaxation theory breaks down. In this article, we review the conventional approach of quantum mechanical theory of NMR relaxation and show that, under the usual assumptions, it is equivalent to the Lindblad formulation. We also comment on the debate on semi-classical versus quantum versions of spectral density functions involved in relaxation.

Kees van Schenk Brill

This thesis consists of two parts. I describe an approach for a physical realization of a quantum computer by Nuclear Magnetic Resonance (NMR). I propose a new framework for NMR that gives such a physical realization. I construct a quantum mechanical description of NMR from which I can build the fundamental elementary operators for quantum computation. I describe the experiments that build these operators. I give a polynomial time quantum algorithm to solve simultaneous Pell equations as an extension of Hallgren's algorithm for simple Pell equations.