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Optically Stimulated andSpontaneously Generated Electron SpinCoherence inQuantuin Dots

Guy Lewis Steel, A. S. Bracker, J. Sham, SanDiego LaJolla

Published Jan 1, 2005• 0 citations
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Abstract

Wereport theobservation oflong-lived quantum beats inquantum dots(ensemble andsingle) duetoelectron spincoherence, resulting fromstimulated Ramantransition aswell asspontaneous radiative decay ofthetrion state. © 2004Optical Society ofAmerica OCIScodes:(300.6240) Coherent transient spectroscopy; (300.6420) Nonlinear spectroscopy; (300.6470) Semi- conductors spectroscopy Theelectron spininquantumdots(QD's) isapromising candidate foraqubit forquantuminformation processing duetoitslonglifetime andanticipated robust coherence (1). Suchstructures havefeatured in numerous proposals using ultrafast optical coupling tocoherently manipulate thespinstates. Inthis paper, wedemonstrate suchcoupling andfindanewcontribution tothecoherence observed through quantum beats.

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•Jan 1, 2013•0 citations
Wereport theobservation oflong-lived quantum beats inquantum dots(ensemble andsingle) duetoelectron spincoherence, resulting fromstimulated Ramantransition aswell asspontaneous radiative decay ofthetrion state. © 2004Optical Society ofAmerica OCIScodes:(300.6240) Coherent transient spectroscopy; (300.6420) Nonlinear spectroscopy; (300.6470) Semi- conductors spectroscopy Theelectron spininquantumdots(QD's) isapromising candidate foraqubit forquantuminformation processing duetoitslonglifetime andanticipated robust coherence (1). Suchstructures havefeatured in numerous proposals using ultrafast optical coupling tocoherently manipulate thespinstates. Inthis paper, wedemonstrate suchcoupling andfindanewcontribution tothecoherence observed through quantum beats.
Electron spin coherence isinduced vialight-hole transitions inaquantum well waveguide without aDC magnetic field. Thespincoherence isdetected through effects ofquantum interference inspectral domain nonlinear optical response. 02005 Optical Society ofAmerica OCIScodes: (190.5970) Semiconductor nonlinear optics including MQW;(300.6470) Spectroscopy, semiconductors Coherent spin manipulation plays animportant role inspin-based electronics andphotonics andinquantum information technologies (1). Inmostexperiments, coherent spin manipulation wascarried outinthepresence ofan external DC magnetic field that induces aZeemansplitting between theconduction bandelectron spin states. Coherent superposition ofthese spin states leads toaLarmor spin precession, which canbedetected with transient optical techniques. Coherent spin manipulation without external magnetic fields innon-magnetic semiconductors hasalso beendemonstrated inarecent study (2), inwhichaneffective internal magnetic field induced bystrain results inaspin splitting intheconduction band. Here, wereport experimental demonstration ofinducing anddetecting electron spincoherence inaGaAs quantum well(QW)without theuseofeither anexternal oreffective internal magnetic field. We havetaken advantage ofthespin-orbit coupling inthevalence bandandhaveusedlight-hole (LH)transitions inwaveguide geometry toinduce electron spincoherence. Intheabsence ofspin precession, theinduced spincoherence is detected through quantum interference inthespectral domain, instead oftimedomain, coherent nonlinear optical response. (a)
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.
The optically-induced coherent spin dynamics in a charged quantum dot (QD) is studied theoretically using a new dynamical model for rigorous description of circularly polarized ultrashort optical pulse resonant interactions with the electron-trion system. Generalized pseudospin master equation is derived for description of the time evolution of spin coherences and spin populations in terms of the real state pseudospin (coherence) vector including dissipation in the system through spin relaxation processes. The equation is solved in the time domain self-consistently with the vector Maxwell equations for the optical wave propagation coupled to it via macroscopic medium polarization. Using the model the long-lived electron spin coherence left behind a single resonant ultrashort optical excitation of the electron-trion transition in a charged QD is simulated in the lowand high-intensity Rabi oscillations regime. Signatures of the polarized photoluminescence (PL) resulting from the numerical simulations, such as the appearance of a second echo pulse after the excitation and a characteristic PL trace shape, specific for initial spin-up orientation, are discussed for realization of high-fidelity schemes for coherent readout of a single spin polarization state.
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