University of Groningen

Electromagnetically induced transparency with an ensemble of donor-bound electron spins ina semiconductorSladkov, Maksym; Chaubal, A. U.; Bakker, M. P.; Onur, A. R.; Reuter, D.; Wieck, A. D.; vander Wal, C. H.Published in:Physical Review. B: Condensed Matter and Materials Physics

DOI:10.1103/PhysRevB.82.121308

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Citation for published version (APA):Sladkov, M., Chaubal, A. U., Bakker, M. P., Onur, A. R., Reuter, D., Wieck, A. D., & van der Wal, C. H.(2010). Electromagnetically induced transparency with an ensemble of donor-bound electron spins in asemiconductor. Physical Review. B: Condensed Matter and Materials Physics, 82(12), 121308-1-121308-4.[121308]. https://doi.org/10.1103/PhysRevB.82.121308

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Electromagnetically induced transparency with an ensemble of donor-bound electron spinsin a semiconductor

Maksym Sladkov,1 A. U. Chaubal,1 M. P. Bakker,1 A. R. Onur,1 D. Reuter,2 A. D. Wieck,2 and C. H. van der Wal11Zernike Institute for Advanced Materials, University of Groningen, NL-9747AG Groningen, The Netherlands

2Angewandte Festkörperphysik, Ruhr-Universität Bochum, D-44780 Bochum, GermanyReceived 6 July 2010; revised manuscript received 4 September 2010; published 24 September 2010

We present measurements of electromagnetically induced transparency with an ensemble of donor-boundelectrons in low-doped n-GaAs. We used optical transitions from the Zeeman-split electron-spin states to abound trion state in samples with optical densities of 0.3 and 1.0. The electron-spin dephasing time T2

2 ns was limited by hyperfine coupling to fluctuating nuclear spins. We also observe signatures of dynamicalnuclear polarization but find these effects to be much weaker than in experiments that use electron-spinresonance and related experiments with quantum dots.

DOI: 10.1103/PhysRevB.82.121308 PACS numbers: 78.47.jh, 71.55.Eq, 42.50.Gy, 71.35.Pq

A localized electronic spin in a semiconductor is a prom-ising candidate for implementing quantum information tasksin solid state. Optical manipulation of single-electron andsingle-hole systems has been realized with quantum dots1–5

and by using donor atoms that are not ionized at low tem-perature D0 systems.6–8 These results illustrate the potentialof quantum-optical control schemes that come within reachwhen adapting techniques from the field of atomic physics.An advantage of the D0 systems over dots is that these can beoperated as an ensemble with very little inhomogeneity forthe optical transition energies. Such ensembles at high opti-cal density are key for robust quantum-optical controlschemes that have been designed for preparing nonlocal en-tanglement between spins, quantum communication, and ap-plying strong optical nonlinearities.9,10 A critical step towardimplementing these schemes is the realization of electromag-netically induced transparency EIT. We present here mea-surements of EIT with an ensemble of donor-bound electronspins in low-doped n-GaAs, in samples with optical densitiesof 0.3 and 1.0.11 We build on an earlier indirect observationof coherent population trapping with this system.6 Extendingthis to a direct realization of EIT with an optically densemedium is essential for getting access to strong field-matterinteractions without using optical cavities and for the appli-cation and study of transmitted signal fields.9,10

We implemented EIT in its most typical form where aspin-up and a spin-down state ↑ and ↓ of the electron inthe D0 system have an optical transition to the same excitedstate e Fig. 1e. We Zeeman split the states ↑ and ↓ with an applied magnetic field. For the state e we used thelowest energy level of a donor-bound trion system D0X withtwo electrons in a singlet state and a spin-down hole withmh=− 1

2 Ref. 8 localized at the donor site. EIT is then thephenomenon that absorption by one of the optical transitionsis suppressed because destructive quantum interference withthe other transition prohibits populating the state e. The D0

systems are then trapped in a dark state that is in the idealcase a coherent superposition of the states ↑ and ↓ only.6,11 This state is proportional to c↑ −p↓ with cand p the Rabi frequencies of the control and probe fieldthat drive the two transitions.10

We present results of implementing EIT in GaAs, and we

studied the interactions between the solid-state environmentand driving EIT. In particular, the D0 systems have a singleelectron in a hydrogenlike 1s wave function with a Bohrradius of 10 nm and each electron spin has hyperfine cou-pling to 105 fluctuating nuclear spins. We studied how thislimits the electron-spin dephasing time and how driving EITcan result in dynamical nuclear polarization DNP. In addi-tion, we find that it is crucial to suppress heating effects fromthe nearby free exciton resonance, and demonstrate that withdirect heat sinking of GaAs layers EIT can be driven withc /2 up to 2 GHz, while keeping the spin dephasing timeT2

2 ns near the level that results from the nuclear-spinfluctuations.

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FIG. 1. Color a Transmission spectroscopy at B=0 T. bTransmission at B=5.0 T for H and V polarization. c Pump-assisted spectroscopy with H-polarized pumping at the A transitionshows enhanced absorption for the A transition for the scan with aV-polarized probe blue trace but not with an H-polarized probered trace. d Complementary to c, V-polarized pumping at Ashows enhanced absorption for the A transition with anH-polarized probe. e Energy levels and optical transitions of theD0-D0X system.

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We used epitaxially grown GaAs films of 10 m thick-ness with Si doping at nSi=31013 and 11014 cm−3. Atthese concentrations the wave functions of neighboring do-nor sites do not overlap, which yields an ensemble of nonin-teracting D0 systems. The films were transferred to a wedgedsapphire substrate with an epitaxial lift-off process12 andfixed there by van der Waals forces which assures high heatsinking. The sapphire substrate was mounted on the coppercold finger of a bath cryostat 4.2 K in the center of a su-perconducting magnet with fields B up to 8 T in the plane ofthe sample z direction. Laser light was brought to the filmsat normal incidence Voigt geometry via a polarization-maintaining single-mode fiber. The two linear polarizationssupported by the fiber are set parallel V polarization andorthogonal H polarization to the applied magnetic field.The V polarization can drive transitions no change inz-angular momentum and the H polarization can drive tran-sitions with a change in z-angular momentum of .

Two cw Ti:sapphire lasers Coherent MBR-110, linewidthbelow 1 MHz provided tunable probe and control fields.Focusing in the sample volume was achieved with a piezo-motor controlled confocal microscope. During transmissionexperiments we defocused the microscope to a spot of16 m diameter to avoid interference effects from thecavity that is formed between the sample surface and thefacet of the fiber. The probe field was amplitude modulatedat 6 kHz and we used lock-in techniques for detecting lightthat is transmitted trough the sample with a photodiode di-rectly behind the sample. The signal due to unmodulatedcontrol field is rejected by ac coupling of the measurementelectronics.

We first report transmission experiments that identify thespectral position of the D0X related resonances. Only theprobe laser was used. Figure 1a shows a spectrum taken atB=0 T identical result for H and V polarization and Fig.1b shows a result for B=5.0 T with a separate trace for Hand V polarization. The strong absorption labeled X is due toexcitation of free excitons. Resonant absorption by donor-bound excitons D0X occurs at 8187.5 Å for B=0 T and at8179.5 Å for B=5.0 T. The shift of the resonances withmagnetic field is the diamagnetic shift. The spacing of 5 Åbetween the X and D0X resonances is in good agreementwith previously reported binding energies.13,14 The oscillat-ing background superimposed on the resonances is due to aFabry-Perot effect in the GaAs film and its chirped wave-length dependence around X is due to the wavelength-dependent refractive index that is associated with the strongfree exciton absorption.

For identifying the A and A transitions of Fig. 1e withinthe fine structure of D0X spectra at high fields we performedscanning-probe laser spectroscopy while the control laser isapplied for optical pumping of a particular D0X transitionthis also eliminates bleaching by the probe. Figure 1cshows spectra obtained with pumping at A 8179.3 Å withH polarization. This leads to enhanced absorption at the Aresonance 8180.0 Å for the probe scan with V polariza-tion. The complementary experiment with pumpingV-polarized light into this A transition leads to enhanced ab-sorption of H-polarized light at transition A Fig. 1d. Wecould also perform such cross-pumping experiments using

the B and B transitions to the level e the first excitedstate of the series of energy levels of the D0X complex, seeFig. 1e. We thus confirmed that the pair of transitions la-beled as A and A address a so-called closed three-level system and that this is the pair with lowest energies withinthe D0X resonances. This interpretation is also consistentwith the polarization dependence of these transitions.6,14 Inthe field range 5–8 T, the A and A transitions are spectrallywell separated from the transitions B, B, and transitions tohigher excited states of the D0X complex. The observed D0

Zeeman splitting corresponds to an electron g factor g=0.42 and also agrees with previous reports.6,14

We now turn to the observation of EIT Fig. 2. For theseresults we fixed the control laser central on the A transitionV polarization while the probe laser is scanned across theA transition H polarization. When the control and probefield meet the condition for two-photon Raman resonancethe difference in photon energy exactly matches the D0 spinsplitting, a narrow peak with enhanced transmissionappears inside the broader A absorption dip, which is thefingerprint of EIT. In Fig. 2a this occurs inside an A ab-sorption with optical density 1.0 while for the sample withnSi=31013 cm−3 this is 0.3 Fig. 2b. We further focus onthis latter sample since higher resolution of the EIT spectramakes it more suited for our further studies.

The lines in Figs. 2 and 3 are results of fitting EIT spectrawith the established theory.10 This involves calculating thesteady-state solution of a density-matrix equation for thethree-level system, and accounts for coherent driving by thelasers and relaxation and dephasing rates between the levels.

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FIG. 2. Color online a EIT spectrum from sample with Sidoping at 11014 cm−3. Dots—experiment. Line—numerical fit.b EIT spectra from sample with Si doping at 31013 cm−3, forprobe-field intensity 0.04 W cm−2 and a range of control-field in-tensities Ic with I0=0.4 W cm−2. The inset shows the fitting resultsfor Rabi frequency c and spin dephasing time T2

.

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The free parameters are the inhomogeneous broadening A

typically 6 GHz for the optical transition A, the spindephasing time T2

and the control-field-induced Rabi fre-quency c and pc. The rest of the parameters are thesame as in Ref. 6 and we found c always consistent with anindependent estimate from the optical intensity and electricdipole moment. We obtain good fits and the main features inour results are consistent with EIT, as we discuss next.

Figure 2b shows EIT spectra taken at different intensi-ties Ic of the control field, where a stronger control fieldyields a higher and broader EIT peak. As expected for EIT,we observe that c from fits scales linearly with Ic Fig.2b, inset. The c values reach 22 GHz and we couldonly obtain clear EIT spectra with such high c in sampleswith complete adhesion onto the sapphire substrate. Our re-sults from samples with incomplete adhesion and work withepilayers that are not removed from the original GaAssubstrate6–8 suffer from heating, which is observed as abroadening of the free exciton line into the region of the D0Xresonances. The values of T2

that we find in our experimentsare discussed below.

Figure 3 shows how the EIT peak position depends ondetuning of the control field from the A transition. As ex-pected, the EIT peak follows the detuning of the controlfield. However, the EIT peak in the blue-detuned traces isclearly more prominent than in the red-detuned cases. Weattribute this to a change in the effective Rabi frequency cthat results from the weak Fabry-Perot interference withinthe GaAs film, and we can indeed fit the results with fixedT2

=2 ns and varying c Fig. 3, inset. We can exclude thatthe difference in the quality of EIT spectra is coming fromoptical coupling to a level outside our system since allother transitions are well separated spectrally and in polar-ization dependence e.g., the B and B transitions, see Fig.1e.

An important topic that needs to be addressed next withthis realization of EIT concerns the influence of the hyperfinecoupling between each electron spin and 105 nuclear spins.A polarization of the nuclear spins acts on the electron spinas an effective magnetic field Bnuc. The average polarizationaffects the Zeeman splitting, and this can be directly ob-served in EIT spectra as a red blue shift of the EIT peak fora reduced enhanced Zeeman splitting. The nuclear-spinfluctuations around the average dominate via this mechanismthe inhomogeneous electron-spin coherence time T2

. This isa key parameter for the shape of the EIT peak longer T2

gives a sharper peak and the magnitude of these fluctuationscan therefore be derived from the EIT spectra as well. At ourfields and temperature nuclear spins are in equilibrium closeto full random orientation. The expected value for T2

for thiscase is 2 ns,6,15 and is in agreement with the values thatwe observe.

The hyperfine coupling can also result in DNP, which isthe transfer of angular momentum from the electron to thenuclear spins when the electron spin is driven out of equilib-rium. Earlier experiments on our type of D0 system withmicrowave-driven electron-spin resonance ESR Ref. 15and optical experiments on quantum dots showed strongDNP.3,4 In both cases the effects were so strong that it gavean unstable resonance condition for tuning at ESR and EITthe systems trigger a DNP cycle that drives them out ofresonance. DNP can also result in a suppression of thenuclear-spin fluctuations, which yields a longer T2

.2–4,16 Ourexperiment, however, only shows weak DNP. We never ob-served a significant change in the Zeeman energy as derivedfrom subtracting the probe and control photon energies at theEIT peak from the EIT driving itself. We only observed inseveral data sets a moderate EIT peak narrowing over thecourse of a few hours of data taking at fixed settings of theEIT parameters. In order to confirm the role of nuclear spinswe carried out various attempts to induce stronger DNP ef-fects.

An example of the strongest DNP effects that we couldinduce is presented in Fig. 4. Here we first applied strongdriving of the A transition for 30 min with an intensityequivalent to a Rabi frequency of 210 GHz. This pumpsthe system fully into ↓ . After pumping we take fast “snap-shots” of the EIT peak 50 s A scans, p /2=25 MHz, andcontrol at A with c /2=1 GHz. Between scans we keptthe system in the dark for 10 min. Figure 4 shows six sub-sequent snapshots. Right after pumping we observe a blue-shifted and sharpened EIT peak T2

=3 ns. This enhance-ment of T2

probably results from suppressed nuclear-spinfluctuations, which generally occurs when the polarizationgets squeezed between a polarizing and depolarizing mecha-nism with rates that are both enhanced due to the DNP.3,4,16

The peak shift agrees in sign with Ref. 15 but corresponds toBnuc=21 mT only the ESR studies15 and the work on dotseasily induced 200 mT–1 T. Subsequent spectra show aclear broadening of the EIT peak, which also shifts back tothe red. After about 1 h, T2

Fig. 4, inset and the peakposition stabilize at the values that were observed beforepumping. This agrees with the relaxation time for DNP with

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FIG. 3. Color online Dependence of EIT spectra on control-field detuning. The position of the EIT peak follows precisely thecontrol-field detuning from transition A. Dots—experiment withcontrol probe intensity 60.04 W cm−2. Lines—fits withT2

=2 ns and c as presented in the inset.

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D0 systems.15 Upon exploring how DNP occurs for variousEIT and pump conditions we found the effects to be tooweak for systematic control and drawing further conclusions,and full understanding goes beyond the scope of the present

work. The work with dots showed that the mechanism thatdominates the DNP rate can be complex and needs to ac-count for driving-field-assisted processes.3,4 We can never-theless conclude that our spin dephasing time is indeed lim-ited by coupling to nuclear spins.

In conclusion, we presented direct evidence that a D0 en-semble in GaAs can be operated as a medium for EIT. Theelectron-spin dephasing time limits the quality of the EITand is in the range T2

2 ns that results from hyperfine cou-pling to fluctuating nuclear spins. The EIT spectra form asensitive probe for detecting how DNP changes the fluctua-tions and the average of nuclear-spin polarization. However,direct optical driving of D0 transitions yields much weakerDNP effects than in electron-spin-resonance experimentswith D0 systems and related EIT experiments on quantumdots and a complete physical picture of DNP effects in oursystem is not available. Still, initial signatures of controlledDNP effects show that the electron–spin dephasing time canbe prolonged. Our experimental approach is suited for ex-ploring this further in conjunction with experiments that aimto implement various applications of EIT.9,10

We thank B. Wolfs, J. Sloot, and S. Lloyd for contribu-tions, and the Dutch NWO and FOM, and the German pro-grams DFG-SPP 1285, BMBF nanoQUIT and Researchschool of Ruhr-Universität Bochum for support.

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Phys. Lett. 51, 2222 1987.13 E. Bogardus and H. Bebb, Phys. Rev. 176, 993 1968.14 V. A. Karasyuk, D. G. S. Beckett, M. K. Nissen, A. Villemaire,

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