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Wepresent atheory foradifferential transmission experiment that generated electron spin coherence inquantum wellwaveguides without DCmagnetic fields. We showhowoptical selection rules explain thespin coherence's creation anddetection. 02004Optical Society ofAmerica OCIScodes: (190.5970) Semiconductor nonlinear optics including MQW;(300.6470) Spectroscopy, semiconductors Thedemonstration oflong-lived electron spin coherence atroomtemperature insemiconductors (1)hasenhanced theprospects ofusing coherent spin manipulation inoptoelectronics andhence hasdrawnmuchrecent research effort tothis area. Inmostexperiments, theelectron spin coherence wasdemonstrated bydetecting thespin's precession ineither anexternally applied DCmagnetic field oraninternal magnetic field induced bymagnetic ion (Mn)doping orstrain innonmagnetic materials (2). Recently theexperimental group inthis collaboration (Oregon) reported theobservation ofelectron spin coherence inGaAsquantum wells without thehelp ofmagnetic fields, external orinternal (3). Wepresent here atheoretical analysis ofthephysical processes contributing tothecreation anddetection ofthis spin coherence. A simple model, based mainly onoptical selection rules, gives aresonance structure atthespectral position ofanexperimentally observed peak inthedifferential transmission (DT)spectrum. Itsupports theinterpretation oftheobserved DTpeak asbeing duetoelectron spin coherence intheabsence ofany DCmagnetic field. Wealso calculate theDTinthepresence ofanexternal DCmagnetic field. Inthis case, wefind theconventional Zeemansplitting (inagreement withtheexperiment). Thisrules outtheinterpretation ofthe observed peak interms ofpopulation pulsations (4). Ourexperiment useslight traveling along thequantum well's plane (waveguide geometry, seeFig. 1)toexcite a light-hole exciton theelectron ofwhich isinasuperposition ofbothspin states. Thesimplest version ofourtheory is afour-level model: twoconduction bandstates andtwolight-hole valence bandstates. Fig. 2shows theusual level schematic ofaGaAsquantum well. An electron inalight-hole orbital, e.g. jz=-1/2,canbeexcited byC+ polarized light tooneconduction bandspin orbital (sz=1/2)orbyz-polarized light toanother conduction band spin orbital (s5=-1/2). Underexcitation bylight ofbothpolarizations anelectron canbeexcited into the conduction bandinasuperposition ofthetwospin orbitals. Thisspin coherence cannotbecreated intheusual, normal incidence, geometry where thelight lacks thez-polarized component. Itcanbecreated inthewaveguide geometry adopted inourexperiment, where thelight's TM component isz-polarized andtheTEcomponent contains both circular polarizations. TM

In this work, we study the resonant nonlinear optical response obtained when optical fields are used to excite charged semiconductor quantum dots (QDs). The basic physics of charged excitons (trions) created by optical excitation of charged QDs is of interest from the point of view of optically driven spin based quantum computing (QC). Stimulated Raman excitation, resonantly enhanced by the optical dipole coupling to the trion state, was used to optically generate electron spin coherence in the ground state of charged QDs. The evolution of the spin coherence was monitored through quantum beats in the phase-sensitively detected four wave mixing signal. The decay of the beats is a measure of the spin coherence time, which was found to be at least an order of magnitude greater than either the trion dipole coherence, or the Raman coherence time between excitons in a single neutral QD. A fascinating outcome of the experiment was the first observation of a contribution to the spin coherence induced by the vacuum field, which is also responsible for spontaneous emission from the trion state, known as spontaneously generated coherence (SGC). QC demands that coherent optical manipulations should be performed within the spin coherence time. We performed coherent optical control experiments, with a pair of phase-locked pump pulses, that showed the quantum nature of the coherence through interference of different quantum mechanical pathways. We showed both in experiment and theory that we can manipulate the spin coherence on the time scale of the Larmor frequency, as well as on an ultrafast femtosecond time scale, corresponding to the optical frequency of the trion state. Finally, resonant optical excitation of both the bright and nominally forbidden transitions from a single electron spin in a QD to the trion state were demonstrated. This allows for direct optical access to all the transitions required for optically driven QC with QD electron spins. We used frequency-domain nonlinear spectroscopy measurements on single QD trions to obtain the trion dipole decoherence and decay rates. Further, we demonstrated that the single electron spin coherence could be generated and detected optically, and found that the spin coherence time was significantly greater than in ensemble measurements at the same magnetic field.