Algorithmic cooling of nuclear spins using long-lived singlet order.

Bogdan A Rodin,Christian Bengs,Lynda J Brown,Malcolm H Levitt,Alexandra V Yurkovskaya,Kirill F Sheberstov,Alexey S Kiryutin,Richard C D Brown,Konstantin L Ivanov

doi:10.1063/5.0006742

Abstract

Algorithmic cooling methods manipulate an open quantum system in order to lower its temperature below that of the environment. We achieve significant cooling of an ensemble of nuclear spin-pair systems by exploiting the long-lived nuclear singlet state, which is an antisymmetric quantum superposition of the "up" and "down" Zeeman states. The effect is demonstrated by nuclear magnetic resonance experiments on a molecular system containing a coupled pair of near-equivalent 13C nuclei. The populations of the system are subjected to a repeating sequence of cyclic permutations separated by relaxation intervals. The long-lived nuclear singlet order is pumped well beyond the unitary limit. The pumped singlet order is converted into nuclear magnetization which is enhanced by 21% relative to its thermal equilibrium value.

Highlights

A quantum system which is in contact with a thermal reservoir eventually comes into equilibrium so that the populations of the quantum states are described by the Boltzmann distribution at the reservoir temperature
The algorithmic cooling of nuclear spin systems has generally been framed in the language of nuclear magnetic resonance (NMR) quantum computation,23 in which a prevailing assumption is that the individual nuclear spins may be treated, to a good approximation, as independent qubits, which are independently addressable by suitable radiofrequency fields
The current work has shown that (i) algorithmic cooling may be achieved on systems which lack independently addressable qubits; (ii) algorithmic cooling may exploit entangled superpositions of the qubit states; (iii) algorithmic cooling does not necessarily require qubits with distinct relaxation behavior; (iv) algorithmic cooling may be used to enhance modes of spin order which do not correspond to spin polarization

Summary

Introduction

A quantum system which is in contact with a thermal reservoir eventually comes into equilibrium so that the populations of the quantum states are described by the Boltzmann distribution at the reservoir temperature. In the vast majority of nuclear magnetic resonance (NMR) experiments, this thermal spin order is manipulated by resonant radiofrequency pulses and is eventually converted into transverse magnetization, which precesses in the magnetic field and induces an electrical signal by Faraday induction. It is a prominent paradigm in NMR spectroscopy that the initial spin order established by thermal equilibration cannot be increased by the application of resonant radiofrequency pulses, but only transformed into different spin order modes, with the total quantity of spin order being either conserved or decreased by irreversible decoherence effects

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Conclusion