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arXiv:cond-mat/0508297 · Physical Review B

Quantum dynamics of spins coupled by electrons in a one-dimensional channel

Dmitry Mozyrsky, Alexander Dementsov, Vladimir Privman A

Published Dec 9, 2005• 9 citations
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Abstract

We develop a unified theoretical description of the induced interaction and quantum noise in a system of two spins (qubits) coupled via a quasi-one-dimensional electron gas in the Luttinger liquid regime. Our results allow evaluation of the degree of coherence in quantum dynamics driven by the induced indirect exchange interaction of localized magnetic moments due to conduction electrons, in channel geometries recently experimentally studied for qubit control and measurement.

DOI
10.1103/physrevb.72.233103

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We develop a unified theoretical description of the induced interaction and quantum noise in a system of two spins (qubits) coupled via a quasi-one-dimensional electron gas in the Luttinger liquid regime. Our results allow evaluation of the degree of coherence in quantum dynamics driven by the induced indirect exchange interaction of localized magnetic moments due to conduction electrons, in channel geometries recently experimentally studied for qubit control and measurement.
We discuss the properties of interacting electrons on a finite chain with open boundary conditions. We extend the Haldane-Luttinger-liquid description to these systems and study how the presence of the boundaries modifies various correlation functions. In view of possible experimental applications to quantum wires, we analyze how tunneling measurements can reveal the underlying Luttinger-liquid properties. The two-terminal conductance is calculated. We also point out possible applications to quasi-one-dimensional materials and study the effects of magnetic impurities.
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Abstract — We review results in theoretical modeling of quantum systems in support of the studies of decoherence and qubit interactions for quantum information processing. The developed modeling tools have been applied to semiconductor materials and nanostructures that show promise for implementation of coherent, controlled quantum dynamics at the level of registers of several quantum bits (qubits), such as spins. Field-theoretical techniques have been utilized to address decoherence and more generally the origin and effects of quantum noise and the loss of entanglement in quantum dynamics of qubits and several-qubit registers. Qubit coupling mechanisms via the indirect exchange interaction have been investigated, and quantum computing designs have been evaluated for scalability. We also describe general and specific research challenges, the solution of which will advance the field of modeling “open quantum systems ” to further our understanding of how environmental influences affect quantum coherence and its loss during quantum dynamics.
In contrast to the well-known Fermi-liquid theory of three dimensions, interacting one-dimensional and quasi-one-dimensional systems of fermions are described at low energy by an effective theory known as Luttinger liquid theory. This theory is expressed in terms of collective many-body excitations that show exotic behavior such as spin-charge separation. Luttinger liquid theory is commonly applied on the premise that ``low energy'' describes both the spin and charge sectors. However, when the interactions in the system are very strong, as they typically are at low particle densities, the ratio of spin to charge energy may become exponentially small. It is then possible at very low temperatures for the single-spin excitation energy to be low compared to the characteristic single excitation charge energy, but still high compared to the characteristic spin energy. This energy window of near ground-state charge degrees of freedom but highly thermally excited spin degrees of freedom is called a spin-incoherent Luttinger liquid. The spin-incoherent Luttinger liquid exhibits a higher degree of universality than the Luttinger liquid and its properties are qualitatively distinct. In this Colloquium some recent theoretical developments in the field are detailed and experimental indications of such a regime in gated semiconductor quantum wires are described.