Polarization of Nuclear Spins from the Conductance of Quantum Wire

Abstract

We devise an approach to measure the polarization of nuclear spins via conductance measurements. Specifically, we study the combined effect of external magnetic field, nuclear spin polarization, and Rashba spin-orbit interaction on the conductance of a quantum wire. Nonequilibrium nuclear spin polarization affects the electron energy spectrum making it time-dependent. Changes in the extremal points of the spectrum result in time-dependence of the conductance. The conductance oscillation pattern can be used to obtain information about the amplitude of the nuclear spin polarization and extract the characteristic time scales of the nuclear spin subsystem.PACS numbers: 72.25. Dc, The promise of spintronics and quantum computing has motivated recent theoretical and experimental investigations of spin-related effects in semiconductor heterostructures [1,2,3,4,5,6,7,8,9,10]. Nuclear and electron spins have been considered as candidates for qubit implementations in solid state systems [1,2,3,4,5,6]. The final stage of a quantum computation process involves readout of quantum information. In the case of a spin qubit one would have to measure the state of a single spin. Yet, in spite of recent efforts in this field, a single nuclear spin measurement is still a great challenge.There are several proposals for single-and few-spin measurement. For example, a change of the oscillation frequency of a micro-mechanical resonator (cantilever) [11] is used. Another possibility to obtain information about a qubit state lies in the measurement [12] of current or its noise spectrum in a mesoscopic system (e.g., quantum wire, quantum dot, or single electron transistor) coupled to a qubit [13,14,15]. Significant progress in spin measurements has been made using magnetic resonance force microscopy [16], which presently allows one to probe the state of 100 fully polarized electron spins. Recently, an experimental architecture to manipulate the magnetization of nuclear spin domains was proposed [5,6].The present work demonstrates that a relatively small ensemble of nuclear spins can significantly influence transport through a quantum wire (QW). This offers a new detector design, with the operation based on a new effect arising as a consequence of the combined influence of the spin-orbit interaction and nuclear spin polarization on the electron subsystem. Recent progress in investigations of QWs [17,18,19,20,21,22,23,24,25,26,27,28] makes them a promising nanoscale device component.We consider transport through a QW in the presence of an external in-plane magnetic field, Rashba spin-orbit coupling [29] and a nonequilibrium nuclear spin polarization. We assume that the external magnetic field is directed along a wire. If the nuclear spin polarization has a non-zero component perpendicular to the external field at the initial moment of time (i.e. the two vectors are not aligned), then we will demonstrate that the conductance of the wire exhibits damped oscillations. These oscillations are a direct consequence of the interplay between the evol...

Rashba interaction in quantum wires with in-plane magnetic fields

“…Interestingly, these systems have been proposed as basic elements for practical applications such as spin-dependent field-effect transistors 5 and spin filters 6 and have been also considered as detectors of entangled pairs of electrons 7 and of the hyperfine nuclear spin dynamics. 8 The Rashba interaction is described by the Hamiltonian,…”

“…It also influences the spin dynamics since whereas the Rashba precession randomizes the spin direction (a common spin quantization axis can be defined only for large wavevectors), the magnetic field tends to align the spins parallel to it. Many works neglect 8,11,12,13 the effect of Rashba intersubband coupling (RIC) in quantum wires in the presence of in-plane magnetic fields. Here we demonstrate that both Rashba precession and intersubband coupling must be treated on equal footing for wavevectors near the subband gaps.…”

Strongly modulated transmission of a spin-split quantum wire with local Rashba interaction

“…This fact has important consequences for the electronic transport. 14,16,17,26 ͑Larger magnetic fields, ⌬ Z Ͼ 2m␣ 2 / ប 2 , turn the local maximum into a local minimum, but this case is less interesting and will not be treated in this work.͒ For Fermi energies lying in the pseudogap region, −⌬ Z / 2 Ͻ E F Ͻ⌬ Z / 2, there is only a wave function with a given spin direction for each mover ͑right moving or left moving͒. In addition, there also exist evanescent waves, which are crucial when the Rashba interaction is confined to a finite region.…”

Spin photovoltaic effect in quantum wires with Rashba interaction

“…9 In particular, it was recently discovered that the joint action of the Rashba SOI and in-plane magnetic field on electrons confined in one-dimensional quantum wires ͑QW͒ results in unique properties. [2][3][4] Several useful applications based on these properties were proposed, including a scheme for measuring nuclear spin polarization 2 and a spin filter. 3 In this letter, we theoretically investigate the effect of a microwave radiation in a QW with Rashba SOI and an inplane magnetic field.…”

“…The Hamiltonian for the conduction electrons in the QW in the presence of the microwave radiation can be written in the form, [2][3][4] …”