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Physical Review Letters

Indirect Phase Detection of NMR Spinor Transitions

Dieter Suter, Alexander Pines, M. Mehring

Published Jul 14, 1986• 23 citations
Publisher

Abstract

The behavior of quantum mechanical state functions under selective rotations is discussed. If a two-level transition is phase shifted with composite $z$ pulses, the component state function shared with a connected transition can be multiplied by $i$, thereby shifting the corresponding coherence into an orthogonal channel. Application to the sensitive indirect detection of NMR transitions is demonstrated.

DOI
10.1103/physrevlett.57.242

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The behavior of quantum mechanical state functions under selective rotations is discussed. If a two-level transition is phase shifted with composite zzz pulses, the component state function shared with a connected transition can be multiplied by iii, thereby shifting the corresponding coherence into an orthogonal channel. Application to the sensitive indirect detection of NMR transitions is demonstrated.
The components of spinors corresponding to half integral spin value transform under rotation of the spatial coordinate system with a matrix of even dimensionality. This leads to a state function phase factor with period 4π rad in the rotation angle. A spectroscopic interference experiment to observe such phase factors is described in analogy with double-beam interferometry. The experiment is performed with the techniques of high resolution nuclear magnetic resonance spectroscopy and the rotational symmetry of composite spin [Formula: see text], 1, and [Formula: see text] particles is explored by calculation and observation. Side effects relating to inhomogeneity dephasing and relaxation are evident in the experimental recordings, but they are discussed only briefly. A relation is established between the spectroscopic interference experiment and earlier "spin tickling" experiments.
A family of double-quantum excitation schemes is described for the solution nuclear magnetic resonance (NMR) of near-equivalent spin-1/2 pairs. These new methods exploit the spinor behaviour of 2-level systems, whose signature is the change of sign of a quantum state upon a 2π2π2π rotation. The spinor behaviour is used to manipulate the phases of single-quantum coherences, in order to prepare a double-quantum precursor state which is rapidly converted into double-quantum coherence by a straightforward π/2π/2π/2 rotation. One set of spinor-based methods exploits symmetry-based pulse sequences, while the other set exploits SLIC (spin-lock-induced crossing), in which the nutation frequency under a resonant radiofrequency field is matched to the spin-spin coupling. A variant of SLIC is introduced which is well-compensated for deviations in the radiofrequency field amplitude. The methods are demonstrated by performing double-quantum-filtered 19^{19}19F NMR on a molecular system containing a pair of diastereotopic 19^{19}19F nuclei. The new methods are compared with existing techniques.
Quantum entanglement has long been recognized as an important resource for quantum sensing. In this work, we demonstrate the use of multiple-quantum solid-state NMR for quantum sensing by creating, manipulating, and detecting large clusters of correlated nuclear spins. We show that such clusters can sensitively detect pulse-width jitters in radio-frequency control fields at the level of tens of nanoseconds. By analyzing the response of high-order quantum coherences to these control-field jitters, we investigate the critical interplay between the enhanced sensitivity offered by large coherence orders, their relative distributions, and their varying susceptibility to decoherence. We further demonstrate that, even within a non-uniform distribution of coherence orders, there exists an optimal maximum coherence order that maximizes sensing efficiency. To support our interpretation, we supplement the experimental results with a simplified numerical model that estimates the corresponding quantum Fisher information. These results support the solid-state NMR platform as a valuable testbed for investigating many-body quantum metrology protocols.
The question of whether a molecule can be made to absorb and emit photons only in groups of n is treated. Pulse sequences are introduced which in effect selectively induce the absorption of only groups of n photons. This causes only n-quantum transitions even when many other transitions might be resonant. The technique involves repeated phase shifts of 2π/n in the radiation to build up the selected coherences and cancel all other coherences, and is applicable to a wide range of spectroscopic systems. Coherent averaging theory is extended to describe selective sequences and demonstrates that n-quantum selectivity is possible to arbitrarily high order in the average Hamiltonian expansion. High-order selectivity requires many phase shifts, however, and for this reason the residual nonselective effects of sequences which are selective to only a finite order are calculated. Selective sequences are applied to the multiple-quantum NMR of oriented molecules, where in combination with time reversal sequences they produce a much more efficient transfer of the population differences into selected coherences than is obtainable by normal wideband pumping. For example, the 10-quantum transition in a 10-spin system can be enhanced by more than four orders of magnitude. Experiments on selective excitaiton of the 4-quantum transitions in oriented benzene verify the expected enhancement.
The interference effect between the neutron spinor components is investigated. It is shown that the diffusion of the neutron wave-packet under an unhomogeneous magnetic field is related to the phase shift angle between the two spinor components. We propose that this effect could be used to detect the phase-shift of a coherent neutron beam having passed through some medium. In the interference experiment based upon this principle one will not need to use Bragg reflection from crystal planes for splitting and recombining the beam, and the dimension of the phase shift region will be much longer than that of the usual Bonse-Kart type neutron interferometer.