All-optical formation of coherent dark states of silicon-vacancy spins in diamond
Benjamin Pingault, Jonas N. Becker, Carsten H. H. Schulte, Carsten Arend, Christian Hepp, Tillmann Godde, Alexander I. Tartakovskii, Matthew Markham, Christoph Becher, Mete Atature
AAPS/123-QED
All-optical formation of coherent dark states of silicon-vacancy spins in diamond
Benjamin Pingault, ∗ Jonas N. Becker, ∗ Carsten H. H. Schulte, Carsten Arend, Christian Hepp, TillmannGodde, Alexander I. Tartakovskii, Matthew Markham, Christoph Becher, † and Mete Atat¨ure † Cavendish Laboratory, University of Cambridge, JJ Thomson Ave, Cambridge CB3 0HE, UK Fachrichtung 7.2 (Experimentalphysik), Universit¨at des Saarlandes, Campus E2.6, 66123 Saarbr¨ucken, Germany Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK Element Six Ltd., Global Innovation Centre, Fermi Avenue, Harwell Oxford, Didcot, OX11 0QR, UK (Dated: September 16, 2014)Spin impurities in diamond can be versatile tools for a wide range of solid-state-based quantumtechnologies, but finding spin impurities which offer sufficient quality in both photonic and spinproperties remains a challenge for this pursuit. The silicon-vacancy center has recently attracted alot of interest due to its spin-accessible optical transitions and the quality of its optical spectrum.Complementing these properties, spin coherence is essential for the suitability of this center as aspin-photon quantum interface. Here, we report all-optical generation of coherent superpositionsof spin states in the ground state of a negatively charged silicon-vacancy center using coherentpopulation trapping. Our measurements reveal a characteristic spin coherence time, T ∗ , exceeding250 nanoseconds at 4 K. We further investigate the role of phonon-mediated coupling betweenorbital states as a source of irreversible decoherence. Our results indicate the feasibility of all-optical coherent control of silicon-vacancy spins using ultrafast laser pulses. PACS numbers: 42.50.-p, 42.50.Gy, 61.72.jn, 81.95.ug
Confined impurity spins in spin-free materials such asdiamond and silicon offer a multitude of opportunitiesranging from fundamental studies of engineered meso-scopic spin system dynamics to potential applicationsemerging from quantum control. A fundamental advan-tage of diamond-based impurities, known as color cen-ters, is that they can be optically active in the conve-niently detectable visible to near infrared region of thespectrum [1, 2]. Of these, the nitrogen-vacancy cen-ter (NV) remains the most studied one [3–6]. Sharingits desirable and undesirable properties alike, a handfulof other impurities have recently been investigated [7].These investigations reveal, for the NV center, the pres-ence of crystal-field splitting in the ground state manifoldallowing for feasible microwave control [8–11]. However,the unfavorable, but dominant, emission into phononsidebands also occurs in these centers. Contemporaryresearch efforts focus on two parallel approaches: Ampli-fying the zero-phonon emission by coupling selectively toan optical mode of a cavity [7, 12, 13] and investigatingalternative color centers with sufficiently small phononsideband contribution to the full optical spectrum [7, 13].The negatively charged silicon-vacancy (SiV - ) center isa particularly interesting justification to pursue the latterof the two approaches: The optical transitions couplingthe excited and the ground state manifolds are predom-inantly into the zero-phonon line [14], which can be fur-ther enhanced by making use of the ongoing progress indiamond-based optical cavity nanostructures [15]. Also,the impressively small variation in the emission spectrumamong multiple SiV - centers in a clean diamond matrix[16, 17] deems them desirable for coupling multiple spinsvia a common photonic mode. In parallel, recent demon-strations of the direct optical access to the spin degrees of freedom of single SiV - centers [18] offer the excitingpossibility to employ full quantum control relying onlyon optical fields [19, 20], which can bring the speed-upadvantage of optics over control techniques in the mi-crowave regime. However, there are a number of openquestions that need to be answered before such steps for-ward can be taken. Arguably, the most pressing challengeis to determine the coherence time of the SiV - spin in theground state in the presence of the potentially detrimen-tal coexistence of the spin and orbital degrees of freedom.In this Letter, we achieve coherent population trapping(CPT) between Zeeman-split states as a means to gen-erate a coherent superposition, i.e. coherent dark state,of a single SiV - center spin. We report a spin coherencetime (T ∗ ) lower bound of 250 ns - more than two ordersof magnitude longer than the optical transition timescale[17, 21]. We first identify the operational conditions forgenerating the Λ system required for CPT by controllingthe angle of the applied magnetic field. We further in-vestigate the role of phonons as a source of decoherencewithin the ground state by tuning the spin states acrossan avoided crossing, where spin orthogonality is relaxed.We investigate two samples, an electronic grade (001)-oriented CVD diamond used for magnetic-field orienta-tion measurements and a (111)-oriented type IIa high-pressure-high-temperature (HPHT) diamond used forspin coherence measurements. SiV - centers are generatedby Si implantation followed by thermal annealing. Toenhance the optical excitation and collection efficiencies,arrays of solid immersion lenses (SILs) are fabricated onthe surfaces of both samples using a focused ion beam(FIB) (for further details, see [22]). All our experimentsare carried out at 4 K.An SiV - center is formed by a substitutional silicon a r X i v : . [ qu a n t - ph ] S e p Magnetic field [T] W a v e l eng t h [ n m ] B || [111] ** Magnetic Field (T) Magnetic Field (T) W a v e l eng t h ( n m ) W a v e l eng t h ( n m ) (a) (b) (c) B || [111]
FIG. 1: (Color online) (a) Atomic structure of the SiV - color center, consisting of a Si impurity (purple) situated on aninterstitial position along the [111] bond axis and surrounded by a split-vacancy (light grey) and the next-neighbor carbonatoms (blue). (b, left) Resulting energy levels and spin projections for magnetic fields applied along [111]. The level schemeshown here is simplified (a detailed scheme can be found in [22]). Optical transitions (blue arrows) are allowed betweenlevels of the same spin state and the most visible ones are marked by blue dots in the magnetic field-dependent non-resonantfluorescence spectrum at 4 K (excitation at 660 nm) (b, right). Applying the magnetic field along the [¯1¯11] direction on thesame SiV - center, transverse field components lead to a finite spin overlap for all ground and excited states (c, left), resultingin additional optical transitions (pink arrows), observed in the field dependent spectrum (c, right). The spin labels refer to aBloch vector representation, as explained in [22]. atom and a vacancy replacing two neighboring carbonatoms in the diamond matrix along the (cid:104) (cid:105) axes. Thesilicon atom relaxes to the interstitial lattice site toform an inversion-symmetric split-vacancy structure [seeFig. 1(a)] [23]. The spin-orbit coupling dictates an in-herent quantization axis for the spin degree of freedomaligned with the SiV - symmetry axis in both the groundand the excited state manifolds [24]. Figure 1(b) displaysthe fluorescence spectrum from a single SiV - center in the(001) sample under non-resonant excitation with a mag-netic field applied along this inherent [111] quantizationaxis. The dominant optical transitions (four of whichmarked by blue filled circles) conserve the spin state,as illustrated in the accompanying energy level scheme.Weaker transitions, identified by asterisks, arise due toa slight mismatch between the symmetry axis and thedirection of the applied magnetic field. This serves to re-veal the importance of the magnetic field orientation foroptical transition rules in the SiV - center level scheme.A magnetic field, applied at a finite angle to the [111]direction, constitutes an external quantization axis whichcompetes with the SiV - center’s internal counterpart.The ground and excited state manifolds experience differ-ent strength of spin-orbit interaction [24]. Consequently,this configuration gives rise to different effective quanti-zation axes between the two manifolds. The net anglebetween these resultant quantization axes, in turn, de-termines the optical selection rules for the fluorescencespectrum. Figure 1(c) presents the same measurementas Fig. 1(b), but for a [¯1¯11]-oriented magnetic field. Thespin selectivity of the optical transitions no longer holdsand new optical transitions arise as the strength of the magnetic field increases. Four of these additional tran-sitions are indicated by pink open circles and pink ar-rows. In summary, the fully aligned magnetic field case[Fig. 1(b)] yields cycling transitions, whereas a magneticfield at an angle allows for typical Λ schemes, where twoorthogonal spin ground states can have finite transitionmatrix elements to the same excited state. This providesthe desired configuration for all-optical manipulation ofthe SiV - spin via this shared excited state.Figure 2 illustrates the detection strategy and char-acterization of the SiV - center used for coherent popu-lation trapping. We start by identifying a bright SiV - center within the SIL array of the (111) sample. Super-imposed images of electron and fluorescence microscopyscans for the same area of the sample, as shown inFig. 2(a), demonstrate an example of enhanced SiV - flu-orescence under one of the SILs. Figure 2(b) shows thedetection concept for all single- and multi-laser resonantexcitation experiments, where the signal is obtained bymeasuring the integrated fluorescence from the transi-tions in the shaded area as a function of the excitationlaser frequency. Non-radiative decay into the lower or-bital branch of the excited state followed by fluorescenceallows us to monitor excited-state population directlywith no residual laser contribution [18]. In order to al-low Λ schemes, the angle between the external magneticfield and the SiV - center axis is set to 109.4 ◦ , i.e. theangle between [¯1¯11] and [111] directions [see Fig. 1(a)].Pulsed intensity-correlation measurements performed onthe selected SIL suggest the presence of two individualSiV - centers with strong spatial and spectral overlap [22].Single-laser resonant excitation of the D1 transition un- Laser Detuning (GHz) AP D D e t e c t i on R a t e ( H z ) D e t e c t i on E xc i t a t i on ( D ) AP D D e t e c t i on R a t e ( H z ) (a)(b) (c) FIG. 2: (Color online) (a) Scanning electron microscope im-age of the solid immersion lens array on the HPHT sample,superimposed by a corresponding fluorescence image (exc.690 nm, det. 730-750 nm). (b) Optical excitation is performedresonantly to the highest energy exited state (transition D1,thick red arrow), from where a relaxation to lower excitedstates (black arrows) occurs, followed by an optical decay tothe ground state (red/blue arrows). The emitted fluorescencephotons are detected as a function of the excitation frequency.(c) At B = 3 T, resonant excitation reveals the presence of twoSiV - emitters, spectrally separated by approximately 8 GHz. der 3 T magnetic field resolves the resonances of the twocenters spectrally owing to their slightly differing (2%)strain, as shown in Fig. 2(c). This slight variation in thestrain tensor between the two centers is used to addresseach SiV - selectively. The following experiments are per-formed using emitter 1 in Fig. 2(c).If the two transitions of a Λ system are driven simul-taneously, the spin is optically pumped into a coherentsuperposition of the two ground states (dark state) de-termined by the two optical fields; a technique known asCPT [25]. As a consequence of destructive quantum in-terference, optical excitation to the shared excited stateand, consequently any fluorescence originating from thisstate, is suppressed. The reduction of the integrated fluo-rescence, i.e. the CPT dip, is strongly dependent on thecoherence between the two ground states and its spec-tral width allows direct measurement of the coherencetimescale of the ground state [25]. Figure 3(a) presents atwo dimensional CPT scan for the SiV - at 0.7 T magneticfield as a function of the optical frequencies of the twolasers driving the D1 and D2 transitions selectively, asillustrated in Fig. 3(b). The two ground states addressedoriginate from the same orbital branch and have ortho- gonal spin projections [22]. The manifestation of CPTis evident as a significant drop of the fluorescence inten-sity at two-photon resonance ( δ L1 − δ L2 = ∆, where δ L1 and δ L2 denote the laser detunings from the D1 and D2transitions and ∆ is the frequency difference between thetwo states). Figure 3(c) presents the CPT dip obtainedby scanning the frequency of the laser driving the D2transition, while keeping the D1 excitation fixed on res-onance. In order to extract the ground state coherencetime both lasers are kept at sufficiently low excitationpowers (equal to saturation power for the D1 transition -1.0 -0.5 0.0 0.5 1.0-1.0-0.50.00.51.0 AP D c oun t s ( k H z ) B = 0.7 T N o r m a li z ed I n t en s i t y ( a . u . ) Two-Photon Detuning (MHz)Laser Detuning from D1 (GHz) La s e r D e t un i ng f r o m D ( G H z ) AP D D e t e c t i on R a t e ( k H z ) D2D1 (a)(b) (c)
60 60
FIG. 3: (Color online) (a) CPT scan: SiV - fluorescence in-tensity recorded as the frequency of the laser resonant withtransition D2 is scanned and the laser resonant with transi-tion D1 is fixed at a given frequency. Laser powers are equalto approximately four times and seven times the saturationpowers for transitions D2 and D1 respectively. (b) Relevantlevel structure and the driven transitions D1 and D2. (c) CPTscan at low driving power (0.33 µ W each, corresponding to thesaturation power for the D1 transition and half the saturationpower for D2) yielding a dip full width at half maximum of12.1 MHz. The purple line corresponds to a fit using a modelbased on optical Bloch equations [22] and giving a decoher-ence rate between the two ground states of 4 . ± . - center. and half the saturation power for D2) in order to min-imize power broadening effects in the CPT dip. Usinga Lorentzian fit, the full width at half maximum of theCPT dip under these conditions is 12.1 MHz. A theoret-ical model, based on optical Bloch equations which in-clude the excited state dephasing, residual power broad-ening and the mutual coherence of the lasers, is used tofit the data with the decoherence rate between the twoground states as a free parameter. This provides an up-per bound of 4 . ± . - ground-state coherence time exceeding 250 ns.The observed coherence time is more than two ordersof magnitude longer than the timescale for thermaliza-tion, which typically takes place within a nanosecond[18]. Hence, we suggest that it is the spin that dictatesthe decoherence mechanism for the ground states, as thephonon-induced thermalization for ground states of op-posite spin is quenched. To support this argument, wetake advantage of the presence of an avoided crossing at3.5 T between two of the ground states. By sweeping themagnetic field over the region of the avoided crossing,we relax the spin state orthogonality, thus progressivelyallowing for phonon-mediated decoherence of the darkstate. Figure 4(a) depicts the evolution of the spin forthe ground states coupled by CPT, as the magnetic fieldis varied over the avoided crossing. From 0 to 3.5 T, thedark state is generated between states | (cid:105) and | (cid:105) , whileabove 3.5 T the dark state is generated between | (cid:105) and | (cid:105) , as illustrated by the red and blue ribbons respectively[22].Figure 4(b) shows the linewidth of the CPT dip as afunction of the magnetic field ( | (cid:105) - | (cid:105) as red filled circles, | (cid:105) - | (cid:105) as blue filled circles). This width is proportionalto the decoherence rate between the two driven states,on top of a constant power broadening due to the lasers[26]. The dip width increases rapidly when approachingthe avoided crossing, and reaches minimum values forboth low and high field limits. We calculate the spin-overlap between the two driven states and display it asdashed gray lines Fig. 4(b) [22, 27]. This simple approachalready describes the observed trend, emphasizing thecentral role of the spin orthogonality of the two groundstates for decoherence. The spin overlap is multiplied bya Boltzmann factor (red and blue solid lines [22, 27]), thustaking into account the thermal activation of phonons be-tween the addressed ground states, as their energy differ-ence increases with increasing magnetic field. A detaileddescription of the phonon-mediated mechanism, such asphonon scattering or dynamic Jahn-Teller distortion, canbe identified after a temperature-dependent investigationis performed. The agreement between our simple modeland the experimental data confirms the hypothesis thatthe ground state coherence time of 250 ns measured awayfrom the avoided crossing corresponds to the coherenceof the spin in the driven ground states. This spin coher- ence time is identified as the free induction decay time( T ∗ ). It is worth noting that the sample employed forthe CPT measurement shows evidence for a considerableconcentration of substitutional nitrogen [N S ] [22], whichis known to be the main limitation for T ∗ of the nitrogenvacancy spin [28]. The same mechanism is likely to affectthe measured T ∗ for the SiV - center. Consequently, thiscoherence time can be extended using all-optical pulsedprotocols analogous to the dynamical decoupling tech-niques commonly applied to the NV center [29]. Magnetic Field (T) C P T L i ne w i d t h ( M H z ) Magnetic Field (T) E ne r g y ( G H z ) (a)(b) FIG. 4: (Color online) (a) Simulated ground states [22], illus-trating the spin state for magnetic field values below, aboveand at the avoided crossing (3.5 T). (b) Full width at halfmaximum of the CPT dip as a function of the magnetic field,using a Lorentzian fit. Filled circles denote measured widths(for each transition, laser powers equal to four times the sat-uration power), with the error bars being the standard devi-ation of multiple measurements. The solid lines display thespin overlap (grey dashed lines) between states used for CPT,multiplied by a Boltzmann factor [22]. In panels (a) and (b),the color red (blue) indicates CPT realized between states | (cid:105) and | (cid:105) for B < . | (cid:105) and | (cid:105) for B > . In this work, we verified the presence of a spin in theground state of the SiV - center in diamond, and probedits coherence using CPT. The ability to generate a coher-ent superposition of the SiV - spin state relying solely onoptical fields establishes the route to full quantum con-trol of the SiV - spin with picosecond operation timescale.This also allows for the implementation of all-optical dy-namical decoupling schemes, enabling to further extendthe coherence time of the spin state. 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