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Physical Review B

Coherent spin dynamics of donor bound electrons in GaAs

Carey E. Phelps, Shannon O’Leary, John P. Prineas, Hailin Wang

Published Aug 24, 2011• 1 citation
Publisher

Abstract

We report experimental studies of coherent spin dynamics of donor-bound electrons in high-purity GaAs by using transient differential transmission. The donor-bound exciton transitions, which are not visible in the linear absorption spectrum, are spectrally resolved in the nonlinear differential transmission spectra. The spin beats in the transient differential transmission response, arising from electron spin precession in an external magnetic field, are investigated with the pump and probe coupling to various donor-bound exciton transitions. The spectral dependence of the spin beats provides important information on the polarization selection rule for the underlying donor-bound exciton transitions. The polarization selection rules deduced from these experiments indicate that contributions from higher-energy donor-bound exciton transitions can severely limit the effectiveness of optical spin control using mechanisms such as polarization-dependent optical Stark shifts.

DOI
10.1103/physrevb.84.085205

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We report experimental studies of coherent spin dynamics of donor-bound electrons in high-purity GaAs by using transient differential transmission. The donor-bound exciton transitions, which are not visible in the linear absorption spectrum, are spectrally resolved in the nonlinear differential transmission spectra. The spin beats in the transient differential transmission response, arising from electron spin precession in an external magnetic field, are investigated with the pump and probe coupling to various donor-bound exciton transitions. The spectral dependence of the spin beats provides important information on the polarization selection rule for the underlying donor-bound exciton transitions. The polarization selection rules deduced from these experiments indicate that contributions from higher-energy donor-bound exciton transitions can severely limit the effectiveness of optical spin control using mechanisms such as polarization-dependent optical Stark shifts.
We report the experimental demonstration of coherent Raman resonance from electron spin coherence in GaAs\mathrm{GaAs}GaAs quantum wells. Coherent Raman resonance, which is a precursor for electromagnetically induced transparency, appears in the differential transmission response from localized excitons in an external magnetic field applied in Voigt geometry. The spectral domain spin study reveals that the optical processes involved differ from those in the transient domain, leading to distinct polarization and intensity dependences.
Coherent spin-photon interfaces are essential for scalable quantum networks, but their realization requires optically bright transitions, long-lived spin coherence, and complete coherent control. Donor-bound electron spins in II-VI semiconductors offer an attractive platform for optically active spin qubits because they combine strong donor-bound exciton transitions in a direct-bandgap material with a potentially nuclear-spin-free environment. However, coherent control of an individual optically active donor spin has remained elusive. Here we demonstrate optical initialization, coherent control, and readout of a single donor-bound electron spin in ZnSe. Using spin-selective donor-bound exciton optical transitions, we initialize the electron spin and directly resolve its spin-relaxation dynamics. We achieve coherent spin control with off-resonant picosecond optical pulses, as demonstrated by spin Rabi oscillations and Ramsey interference. We further coherently drive two spin-selective optical transitions and observe high-contrast coherent population trapping, demonstrating the formation of an optically controlled dark state. At higher driving strengths, multiple dark resonances reveal the hyperfine interaction between the electron and the I = 3/2 Cl nucleus. These results establish the first coherent optical control of a single donor electron spin in a II-VI semiconductor and identify isolated optical donors as a promising platform for solid-state optically active qubits.
The nonlinear optical response of quantum well excitons is investigated experimentally using polarization resolved four wave mixing, optical-pump optical-probe, and optical-pump Terahertz-probe spectroscopy. The four-wave mixing data reveal clear signatures of coherent biexcitons which concur with straight-forward polarization selection rules at the Γ point. The type-I samples show the well-established time-domain beating signatures in the transients as well as the corresponding spectral signatures clearly. The latter are also present in type-II samples; however, the smaller exciton and biexciton binding energies in these structures infer longer beating times which, in turn, are accompanied by faster dephasing of the type-II exciton coherences. Furthermore, the THz absorption following spectrally narrow, picosecond excitation at energies in the vicinity of the 1s exciton resonance are discussed. Here, the optical signatures yield the well-established redshifts and blueshifts for the appropriate polarization geometries in type-I quantum well samples also termed “AC Stark Effect”. The THz probe reveals intriguing spectral features which can be ascribed to coherent negative absorption following an excitation into a virtual state for an excitation below the 1s exciton resonance. Furthermore, the scattering and ionization of excitons is discussed for several excitation geometries yielding control rules for elastic and inelastic quasiparticle collisions.
Optical control of the spin coherence of quantum well electrons by short laser pulses with circular or linear polarization is studied experimentally and theoretically. For that purpose the coherent electron spin dynamics in a nnn-doped CdTe/(Cd,Mg)Te quantum well structure was measured by time-resolved pump-probe Kerr rotation, using resonant excitation of the negatively charged exciton (trion) state. The amplitude and phase shifts of the electron spin beat signal in an external magnetic field, that are induced by laser control pulses, depend on the pump-control delay and polarization of the control relative to the pump pulse. Additive and nonadditive contributions to pump-induced signal due to the control are isolated experimentally. These contributions can be well described in the framework of a two-level model for the optical excitation of the resident electron to the trion.
We experimentally demonstrate how coherent population trapping (CPT) for donor-bound electron spins in GaAs results in autonomous feedback that prepares stabilized states for the spin polarization of nuclei around the electrons. CPT was realized by excitation with two lasers to a bound-exciton state. Transmission studies of the spectral CPT feature on an ensemble of electrons directly reveal the statistical distribution of prepared nuclear-spin states. Tuning the laser driving from blue to red detuned drives a transition from one to two stable states. Our results have importance for ongoing research on schemes for dynamic nuclear-spin polarization, the central spin problem, and control of spin coherence.
We perform femtosecond spectrally resolved pump-probe differential reflectivity measurements on excitons in GaAs quantum wells in both coherent and incoherent regimes. The spectral signal is nonzero and oscillatory at $\ensuremath{-}\mathrm{ve}$ delay up to a few ps indicating persistent coherence between excitonic polarization induced by the probe pulse and the delayed pump pulse. The signal for small +ve+ve+ve and $\ensuremath{-}\mathrm{ve}$ delay $(\ensuremath{\tau})$ shows modulation caused by quantum beats due to coexcitation of heavy and light hole excitons. The rise of the signal with $\ensuremath{\tau}$ for $\ensuremath{\tau}<0$ is rather nonexponential and is sensitive to detuning of the detection energy with respect to the exciton energy. The signal decay with $\ensuremath{\tau}$ for small +ve+ve+ve $\ensuremath{\tau}$ shows dependence on pump-probe relative polarization. The excitonic reflectivity shows a large reduction caused by excitonic absorption saturation for both +ve+ve+ve and $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}$ when the pump pulse intensity is increased to large values. To compare the experimental results with theory, we obtain an expression for the PPDR signal in terms of the third order excitonic polarization. This has an additional term not considered earlier to describe pump-probe experiments. The calculations are performed using optical Bloch equations, modified to incorporate exciton inhomogeneous broadening, quantum beats, and many body effects such as local field, excitation induced energy shift, and dephasing. These effects are found essential in explaining the observed PPDR spectral data. The delay dependence of the signal near the exciton energy is mainly controlled by inhomogeneous broadening for $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}.$ The signal decay for large +ve+ve+ve $\ensuremath{\tau}$ has an exponential behavior determined by the lifetime of incoherent excitons. Experiments for collinear polarization reveal an additional exponential component for small +ve+ve+ve delay. Theoretically, this is found to be related to exciton dephasing and is present only when many body effects are included.