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Japanese Journal of Applied Physics

Measurement of Electron Spin States in a Semiconductor Quantum Well Using Tomographic Kerr Rotation

Takahiro Inagaki, Hideo Kosaka, Yoshiaki Rikitake, Hiroshi Imamura, Yasuyoshi Mitsumori, Keiichi Edamatsu

Published Apr 1, 2010• 2 citations
Publisher

Abstract

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.

DOI
10.1143/jjap.49.04dj09

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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.
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 is a quantum property of electrons. For spin-based quantum information technology, preparation and read-out of the electron spin state should be spin coherent. We demonstrate that the polarization coher ence of light can be transferred to the spin coherence of electrons in a semiconductor quantum nanostructure [1], and the prepared coherence of the electron spin can also be read out with light by the developed tomographic Kerr rotation method [2]. We also demonstrate that a single photon is efficiently converted (~27%) into a single electron trapped in a gate-defined quantum dot, where the g-factor of electrons is tuned to zero, and the charge state is detected with an adjacent quantum point contact without destructing the spin state [3]. We further demonstrate that the spin coherence of a single electron trapped in one of double quantum dots is electrically manipulated with a microwave applied to the gate and read out via the Pauli spin blockade phenomenon [4]. These demonstrations were carried out in a condition where the up/down spin basis states of electrons remain ed degenerated under an in-plain magnetic field. As this condition ensures the energy conservation between photons and electrons, the entire Poincare sphere representing polarization states of photons can be mapped onto the Bloch sphere representing spin polar ization states of electrons. We theoretically showed that relative spin coherence of two electrons can be also measured with the help of spin-flip tunneling of electrons between the dots [5]. Full Bell state measurement is also possible by the single -spin manipulation and Pauli spin blockade [6]. All of these functions are needed to build all semiconductor quantum repeaters and distributed quantum computers.
We performed process tomography of a coherent state transfer from light polarization into electron spin polarization in a semiconductor quantum well. The density matrix of the generated electron spin state was reconstructed by a three-dimensional tomographic Kerr rotation measurement so that we could quantitatively evaluate the transfer process. We found that the process fidelity of the state transfer was 81% and clarified that the phase-flip error caused by mixing with another Zeeman sublevel at the hole state was the major contributor to fidelity degradation.