A realistic fabrication and design concept for quantum gates based on single emitters integrated in plasmonic-dielectric waveguide structures

Tremendous enhancement of light-matter interaction in plasmonic-dielectric hybrid devices allows for non-linearities at the level of single emitters and few photons, such as single photon transistors. However, constructing integrated components for such devices is technologically extremely challenging. We tackle this task by lithographically fabricating an on-chip plasmonic waveguide-structure connected to far-field in- and out-coupling ports via low-loss dielectric waveguides. We precisely describe our lithographic approach and characterize the fabricated integrated chip. We find excellent agreement with rigorous numerical simulations. Based on these findings we perform a numerical optimization and calculate concrete numbers for a plasmonic single-photon transistor.

Scientific RepoRts | 6:28877 | DOI: 10.1038/srep28877 fields are accessible from the outside 17 rendering SPPs interesting for functionalization with single emitters in hybrid approaches. In contrast to approaches that use directly incorporated emitters 18 , assembly of hybrid devices allows for independent optimization of the quantum emitters and the light guiding structures 19 . Accordingly, theoretical proposals predict switches working at the single SPP level 4 and devices achieving strong coupling of emitters to propagating SPPs 14 . We show here how the rather idealized system of a single emitter controlling the transmission of SPPs in a cylindrical nanowire considered in the proposal by Chang et al. 4 can be actually transformed into a practical on-chip device. First, we introduce an elaborate fabrication process allowing for the realization of highly integrated and efficient plasmonic-dielectric elements. The excellent agreement between the experimental optical response and the corresponding numerical simulation then enables us to provide a realistic design for an integrated plasmonic single-photon transistor. In particular, we investigate a structure that is optimized for single molecules as sources of the non-linearity. Concrete parameters for experimentally expectable non-linearities and throughput are provided.

Results
Design considerations for a quantum plasmonic non-linear element. For an experimental realization of a single photon non-linear device, based on a hybrid approach like discussed before, there are two key ingredients: • An efficient, integrated dielectric-plasmonic structure that allows for high coupling rates between emitter and guided mode, i.e., high Purcell factors and low quenching rates, • A stable single quantum emitter with predictable properties, large optical dipole moment, and -importantly -with a large branching ratio η ZPL of emission into its zero phonon line (ZPL) with respect to phonon-assisted emission (η ZPL is also referred to as (photonic) Debye-Waller factor).
In this paper, we focus on the dielectric-plasmonic structure. However, with respect to emitters we refer to organic molecules throughout this paper. Even more specific we consider dibenzoterrylene (DBT) hosted in anthracene (AC) crystals with emission lines around 785 nm. This bright emitter features high photo-stability and a narrow lifetime-limited linewidth at cryogenic temperatures 20 with a high branching ratio of up to η ZPL = 50% 21 . Assembly of the hybrid system would be finally performed by spincoating of a DBT-toluene mixture with AC in diethylether or by evaporation of this solution onto the chip. By this, DBT-doped AC crystals will form all over the chip. Here the aim is to avoid the need of a deterministic placement of individual DBT molecules. When the linewidth of the emitters is decreased to its Fourier-limit (<100 MHz) by cooling in a cryostat (to ≈2 K), individual emission and absorption lines are selectively accessible due to the inhomogeneous broadening. In this way emitters can be addressed individually by bringing the excitation laser into resonance with a specific absorption line. Thus, a very high density of DBT emitters can be used, without losing the possibility to address individual emitters, which would be the case at room temperature. This means that thousands of molecules can be hosted even in small volumes like that of a laser focus. At such high densities, finding well-positioned emitters deposited in the near-field region of the plasmonic waveguide is most likely which circumvents the need for spatial post-alignment.
The efficiency of an integrated dielectric-plasmonic structure working on the single photon and single emitter level depends on efficient coupling of far-field optics with on-chip photonics and emitters. Especially SPPs generated on the chip must be extracted with high efficiency to allow for good signal-to-noise ratios in experiments. Further, on the chip, an efficient coupling to SPPs is needed while keeping propagation losses as small as possible.
Coupling into (and out of) the integrated dielectric waveguides is here performed via Bragg-grating far-field couplers 22 . Moreover, an earlier optimized photon-to-plasmon transducer geometry (see ref. 23) allows for very high single mode conversion. Finally, the excited SPP is supposed to interact strongly with a closely positioned emitter. It is essential to address a plasmonic mode that provides a high Purcell factor P = Γ WG /Γ 0 and a high (ideally near-unity) β-factor: β = Γ WG /Γ tot (where Γ tot is the emitter's total decay rate, Γ WG the coupling rate to the guided SPP and Γ 0 is the vacuum decay rate of the emitter). Strong field enhancement close to the plasmon waveguide does not guarantee that the emitter's decay rate Γ tot is dominated by the emission into a single guided SPP mode with rate Γ WG 14 . In a realistic scenario various channels can contribute to Γ tot , such as coupling to weakly guided or radiating modes 24 , the presence of more than one bound mode in waveguides 25 and especially quenching by surface energy transfer (SET) 26 . At the same time, the coupling strength to the plasmonic mode has to be balanced with the unavoidable propagation losses. The plasmonic waveguide has to be as short as possible without introducing direct coupling between dielectric waveguides which would undermine the signal-to-noise ratio of the entire device: ideally any photon that passes the integrated structure must have interacted with the emitter. The design must allow for practical coupling of emitters after fabrication. Figure 1 illustrates schematically our (symmetric) device architecture. A Bragg-grating coupler funnels far-field photons into a dielectric Si 3 N 4 waveguide. Then, an efficient V-type photon-to-plasmon transducer (details of its design and numerical simulation via finite element method (FEM) in ref. 23) transfers excitations into a short SPP-waveguide with tight confinement. There, organic dibenzoterrylene (DBT) molecules precisely positioned next to the plasmonic waveguide will either reflect or give way to incoming single SPPs depending on the molecule's internal state and the detuning between SPP and optical transition of the emitter, yielding a non-linear behavior. Finally, transmitted SPPs are converted into guided photons and eventually coupled into free-space again. is almost absorption-free in the desired wavelength range (785 nm). For the plasmonic part of the chip we use a bi-layer consisting of 5 nm Cu and 60 nm Au, evaporated on the chip. This material system represents a compromise between fabrication constraints, stability under ambient conditions and propagation losses by Ohmic resistance in the metallic structure. To produce the combined photonic-plasmonic structures two complementary lithographic techniques are used. The Si 3 N 4 can only be structured by a subtractive method 27 , i.e., a positive etch-mask is fabricated and the nitride is removed via etching. In contrast, the plasmonic gold parts have to be built up via additive nanostructuring. Both methods need masks in opposite tones. In addition the additive structuring needs a sacrificial layer for a lift-off process. These circumstances and the gap between the dielectric and plasmonic part in the nanometer range impede a separation into consecutive structuring steps. Figure 2 gives an overview of the fabrication process of the transducer region. For the electron beam lithography (EBL) steps we use a Vistec EBPG5000plus system with 100 kV acceleration voltage, an Oxford plasmalab 80 plus for reactive ion etching (RIE) and a Leybold thermal evaporation system. In the first EBL step, square markers with an edge length of 20 μm are fabricated using a Ti-Au-Ni-layer system (not shown in Fig. 2). Later on, these markers allow alignment of the three subsequent EBL steps for which an accuracy of at least 5 nm was found. In the second EBL step, the coupler gratings of the dielectric grating couplers (consisting of coupler grating and reflection grating) are fabricated (not shown in Fig. 2). A PMMA (2.2 M, Microchemicals) resist layer is used as an etch-mask and the structure is transferred to the substrate via a highly anisotropic CHF 3 -RIE-process (etch-depth 60 nm). In a third EBL step a nickel etch-mask for the dielectric waveguides and the reflecting gratings (Bragg mirrors) of the grating couplers are prepared. The recoated substrate (PMMA 2.2 M) is then exposed by EBL and the resulting positive mask is coated with 10 nm Ni by evaporation. The subsequent lift-off step is done using dimethylformamide (DMF) (Fig. 2b). To achieve the required small gaps between plasmonic and dielectric waveguide, the Si 3 N 4 -layer is also used as a mask for the plasmonic parts in the fourth lithography step. Therefore the substrate is coated with a 150 nm thick ZEP 7000 (Zeon Corporation, Japan) resist layer (burying the thin Ni etch-mask underneath it), which is structured with the positive tone of the plasmonic transducer. Compared to standard PMMA, the ZEP resist has a higher etch-resistance, thus the resist remaining after etching is still thick enough to be used as sacrificial layer in the following lift-off process. A thicker PMMA layer cannot be used as the high aspect ratio at the required structure sizes could not be achieved. The Si 3 N 4 layer is partially removed in a highly anisotropic CHF 3 -RIE process at the designated positions of the plasmonic parts ( Fig. 2c). At this step the control of the etch-depth allows adjusting of the vertical placement of the plasmonic transducer, which might be used in principle as an additional control parameter to achieve coupling efficiencies even higher than predicted in ref. 23. Actually, for the structures characterized in this study, the plasmonic parts are fabricated on top of a 115 nm Si 3 N 4 plateau of the same cross section, elevating the plasmonic waveguide to the center of the dielectric waveguide (not shown in Fig. 2 for simplicity). This particular chip was used here, as its overall quality was very high. Adapted numeric simulations for this specific elevated design however reveal that its transducer efficiency is not optimal A stream of photons is coupled via a dielectric grating coupler to a dielectric waveguide made from Si 3 N 4 (blue color) which guides the photons to a V-shaped photon-to-plasmon transducer, where SPPs in a short plasmonic gold stripe waveguide (golden color) are excited. Well aligned emitters (e.g., DBT molecules in AC) experiencing high Purcell factors in the near-field of the plasmonic waveguide, intensely interact with the SPPs. After the interaction, SPPs are transduced back to photons and guided away by a second dielectric waveguide. These photons are eventually coupled out through a second grating coupler. and will drop from 60% (in ref. 23) to around 40%. The plasmonic Cu-Au layer system is evaporated with a high working distance of 45 cm which results in only thin walls at the edges of the plasmonic transducer (Fig. 2d). The particular choice of Cu guarantees a smooth gold surface, Cu is not affected by the last wet etch-process and it has relatively small Ohmic losses. Additionally, the gold is covered with a 10 nm Nickel layer (not shown in Fig. 2 for simplicity) for high resistance to the final CHF 3 -RIE process. Removal of the sacrificial ZEP layer is again done with a DMF lift-off (Fig. 2e). The final process steps are the etching of the dielectric waveguides in a highly anisotropic CHF 3 -RIE process and the removal of the Ni etch-masks by wet etching with hydrochloric acid (Fig. 2f).   They consist of two gratings, where the coarse grating performs the actual coupling and the second, finer grating acts as a Bragg-mirror to enhance the directionality of the coupling, into the dielectric waveguide. For the measurements on the efficiency of the grating couplers, a focused beam coming from an objective with a numerical aperture (NA) of 0.4 is used. In order to derive the efficiency, the total irradiated laser power needs to be known. To this end, the reflection of the laser spot from a flat silver mirror (assumed to be almost 100% reflective) was used to determine the absolute incoming power P tot (measured in counts on an Andor electron multiplying charge-coupled device (EMCCD) camera). During the analysis of the grating couplers, the reflection of the laser on a flat chip-area next to the waveguide structures (P reflect ) was repeatedly measured to track the laser's power stability. The actual in-and out-coupling to and from the waveguide structures was adjusted with micrometer screws, an x-y piezo stage and a piezo to align the focus until the out-coupling (P out ) was optimized. As two grating couplers are used here that are connected via a waveguide, we actually measure the product of two efficiencies η in ⋅ η out ≈ η GR 2 (where η GR 2 = P out /P tot ), so that the root of the result gives the average coupling efficiency η GR of a single grating coupler. The procedure was performed for a series of waveguide structures (Fig. 4a,b) and an efficiency of η GR = 35 ± 2% was found. Now we study the performance of the photon-to-plasmon transducers. In particular the coupling efficiency η spp is determined, given by the ratio of the excited SPPs to the number of the incoming photons in the dielectric waveguide. To this end, we compare the transmission of the fabricated photonic-plasmonic structures to the transmission of purely dielectric reference structures fabricated on the same sample. Note that variations in 2 ) measured at the 'out-coupler' gratings of ten different test waveguide-structures (without plasmonic elements). The dashed vertical line and the shaded region show the mean value of η GR 2 = 12.4 ± 1.7% and the uncertainty region of one standard-deviation, respectively. This mean value yields an efficiency of a single grating coupler of η GR = 35 ± 2%. (c) CCD camera image corresponding to a measurement for estimating the coupling efficiency η spp of the photon-to-plasmon transducer. The large upper spot stems from scattering of an expanded laser at the first Bragg-grating, the small spot (marked by a black circle) correspond to scattered out-coupled photons from the second Bragg-grating. The distance between two opposing grating couplers is approximately 50 μm. (d) Measured relative out-coupled flux (crosses) as a function of plasmonic waveguide length L. The solid blue curve is a double exponential fit to the signal, showing that typical SPP damping is present. Dashed lines show the contributions of the fast and slowly decaying components, respectively. Fitting the slow decay at zero waveguide length yields a coupling efficiency of η spp = (57 ± 21)%. The coupling efficiency seems to be high for short length L only due to direct coupling of the photonic waveguides by scattered photons (fitted by the fast exponential decay). transmission through the reference structures are below 2% due to the high quality of the fabrication process, ensuring the comparability with the results from Fig. 4a,b). In this series of measurements, we use an inverted microscope with a CCD camera for detection. One of the Bragg-gratings on the end of the dielectric waveguide is fully illuminated by a weakly focused laser (λ = 785 nm). The sample is aligned to optimize the transmission to the Bragg-grating at the opposite end. Images are taken by the CCD camera and analyzed (Fig. 4c). By normalizing the intensity at the output grating with respect to the flux emerging from the reference structures without plasmonic components, the overall efficiency of the plasmonic components is determined. To determine the propagation losses in the plasmonic waveguides and to extract the efficiency η spp of the photon-to-plasmon transducers, the measurement is repeated for a series of waveguide structures with different plasmon-waveguide length L (Fig. 4c,d): A fitting with a double-exponential (f(z) = Ae −αz + Be −βz ) is performed. The extrapolation of the slowly decaying component of this fit to L = 0 reveals a conversion efficiency η spp 2 = (32 ± 12) % for two transducers and hence η spp = (57 ± 21) % can be deduced for a single photon-to-plasmon transducer. This value is consistent with numerical simulations (analog to ref. 23) of the fabricated structures predicting η spp,FEM = 40%. The exponential fit in Fig. 4d) matches the data points for large lengths L as it is expected for a plasmon waveguide with propagation losses leading to an exponential damping. The lower decay-constant corresponds to an attenuation constant α = (0.54 ± 0.14) μm −1 or a SPP propagation length of λ spp = (1.84 ± 0.47) μm, i.e., the distance at which the SPP's intensity decays to 1/e of the initial intensity. This is in agreement with FEM simulations where α FEM = 0.49 μm −1 and λ spp,FEM = 2.05 μm were found, respectively. For very short waveguide lengths the apparent coupling is larger than the estimated photon-to-plasmon conversion efficiency, since photons directly couple into the second dielectric waveguide by scattering. From the fast decay-constant, we can conclude, that the plasmon waveguide in this device needs to have a length of about L min ≈ 2 μm in order to avoid direct photon-coupling between the dielectric waveguides. Such direct coupling would manifest in a reduced signal-to-noise ratio of the envisioned effects as photons could pass the quantum emitter without interacting with it.
Based on this result, we conclude that our numerical approach (discussed in detail elsewhere 23 ) can indeed give a quantitative estimate for the performance of the on-chip structures. Further we conclude that although the fabrication procedure is more complicated than for purely dielectric or purely plasmonic structures and although idealized conditions (ignoring roughness, defects, etc.) have been assumed within the computations, we can indeed reach the high efficiencies found in numerical simulations.

Numerical optimizations for high Purcell and β-factors. In this section we estimate the non-linear
performance of the device when coupled to emitters. It is essential to establish a high Purcell factor P and a high β-factor at the same time. This can be seen, e.g., by looking at the reflectance R of a single emitter onto a single impinging guided photon/SPP (according to Chang et al. 4 ): with the detuning between the emitter's transition and the SPP's frequency δ, the Debye-Waller factor η ZPL and the unperturbed (vacuum) decay rate of the emitter Γ 0 . At resonance (δ = 0) this simplifies to R = (η ZPL ⋅ β) 2 . In a concrete experiment, the transmittance T would drop when the incoming light, e.g., from an attenuated laser, is scanned over the emitter's transition. A large magnitude of the Purcell factor P is relevant, as two features will be enhanced: (i) the width of the transmittance dip and (ii) the potential rate of impinging SPPs that the emitter can handle before it saturates, which would destroy its ability to reduce the transmittance. As mentioned earlier, β relates the decay rate Γ WG induced by the guided mode to the overall decay rate Γ tot . In any plasmonic structure the latter will typically exceed Γ WG by orders of magnitude when the corresponding emitter is very close to a metallic surface (see e.g. 26,29,30 ) which is typically ascribed to electron-hole pair creation. As the field of the excited mode in the simple plasmonic stripe waveguide is closely localized to the metal, the hot spots coincide spatially mainly with areas of strong quenching (high Γ tot ) leading to poor β-factors. Thus, Chang et al. 4 suggest to taper the plasmonic waveguide down to less than 50 nm to enter a regime where both P and β reach sufficiently high values for the fundamental guided mode. It turns out, that this approach of tapering the width of the on-chip waveguide fails for our transducer-design, as the transducer does not couple to the fundamental mode but almost entirely to the next higher mode which experiences a cut-off during tapering. The dielectric waveguides on the chip support almost purely transversal magnetic (TM) or transversal electric (TE) modes (Fig. 5a,b) with a nearly linear polarization perpendicular to the propagation direction. In contrast, the fundamental plasmonic mode, i.e., the only plasmonic mode, which does not suffer from a cut-off when tapered down, features a nearly radial polarization of a breathing mode (Fig. 5c). Consequently, the symmetries of the guided dielectric and the fundamental plasmonic mode do not fit to each other and a high coupling efficiency between these modes cannot be expected with our transducer design. It rather exclusively couples to the mode depicted in Fig. 5d). This problem can be tackled with a plasmonic slot-waveguide. These waveguides can be constructed simply by a slot in a metallic film (Fig. 5h) or by two parallel stripe waveguides, yielding a 'slot-stripe' waveguide ( Fig. 5e-g). Specifically, a mode is supported, that channels most of the electromagnetic flux through the slot which promises high Purcell factors. Most importantly, the polarization matches better to the dielectric waveguide modes. For this reason we adapted our transducer design to work with a slot-waveguide. Figure 6 shows a simulation of an adapted transducer feeding a slot-waveguide in a metal film (similar to the transducer-design by Tian et al. but with a much narrower slot 31 ) and a slot-stripe waveguide, respectively. On first glance the slot-stripe waveguide (Fig. 6b) promises much better coupling efficiency with respect to the ordinary slot-waveguide (Fig. 6a) where film SPPs are excited that represent a loss channel. However, the transmission through the slot-stripe waveguide is not based on a single mode. Actually, mainly a mode with hot-spots at the outer edges of the two stripes is excited, thus bypassing emitters inside the slot. In an optimization for the coupling efficiency to the simple slot-waveguide, we found an efficiency of η slot = 11.2%. The efficiency can be significantly increased for wider slots 31 , thus a high efficiency together with a high Purcell factor can be achieved by tapering the slot-waveguide (which does not suffer from a cut-off).
A realistic single photon transistor. We will now investigate the Purcell factor P and β-factor β for a straight (no tapering) slot-waveguide, as it was used in the simulations shown in Figs 5h and 6a. We chose a slot-waveguide cross-section with the same gold-thickness as for the fabricated structures and a slot width of 30 nm. This slot width is within the current fabrication accuracy. As strong quenching typically sets in at emitter-metal distances below 5 nm 29,30 , we expect regions of both high P's and β's centered in the slot. For the corresponding slot-mode (Fig. 5h) we find propagation losses of α slot = 1.02 μm −1 . To compute P we follow the method published by Barthez et al. 30 using: Here ẑ is a normalized vector pointing in direction of propagation along the waveguide which is normal to the surface dA. k 0 is the absolute value of the photon momentum in air. E u denotes the electric field components parallel to the dipole orientation of an emitter. This computation can be performed very quickly, as only the solution of a frequency-domain guided-mode solver (here JCMwave) is needed. The resulting map of P is shown in Fig. 7a) for three linearly independent dipole orientations. The computation of the β-factor is more complicated as Γ tot is needed. A common method to derive Γ tot is to let a dipolar point-source radiate in a full 3D calculation and to monitor its total emitted power with respect to the emitted power in vacuum. To avoid any back-action of the emitted power onto the dipole like additional resonant Purcell effects, we use here a straight slot-waveguide that is long (9 μm) compared to the mean-propagation distance of 1/α slot = 0.98 μm to damp away all outgoing power. In principle for each emitter-position of interest a new computation is needed. Here we can significantly reduce the amount of computations as we are looking for the optimum performance. Specifically only a single emitter orientation promises high values of P and only positions in the very center of the slot are of interest. Any position closer to the gold will for sure enhance the quenching 26,29,30 but only slightly affect P, as P is quite homogeneous in the slot (see Fig. 7a). The (normalized) total decay rate Γ tot /Γ 0 , P and β scanned along the center of the slot, are shown in Fig. 7b,c) yielding an optimum of β = 97% at P ≈ 64. Γ 0 denotes the undisturbed decay rate of the emitter (in vacuum).
We can now quantify the performance of a non-linear quantum device. When we consider a single emitter in the slot waveguide controlling the transmittance T and reflectance R, then a figure of merit can be defined as the product of the collected photons from the chip γ out and the visibility VIS of a transmission dip. This figure of merit corresponds perfectly to experimentally accessible quantities as was shown in ref. 5. In order to do this we insert values for β and P into equation 1 assuming a branching ratio for DBT of η ZPL = 50%. With this we can directly plot T, R and the losses to the environment κ (κ = 1 − R − T) (Fig. 8a). We define the visibility VIS of the corresponding transmission dips by VIS = 1 − T, which is maximal at zero detuning (δ = 0): To derive the rate of outcoupled photons γ out we first estimate the rate of impinging photons (SPPs) γ in , that are allowed without introducing saturation effects. To avoid saturation, two-photon events have to be avoided and the emitter has to be relaxed back to its ground state before the next excitation takes place. Now, we assume that the impinging photons or SPPs obey a Poisson distribution: A dipole orientation along x features high P's in the entire slot. (b) Purcell factor P (blue) and the normalized total decay rate Γ tot /Γ 0 (green) for an emitter's dipole oriented along x, centered in the slot and scanned along y.