All-optical preparation of coherent dark states of a single rare earth ion spin in a crystal
Kangwei Xia, Roman Kolesov, Ya Wang, Petr Siyushev, Rolf Reuter, Thomas Kornher, Nadezhda Kukharchyk, Andreas D. Wieck, Bruno Villa, Sen Yang, Jörg Wrachtrup
AAll-optical preparation of coherent dark states of a single rare earth ion spin in acrystal
Kangwei Xia, Roman Kolesov, Ya Wang, Petr Siyushev, Rolf Reuter, Thomas Kornher, Nadezhda Kukharchyk, Andreas D. Wieck, Bruno Villa, Sen Yang, and J¨org Wrachtrup
3. Physikalisches Institut, Universit ¨a t Stuttgart, 70550 Stuttgart, Germany andStuttgart Research Center of Photonic Engineering (SCoPE), 70569 Stuttgart, Germany Institute for Quantum Optics and Center for Integrated QuantumScience and Technology (IQst), Universit ¨a t Ulm, D-89081 Germany Ruhr-Universit ¨a t Bochum, Universit ¨a tsstra β e 150 Geb ¨a ude NB, D-44780 Bochum, Germany (Dated: October 11, 2018)All-optical addressing and coherent control of single solid-state based quantum bits is a key toolfor fast and precise control of ground state spin qubits. So far, all-optical addressing of qubitswas demonstrated only in very few systems, such as color centers and quantum dots. Here, weperform high-resolution spectroscopic of native and implanted single rare earth ions in a solid,namely a cerium ion in yttrium aluminum garnet (YAG). We find narrow and spectrally stableoptical transitions between the spin sublevels of the ground and excited optical states. Utilizingthose transitions we demonstrate the generation of a coherent dark state in electron spin sublevelsof a single Ce ion in YAG, by coherent population trapping. Coherent population trapping (CPT) [1–4] is an all-optical way of coherent manipulation of electron andnuclear spin qubits. CPT and related physical phe-nomena (slow light, electromagnetically induced trans-parency, etc.) were initially applied to quantum ensem-bles. In recent years, however, it has been demonstratedon single fluorescent centers in solids [5–9] resulting inall-optical control of single qubits [10, 11], which is asignificant step towards fast and high fidelity control ofsingle qubit spins [12, 13].Rare-earth ions residing in inorganic crystal have beenwidely studied and applied in fields ranging from solid-state spectroscopy and laser physics [14] to quantum in-formation processing [15], due to their narrow opticaltransitions [16, 17] and long spin coherence time [18, 19].In particular, rare-earth ions in solids are promisingsystems for quantum information storage and process-ing [20, 21]. Achievements comprise six hours coherencetime of nuclear spins in Eu:Y SiO crystal [22], coher-ent storage of single photon states in Nd:YVO [23] andentangled photon pairs in Nd:Y SiO crystals [24]. Inaddition to progress made with ensembles of rare-earthions, the detection of individual ions have been demon-strated in three rare-earth species recently [25–29]. Highfidelity spin control of single Ce ion has been demon-strated by applying a resonant microwave field [30]. Withthis microwave control, the electron spin coherence timewas extended from 150 ns to 2 ms by using the dynam-ical decoupling technique. Extending these finding toall-optical spin control would enable much faster controland make best use of the photon-spin coupling of rareearth ions.Here, we report on CPT in a ”dark” coherent superpo-sition of the electron spin sublevels of a single Ce ion inYAG based on resonant optical excitation. CPT resultsin lower fluorescence yield of a Ce center when it is FIG. 1. (a). Unit cell of a YAG crystal. (b) Energy levelsof Ce ions in YAG. (c) SEM image of a SIL on the surfaceof the YAG crystal. (d) Laser scanning microscopy image ofCe ions underneath the SIL. The Ce ion is excited by a440 nm pulsed laser through the phonon absorption sideband.Bright spots correspond to individual Ce ions. excited by two laser fields in two-photon resonance withthe ground-state spin transition. Spectroscopic proper-ties of resonant optical transitions of single native ions aswell as single implanted ions have been studied. Thesestudies reveal an optical linewidth of ∼ π ×
80 MHz andsmall spectral diffusion compared to color centers in di-amond [31, 32] and quantum dots [33].Figure 1(a) shows the unit cell of a YAG (Y Al O )crystal. Trivalent cerium ions substitute trivalent yt-trium ions and form color centers. Cerium can be foundin yttrium-containing crystals as residual impurities. Al- a r X i v : . [ phy s i c s . op ti c s ] J un FIG. 2. (a) Emission spectrum of a single Ce ion at cryogenic temperature, showing a sharp ZPL and broad phonon absorptionsideband. The single Ce:YAG is excited by a 440 nm femtosecond laser with 7.6 MHz repetition rate. The spectrometer has1800 grooves/mm grating and the integration time is 5 min. (b) Excitation spectrum of the single Ce ion. The CW diode laserwith a wavelength of 489.15 nm is swept. While, the pulsed laser at 440 nm repumps the ion. An additional microwave(MW)field frequency of 1.15 GHz is applied simultaneously. The frequency matches the splitting of the lowest ground state spintransitions. (c) 20 successive photoluminescence excitation sweeps of a native single Ce ion. (d) Consecutive frequency sweepsof a single Ce ion created by focused ion implantation. ternatively, individual Ce can be introduced into the crys-tal artificially by doping during the crystal growth or byion implantation. The energy levels of Ce in YAG areshown in Fig. 1(b) [26, 34]. Ce has only one unpairedelectron, and its ground states are located in the 4 f shell. Electrons in the 4 f shell are efficiently screenedby closed outer lying 5 s and 5 p shells. This screeningis responsible for the weak interaction between ions andtheir surrounding environment. The ground state is splitinto two sublevels F / and F / due to spin-orbit cou-pling. These two sublevels are further split by the crystalfield interaction into three and four Kramers doublets, re-spectively. If an external magnetic field is applied, thedegeneracy of these seven Kramers doublets is lifted. Theexcited state is located in the 5 d shell. It splits into fiveKramers doublets due to the combined action of the spin-orbit coupling and the crystal field. The energy differencebetween the two lowest 5d Kramers doublets is approx-imately 8,000 cm − [26, 34] and, therefore, the excitedstates can be optically addressed individually. In addi-tion, the quantum efficiency of the 5 d → f transitionsis close to 100% [35]. The lifetime of the lowest 5 d stateis 60 ns [26, 36].In the experiment, a [1 1 0] orientated ultrapure YAGcrystal (Scientific Materials) is used. An external mag-netic field ( B ≈
450 G) is applied perpendicular to thelaser beam direction, so that four optical transitions be-tween the two pairs of spin states of the 4 f and 5 d levelsare allowed, as shown in Fig. 1 (c) [26]. A Λ scheme,which is a requirement for CPT, can be formed by op-tically mixing both ground states to either of the ex-cited spin states. Single Ce ions are detected un-der a home-built high resolution confocal microscope atcryogenic temperature ( T ≈ . ion.The emitted photons associated with broad phonon side-band are detected by an avalanche photodiode (APD)in a spectral range between 500-625 nm (see our previ-ous work [30]). A tunable single-mode narrow linewidth( ∼
500 kHz) continuous wave (CW) laser (wavelength of489.15 nm, Toptica Photonics DL pro) is used to reso-nantly excite single Ce ions.A portion of the emission spectrum of a single Ce ionin the vicinity of its zero-phonon line (ZPL), measured bya high resolution spectrometer, is shown in Fig. 2(a). Asharp zero-phonon line (ZPL) is located at 489.15 nm andaccompanied by a red-shifted phonon sideband partlyshown in the figure [38].A CW laser is swept across the ZPL position to obtainthe excitation spectrum of the single Ce ion shown inFig. 2(b). Four individual optical excitation-transitionlines are well resolved. These lines correspond to fourdifferent optical transitions between the lowest Kramersdoublets of the ground state and of the excited state withthe assignment indicated in Fig. 2(b). The full widthat half maximum(FWHM) of the optical transitions is ∼ π ×
80 MHz, which is broader than the lifetime limitedlinewidth 2 π × Al nuclear spin bath, i.e. it represents anintrinsic property of the host material [30].By monitoring the fluorescence during each successivefrequency sweep through the resonant transitions, we ob-serve stable optical resonance lines without obvious spec-
FIG. 3. (a) Fluorescence intensity of a single Ce ion underpulsed and CW laser excitation. (b) Scheme of the laser pulsesequences. The pulsed laser is used to bring the Ce backand the Ce:YAG is ionized by CW laser excitation when thepulsed laser is switched off. The femtosecond pulsed laserwavelength is 448 nm. The repetition rate is 2.5 MHz andthe average laser power is 10 µ W / cm . A blue diode laser(451 nm) with 150 µ W power is used as the CW laser. tral diffusion, as shown in Fig 2(c). It indicates thatnative single Ce ions have a surprisingly good spectralstability under resonant excitation.In addition to the native single Ce centers, the spec-tral stability of Ce ions created by ion implantation hasbeen investigated (see Fig. 2(d)). With high-dose implan-tation, we found about 100 ions in one confocal spot(seeSupplemental Material). The optical transition linewidthof the implanted Ce ions is ∼ π ×
150 MHz, increasedmainly due to extra strain introduced by ion implanta-tion. Since this linewidth is much narrower than theinhomogeneous width of ∼ π ×
550 GHz, it is possible toaddress single Ce ions by tuning the excitation laserwavelength into resonance with the optical transitions.Compared to other solid-state systems, e.g. defects indiamond and quantum dots [6, 8, 9, 31, 32], implantedsingle Ce presents narrow optical transitions and a sta-ble spectrum. The combination of narrow optical transi-tions and spectral stability makes precision optical con-trol of single Ce ion spins possible comparable to singlepraseodymium ions in solids [28, 29, 39].In order to measure the excitation spectrum of a singleCe , a CW laser is applied to resonant excitation aswell as a low repetition rate, femtosecond laser with highpeak intensity. If a single Ce is excited with CW laseronly, its fluorescence intensity shows a smooth decay andquickly goes to background level in a few seconds, asshown in Fig. 3(a). The decay curve in Fig. 3(a) is theobservation of a fluorescence time traces of the singleCe ion under CW laser excitation only. Surprisingly, in contrast to all other single emitters a gradual decay ofthe fluorescence is observed and not as usual a step-wisebleaching. In order to explain such gradual bleachingof a single Ce ion, we propose a model involving twocompeting processes: 1) photo-ionization from Ce intoCe and 2) restoration of Ce by taking an electronfrom a nearby deep donor. As long as there are enoughdeep donors in the vicinity of the ion, the cerium remainsin its trivalent state and fluoresces. However, a gradualreduction of the number of donors reduces the probabilityof restoring the trivalent state of cerium. This leads to agradual decrease of the fluorescence intensity. The chargedynamics of single ions observed here is consistent withprevious observations in ensembles [36, 40, 41]. It alsoexplains why attempts of detecting single Ce ions underCW laser excitation were unsuccessful [26].Surprisingly, a femtosecond laser featuring a high peakintensity restores the population of donors, which helpsthe Ce ion pumping back to the Ce charge state (seeFig. 3(a) and (b)). Therefore, to keep the Ce ion pho-tostable, we apply CW and pulsed lasers simultaneouslyin the experiments. Details of these charge dynamics arediscussed in the Supplementary Material.From the four different optical transitions of single Ceions, a Λ system can be formed, consisting of two groundstates and either one of the excited states. In experi-ments, we choose the Λ system with transitions D1 andD3. To observe CPT, the pump laser frequency is fixedon the transition line D1, and the frequency of the probelaser is swept around the frequency of the D3 transition.Simultaneously, the fluorescence intensity of the singleCe ion is monitored, which is shown in Fig. 4(b). Itcontains a broad peak with a dip going down nearly to thebackground level. The total width of the peak is consis-tent with the optical transition linewidth (Fig. 2(b)). Thedip is centered exactly at the D3 transition, indicatingthat the ground state population is coherently trappedin a dark state.The observed dip width is around 2 π ×
35 MHz, causedby several sources of decoherence, including the intrin-sic linewidth of the ground state spin transition andthe laser power induced broadening. To understandthis 2 π ×
35 MHz CPT linewidth, we perform opticallydetected magnetic resonance (ODMR) on the groundstates, to obtain the intrinsic linewidth of the groundstate spin transition. We use laser excitation resonantwith the D3 transition to initialize the ion into the spinup state. Microwave (MW) radiation is applied throughthe wire located next to the position of the ion underinvestigated. Then, the MW frequency is swept throughresonance of the ground-state spin transition. The powerof both, laser and MW is kept low to avoid power broad-ening (tens of microwatts of laser power and ∼ π × π ×
62 MHz for the D1 transition. The pump laserinduced Rabi splitting with a much weaker dip, as shownin Fig. 4(b), further indicates that the observed dip cor-responds to the successful formation of a coherent darkstate.To quantify the power broadening effect, we mea-sured the CPT dip width for various laser powers. Thelinewidths are linearly dependent on the laser power,as shown in Fig. 4(c), in agreement with expecta-tions. Through a linear fitting, we extract a linewidth ∼ ± by the CPT technique. All-optical control of asingle spin qubit based on a Ce can thus be realizedby dynamically manipulating coherent laser fields. Inaddition, on-chip photonic circuits for this system whichadds another critical element for their use in quantumtechnology.We would like to thank Philippe Goldner, Alban Fer-rier, Rainer St¨ohr and Nan Zhao for discussions. Thework is financially supported by ERC SQUTEC, EU-SIQS SFB TR21 and DFG KO4999/1-1 [1] H. Gray, R. Whitley, and C. Stroud, Opt. 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