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Applied Physics Letters

Electron spin state tomography with coherent Kerr effect

Takahiro Inagaki, Hideo Kosaka, Yasuyoshi Mitsumori, Keiichi Edamatsu

Published Oct 24, 2011• 5 citations
Publisher

Abstract

We developed a scheme for spin coherence measurement based on the coherent Kerr effect, which is the coherent version of the conventional complex Kerr effect, which only gives the projective spin state. In addition to the previously demonstrated tomographic Kerr rotation, which corresponds to the real part of the coherent Kerr effect, we demonstrate here a tomographic Kerr ellipticity, which corresponds to the imaginary part of the coherent Kerr effect. Using the tomographic Kerr ellipticity scheme, we show the coherent rotation, a natural extension of the conventional coherent oscillation, of the precessing electron spin under a magnetic field. We also confirm the complex relationship between tomographic Kerr rotation and ellipticity by measurement of the coherent Kerr spectra.

DOI
10.1063/1.3655676

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We developed a scheme for spin coherence measurement based on the coherent Kerr effect, which is the coherent version of the conventional complex Kerr effect, which only gives the projective spin state. In addition to the previously demonstrated tomographic Kerr rotation, which corresponds to the real part of the coherent Kerr effect, we demonstrate here a tomographic Kerr ellipticity, which corresponds to the imaginary part of the coherent Kerr effect. Using the tomographic Kerr ellipticity scheme, we show the coherent rotation, a natural extension of the conventional coherent oscillation, of the precessing electron spin under a magnetic field. We also confirm the complex relationship between tomographic Kerr rotation and ellipticity by measurement of the coherent Kerr spectra.
Spin coherence is essential for spin-based quantum information technology. The conventional spin measurement technique, however, requires an extra step of spin manipulation or precession to measure the electron spin coherence. To measure the electron spin coherence directly, we have developed the tomographic Kerr rotation (TKR) method, which is based on the magneto-optical Kerr effect on the condition of the coherent transfer of light polarization states into electron spin states in a GaAs/AlGaAs quantum well. The TKR method allows measurement of the coherent superposition state of electron spins |±y>e = (|↑>e±i|↓>e)/√2 in addition to conventionally measured ±z states (|↑>e or |↓>e) (which merely indicate the population of electron spins). Here we demonstrate that electron spin coherence can be measured by linearly polarized probe light to show that TKR is independent of the choice of probe light polarization. We also describe a method to distinguish TKR from the conventional magnetic circular dichroism (MCD) effect.
Spin is a fundamental property of electrons and plays an important role in information storage. For spin-based quantum information technology, preparation and read-out of the electron spin state must be spin coherent, but both the traditional preparation and read-out of the spin state are projective to up/down spin states, which do not have spin coherence. We have recently demonstrated that the polarization coherence of light can be coherently transferred to the spin coherence of electrons in a semiconductor. We have also developed a new scheme named tomographic Kerr rotation (TKR) by generalizing the traditional KR to directly read out the spin coherence of optically prepared electrons without the need for the spin dynamics, which allows the spin projection measurement in an arbitrary set of basis states. These demonstrations were performed using g-factor-controlled semiconductor quantum wells with precessing and non-precessing electrons. The developed scheme offers a tool for performing basis-independent preparation and read-out of a spin quantum state in a solid. These results encourage us to make a quantum media converter between flying photon qubits and stationary electron spin qubits in semiconductors.
Spin is a fundamental property of electrons and plays an important role in information storage. For spin-based quantum information technology, preparation and read-out of the electron spin state must be spin coherent, but both the traditional preparation and read-out of the spin state are projective to up/down spin states, which do not have spin coherence. We have recently demonstrated that the polarization coherence of light can be coherently transferred to the spin coherence of electrons in a semiconductor. We have also developed a new scheme named tomographic Kerr rotation (TKR) by generalizing the traditional KR to directly readout the spin coherence of optically prepared electrons without the need for the spin dynamics, which allows the spin projection measurement in an arbitrary set of basis states. These demonstrations were performed using g-factor-controlled semiconductor quantum wells with precessing and nonprecessing electrons. The developed scheme offers a tool for performing basis-independent preparation and read-out of a spin quantum state in a solid. These results encourage us to make a quantum media converter between flying photon qubits and stationary electron spin qubits in semiconductors.
Electron spins in semiconductor nanostructures are considered as one of the most promising candidates of the building blocks for quantum information processing. Initialization, coherent manipulation, and measurement of a single electron spin have been recently established. Here we explore the possibility to manipulate and measure by optical means the states of two electrons as a single qubit in nanostructures and propose methods of spin-state tomography based on Faraday or Kerr rotation for cases of both a single electron and two electrons, as well as a method of the Bell-state measurement for two electrons.