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arXiv:quant-ph/0701056 · New Journal of Physics

Experimental demonstration of a stimulated polarization wave in a chain of nuclear spins

Jae‐Seung Lee, Travis Adams, Anatoly K. Khitrin

Published Apr 4, 2007• 15 citations
arXivHTMLPDF

Abstract

A stimulated wave of polarization, which implements a simple mechanism of quantum amplification, is experimentally demonstrated in a chain of four J -coupled nuclear spins, irradiated by a weak radio-frequency transverse field. The 'quantum domino' dynamics, a wave of flipped spins triggered by a flip of the first spin, has been observed in fully 13 C-labelled sodium butyrate.

DOI
10.1088/1367-2630/9/4/083

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A stimulated wave of polarization, which implements a simple mechanism of quantum amplification, is experimentally demonstrated in a chain of four J -coupled nuclear spins, irradiated by a weak radio-frequency transverse field. The 'quantum domino' dynamics, a wave of flipped spins triggered by a flip of the first spin, has been observed in fully 13 C-labelled sodium butyrate.
Stimulated wave of polarization, triggered by a flip of a single spin, presents a simple model of quantum amplification. Previously, it has been found that such a wave can be excited in a one-dimensional Ising chain with nearest-neighbor interactions, irradiated by a weak resonant transverse field. Here we explore models with more realistic Hamiltonians, in particular, with natural dipole-dipole interactions. Results of simulations for one-dimensional spin chains and rings with up to nine spins are presented.
Radio wave amplification by stimulated emission of radiation (NMR laser) was observed in Al2{\mathrm{Al}}_{2}Al2​O3{\mathrm{O}}_{3}O3​: Cr3+{\mathrm{Cr}}^{3+}Cr3+ (ruby) with the 27Al^{27}\mathrm{Al}27Al spin system pumped to an inverted Zeeman state by means of dynamic nuclear polarization (DNP) and with an LC circuit tuned to the NMR transitions. A theory is developed which combines standard Bloch equations with the dynamic equations of a heat-reservoir model for the spin dynamics. Experimental data concerning the relaxation and polarization mechanisms in the nonradiant state are presented, and the parameters of the reservoir model are determined. In accord with these results, dynamic NMR laser equations for different modes of operation (continuous or pulsed) are derived from which the threshold of the NMR laser, its critical behavior near threshold, and its transient response after QQQ-switch tuning can be calculated. The agreement between theory and experiments in the superradiant state reflects unambiguously the interplay between nuclear-spin relaxation, DNP, spin fluctuations, and the self-induced ordering of the 27Al^{27}\mathrm{Al}27Al spins perpendicular to the applied field. In particular, the results highlight the decisive role of the electronic dipole-dipole system in the spin and NMR laser dynamics of ruby. Special emphasis is placed on the close relationship between the NMR laser, as a system far from thermal equilibrium which shows the phenomenon of cooperative self-organization, and a system at thermal equilibrium which undergoes a second-order phase transition. Thus, the rotating nuclear-spin magnetization is treated as an order parameter.
We report the observation of a coherent, maser-type rf radiation of the 27Al^{27}\mathrm{Al}27Al nuclear-spin system in Al2{\mathrm{Al}}_{2}Al2​O3{\mathrm{O}}_{3}O3​: Cr3+{\mathrm{Cr}}^{3+}Cr3+ pumped by dynamic nuclear polarization to negative temperature. A theoretical description is presented for the sharp, superradiant bursts which follow the fast tuning of a resonant LC\mathrm{LC}LC circuit to a selected NMR line of 27Al^{27}\mathrm{Al}27Al. Experimental results are discussed which demonstrate the interplay between dynamic nuclear polarization, relaxation, and the radiation field.
We study control of electron-nuclear spin dynamics at magnetic field strengths where the Larmor frequency of the nucleus is comparable to the hyperfine coupling strength. The quantization axis for the nuclear spin differs from the static B0{B}_{0}B0​ field direction and depends on the state of the electron spin. The quantization axis can be switched by flipping the state of electron spin, allowing for universal control of nuclear spin states. We show that by performing a sequence of flips (each followed by a suitable delay), we can perform any desired rotation of the nuclear spin, which can also be conditioned on the state of the electron spin. These operations, combined with electron spin rotations, can be used to synthesize any unitary transformation of the coupled electron-nuclear spin system. We discuss how these methods can be used for design of experiments for transfer of polarization from the electron to the nuclear spins.
Electron and nuclear spins have been employed in many of the early demonstrations of quantum technology. However, applications in real world quantum technology are limited by the difficulty of measuring single spins. Here we show that it is possible to rapidly and robustly amplify a spin state using a lattice of ancillary spins. The model we employ corresponds to an extremely simple experimental system: a homogenous Ising-coupled spin lattice in one, two, or three dimensions, driven by a continuous microwave field. We establish that the process can operate at finite temperature (imperfect initial polarization) and under the effects of various forms of decoherence.