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Physical Review B

Quantum coherence of 1s orthoexcitons in Cu2O driven by resonant two-photon excitation

Shunsuke Kono, N. Nagasawa

Published Dec 22, 2006• 1 citation
Publisher

Abstract

The intensity of the resonant emission of the $1s$ orthoexcitons in ${\mathrm{Cu}}_{2}\mathrm{O}$ is observed in a weak magnetic field under two-photon resonant excitation at $1.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ to investigate the quantum interference within the Zeeman sublevels in the Faraday configuration. A specific decrease of $\ensuremath{\sim}15%$ in the emission intensity is observed in the region of $\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. This structure is interpreted as a manifestation of the quantum interference effect between the Zeeman sublevels of the $1s$ orthoexcitons, known as the Hanle effect in atomic spectroscopy. The homogeneous width of the exciton level is estimated to be $5.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{eV}$. The contribution of the quadrupole exciton polariton is discussed by taking into account the geometry-dependent characteristics of the exciton-polariton on the direction of the magnetic field. The Hanle structure observed is attributed to the interference of the polariton wave packets of the longitudinal excitons, where the phase coherence is transferred via transverse excitons driven by resonant two-photon coupling with the radiation field.

DOI
10.1103/physrevb.74.245214

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The intensity of the resonant emission of the 1s1s1s orthoexcitons in Cu2O{\mathrm{Cu}}_{2}\mathrm{O}Cu2​O is observed in a weak magnetic field under two-photon resonant excitation at 1.6K1.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}1.6K to investigate the quantum interference within the Zeeman sublevels in the Faraday configuration. A specific decrease of \ensuremath∼15\ensuremath{\sim}15%\ensuremath∼15 in the emission intensity is observed in the region of \ifmmode±\else\textpm\fi0.2T\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{0.3em}{0ex}}\mathrm{T}\ifmmode±\else\textpm\fi0.2T. This structure is interpreted as a manifestation of the quantum interference effect between the Zeeman sublevels of the 1s1s1s orthoexcitons, known as the Hanle effect in atomic spectroscopy. The homogeneous width of the exciton level is estimated to be 5.5\ensuremathμeV5.5\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{eV}5.5\ensuremathμeV. The contribution of the quadrupole exciton polariton is discussed by taking into account the geometry-dependent characteristics of the exciton-polariton on the direction of the magnetic field. The Hanle structure observed is attributed to the interference of the polariton wave packets of the longitudinal excitons, where the phase coherence is transferred via transverse excitons driven by resonant two-photon coupling with the radiation field.
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The two-photon coherence of infrared pulses is preserved for more than 250ps250\phantom{\rule{0.3em}{0ex}}\mathrm{ps}250ps by dark excitons in Cu2O{\mathrm{Cu}}_{2}\mathrm{O}Cu2​O crystals. Taking into account the nonlocal electron-hole exchange interaction, 1s1s1s orthoexcitons are split into one bright exciton state that is quadrupole active and two dark exciton states that are two-photon active but one-photon inactive. Interference of cold dark exciton waves excited by a phase-locked pulse pair is observed with an almost perfect visibility and a beating pattern indicating and an energy splitting in the $\ensuremath{\mu}\mathrm{eV}$ range is seen. The long-lived two-photon coherence of dark excitons indicates their strong potential for coherence storage applications.
An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.
The quantum beats (QB) in the time-dependent absorption intensity of the probe pulse and the spontaneous luminescence one in Cu2O crystal at the condition of double optical resonance are studied theoretically. It is assumed that the pump is performed by the CO2 laser pulse, which couples dynamically the 1s (Γ 5 + ) and 2p (Γ 4 - , Γ 5 - , Γ 3 - , Γ 2 - ) excitonic states and leads to their splitting into two or three quasienergy levels. The frequency of the probe pulse is in the region of the Γ 5 + exciton resonance. The respective intensities for different directions of the electric field E L of the pump, the polarization ξ of the probe pulse, and the observation q are obtained. The QB take place with the doubled Raby frequency, which at different E L , ξ, and q includes different sets of matrix elements of dipole transitions between 1s (Γ 5 + ) and 2p (Γ 4 - , Γ 5 - , Γ 3 - , Γ 2 - ) levels. These unknown matrix elements can be obtained, measuring the period of the QB.