RESEARCH ARTICLE QUANTUM OPTICS

Single-plasmon interferences Marie-Christine Dheur,1 Eloïse Devaux,2 Thomas W. Ebbesen,2 Alexandre Baron,3 Jean-Claude Rodier,1 Jean-Paul Hugonin,1 Philippe Lalanne,4 Jean-Jacques Greffet,1 Gaétan Messin,1 François Marquier1*

2016 © The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC). 10.1126/sciadv.1501574

Surface plasmon polaritons are electromagnetic waves coupled to collective electron oscillations propagating along metal-dielectric interfaces, exhibiting a bosonic character. Recent experiments involving surface plasmons guided by wires or stripes allowed the reproduction of quantum optics effects, such as antibunching with a single surface plasmon state, coalescence with a two-plasmon state, conservation of squeezing, or entanglement through plasmonic channels. We report the first direct demonstration of the wave-particle duality for a single surface plasmon freely propagating along a planar metal-air interface. We develop a platform that enables two complementary experiments, one revealing the particle behavior of the single-plasmon state through antibunching, and the other one where the interferences prove its wave nature. This result opens up new ways to exploit quantum conversion effects between different bosonic species as shown here with photons and polaritons.

INTRODUCTION The production of the first single-photon states (1, 2) and the first demonstration of trapping of a single ion (3) in the early 80s marked the beginning of a long-standing effort to control and manipulate individual quantum systems. Potential applications require developing new platforms to engineer interaction between them at the nanoscale. Recent advances in the generation of optical nonlinearities at the level of individual photons (4) and in the interfacing of atoms with guided photons (5) clearly demonstrate the benefits of subwavelength confinement of the electromagnetic field. Because plasmonics provides new platforms to concentrate light to scales below that of conventional optics, plasmonic devices are excellent candidates for on-chip operations at the quantum level (6). Plasmons, as well as surface plasmons, are collective excitations of fermions, which are not, strictly speaking, bosons, although their commutation relations can be approximated by bosonic commutation relations with an error that decays as the inverse of the number of electrons (7). The quantized electric field operator for surface plasmon polaritons (SPPs) has been derived by numerous authors (8–10). As a result, SPPs are expected to behave like photons to a high degree of accuracy. The bosonic quantum nature of the plasmons has been demonstrated by several observations that reveal specific quantum features, such as coupling between a quantum emitter and a surface plasmon (11, 12), preservation of quantum correlations such as entanglement and squeezing through surface plasmon channels (13–17), control of spontaneous emission of an emitter by plasmonic structures (emission direction and lifetime) (18, 19), and quantum interferences (20–24). In Kolesov et al. (12), wave-particle duality of plasmons has been inferred from the observation of antibunching and spectral properties of the light coming out of a nanorod through a plasmonic channel and emitted by a single emitter coupled to it. Here, we investigate the dual waveparticle nature of the SPP along the same lines as the single-photon 1

Laboratoire Charles Fabry, Institut d’Optique, CNRS, Université Paris-Saclay, 91127 Palaiseau Cedex, France. 2Institut de Science et d’Ingénierie Supramoléculaire, CNRS, Université de Strasbourg, 67000 Strasbourg, France. 3Centre de Recherche Paul Pascal, CNRS, 33600 Pessac, France. 4Laboratoire Photonique, Numérique et Nanosciences, Institut d’Optique, CNRS, Université de Bordeaux, 33400 Talence, France. *Corresponding author. E-mail: [email protected]

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interferences textbook experiment by Grangier et al. (1) and Loudon (25). We propose the first direct measurement of the wave-particle duality for single SPP, using a true plasmonic beam splitter (BS) for SPP freely propagating on a flat gold-air interface. We generate a single SPP state by sending a photon from a single-photon source onto a photon-to-SPP coupler. A plasmonic BS is used to separate the flux of SPPs into two spatial modes, allowing the analysis of the SPP features using either a Hanbury Brown and Twiss (HBT) setup or a Mach-Zehnder (MZ) interferometer. The detection of anticorrelated events after the plasmonic BS unambiguously provides the which-path information, hence revealing the particle nature of the single SPP in the HBT configuration (26), whereas the wave behavior of the SPP is demonstrated in the MZ configuration with single SPPs. In addition, we observe that the presence of losses in the BS modifies the lossless MZ output signals, following the predictions made by Barnett et al. (27).

RESULTS Single surface plasmon experiment Because the photon-number statistics are preserved through the coupling of a photonic mode to a plasmonic mode (8), we used a singlephoton source and an SPP-photon coupler to produce single SPPs. The single-photon source is a heralded single-photon source delivering two outputs, a single photon at 806 nm with a spectral bandwidth of Dl = 1 nm and its heralding electronic pulse. More details about the source can be found in section S1. The manipulation of the SPPs is performed on the plasmonic chip shown in Fig. 1B. This chip has been designed with in-house electromagnetic software based on the aperiodic Fourier modal method (28). It consists of two unidirectional plasmon launchers, a plasmon splitter, and two large strip slits that decouple the SPPs toward the rear side of the sample. All components are fabricated in a single chip by focused ion beam lithography on a 300-nm-thick gold film sputtered on top of a SiO2 substrate. Single photons that are impinging from the front side of the chip are first converted into single SPPs via asymmetric 11-groove gratings (shown in Fig. 1A). The latter have been designed 1 of 5

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by the SPP launcher at the splitter level or generated by the splitter at the strip-slit level (30) are at least 10 times smaller than the SPP amplitudes. Thus, the plasmonic chip, despite its compactness, provides a true test of the bosonic character of SPPs. We collected the output signal from the substrate of the sample with an appended solid immersion lens, and we coupled it to avalanche photodiodes (APDs) connected to multimode fibers. We measured the transmission and reflection factors of the as-fabricated plasmonic BS depending on the input port. For coupler 1, we obtained T1 = 29 ± 1% and R1 = 18 ± 1%. For coupler 2, we measured T2 = 32 ± 1% and R2 = 15 ± 1%. The losses were equivalent for both ports and were measured to be approximately 53%. We note that the BS factors are unbalanced as a result of the variations of the actual BS dimensions with respect to the simulated BS dimensions. The losses, when propagating along the plasmonic sample, are evaluated to be 2.5%, and, eventually, only 0.1% of the photons emitted by the source do reach detectors A and B (see section S2).

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Fig. 1. The plasmonic platform. (A) Scanning electron microscope top view of the photon-to-SPP launcher. It is made of 11 grooves of asymmetric dimensions (29). (B) Scanning electron microscope top view of the plasmonic chip. Striped rectangles 1 and 2 are the SPP launchers as shown in (A). The groove doublet forms a plasmonic BS. The characterized splitter gives T1 = 29 ± 1% and R1 = 18 ± 1% when shining from coupler 1 and T2 = 32 ± 1% and R2 = 15 ± 1% when shining from coupler 2. For both input ports, the losses of the BS are measured to be approximately 53%. The SPPs propagate from launcher 1 or 2 to the BS and finally reach the large slits (black rectangles) where they are converted into photons in the silica substrate. (C) Line shape of the sample. It exhibits how an SPP can be generated with a Gaussian beam focused orthogonally to the photon-to-SPP converter. The SPP reaches the grooves of the plasmonic BS and finally propagates to the slit. The slit allows the SPP to couple out as photon in the substrate at 42° with an efficiency of about 50%.

to efficiently couple a normally incident Gaussian beam into directional SPPs. Details concerning the SPP launchers can be found in a preliminary report (29). The launched SPPs from couplers 1 and 2 are then combined with a plasmonic symmetric splitter made of two identical grooves oriented at 45°. The width, depth, and spacing of the splitter grooves are 350, 150, and 250 nm, respectively. Finally, the SPPs are decoupled by the two large strip slits on the rear side of the sample to avoid any contamination of the detected photons by straight light resulting from the backscattering at the front side of the sample. Calculation evidences that the decoupling efficiency is 50% for 10-mm-wide slits and that the decoupled photons propagate in the glass at an oblique angle of 42° (Fig. 1C) with a parallel momentum approximately equal to the parallel momentum of the surface plasmons. The single chip has a total footprint of 40 × 40 mm2. The dimension is compatible with experimental requirements for interfacing free-space photons and SPPs. In addition, the 10-mm separation distance between all the plasmonic components guarantees that the amplitudes of quasi-cylindrical waves that are either directly scattered Dheur et al. Sci. Adv. 2016; 2 : e1501574

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Particle behavior of the single surface plasmon We used the plasmonic device to launch and characterize the single SPP with antibunching (Fig. 2A). The box at the top left symbolizes the heralded single-photon source with its two outputs. We denote RC as the rate of the heralding pulse. A heralded single horizontally polarized photon is sent to a half-wave plate (HWP0), which rotates the linear polarization of the photon falling onto a polarizing beam splitter (PBS) cube. This allows us to choose between the plasmonic HBT and MZ configurations later on. Each output mode of the PBS is focused on a photon-to-SPP coupler on the plasmonic chip. The SPP modes are recombined with the plasmonic splitter, and each output is converted back to photons using the slits. The output signals are collected on APDs A and B. When the neutral axis of HWP0 is aligned with those of the PBS, the photon is transmitted and focused on a single coupler of the plasmonic sample. This configuration is analogous to the HBT experiment with heralded single SPPs. The intensity autocorrelation function at zero delay time g(2)(0) for SPPs is obtained by measuring the heralded outcoupled photon rates from the chip on APDs A (RA|C) and B (RB|C) while varying the pump power on the crystal. Because the losses between the crystal and the detection events on APDs A and B are huge, we measured g(2)(0) by integrating the counts over a 20-min period. Near the origin, g(2)(0) can be approximated in a linear regime (see section S3) as g ð2Þ ð0Þ ≈ 2mDT

ð1Þ

where DT = 10 ns is the resolution gate time for the coincidence measurement and m is the intrinsic emission rate of the source of photons without taking into account the heralding efficiency leading to RC. The heralded antibunching measurement is shown in Fig. 2B. We note that g(2)(0) is clearly below the classical limit. g(2)(0) down to 0.03 ± 0.06 is a clear indication that the source emits SPPs one by one (25), and each of them is either transmitted or reflected by the BS but never both at the same time. This antibunching illustrates the particle-like behavior of the single SPP. Wave behavior of the single surface plasmon Next, we made a single SPP interference experiment. We set the pump power to reach g (2) (0) = 0.25. This value establishes a good compromise between the signal-to-noise ratio, which is deteriorated 2 of 5

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Fig. 2. Experiments on SSPs showing the unicity of the SPP state and its wave behavior. (A) Sketch of the SPP experiments. The orientation of the first half-wave plate (HWP0) determines the polarization state impinging on the PBS cube and allows choosing between the HBT and MZ configurations of the SPP setup. HWP1 and HWP2 are half-wave plates that control the polarization of the incident beams on the photon-to-SPP couplers. For both experiments, we recorded the heralding rate RC and the heralded rates RA|C, RB|C, and RAB|C. (B) Intensity correlation function at zero delay g(2)(0) as a function of the mean photon number produced in the gating window DT = 10 ns. The lowest measured value of g(2)(0) obtained is 0.03 ± 0.06, which is well below the classical limit and is a signature of a single SPP state. The data points were obtained with 20 min of integration. (C) The single SPP source was used at g(2)(0) = 0.25 to perform interferences in an MZ interferometer for SPPs. We plotted the heralded photon output rates RA|C (red circles) and RB|C (blue squares) of the MZ interferometer for a varying delay in one arm of the interferometer. The solid lines are the sine fit functions of our experimental data.

by the instability of the interferometer for long acquisition times and the quality of the source to ensure about 90% chance to obtain single SPP events. In the setup described in Fig. 2A, we now sent 45°-polarized photons on the PBS. The output state of the PBS is thus a balanced superposition of the output photonic modes, each of which illuminates one of the plasmon-photon coupler. After conversion to SPPs, the superposition of the two plasmonic modes recombines onto the plasmonic splitter. The two outputs of the plasmonic BS are then converted back to photons that are collected on APDs A and B. The setup is now equivalent to an MZ interferometer where a delay d is adjusted mechanically by elongating one arm with respect to the other. We selected the heralded output signals of the MZ interferometer (RA|C and RB|C) and plotted them as a function of the delay d (Fig. 2C). We observed interference fringes located in an exponentially decaying envelope as the delay increases in one arm of the MZ interferometer, which is the signature of a wave behavior from the SPP. From this envelope, we find that the spectral width is not modified, showing that there is no dephasing process associated with the SPP conversion and propagation. At the central position of the envelope, we obtain a maximal visibility [V = (Rmax − Rmin)/(Rmax + Rmin)] of 62 ± 3% for output A and 79 ± 2% for output B. The difference between the visibilities can be explained by the imperfections of the setup (see section S2). There is also a phase difference of 120° between the two outputs of the MZ interferometer. With a lossless symmetric BS, we would Dheur et al. Sci. Adv. 2016; 2 : e1501574

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have expected the outputs to be in opposition of phase as energy conservation applies. However, because of the losses in the BS, the phase shift can be different from p. Performing a rigorous numerical simulation of the experiment, we found agreement between the experiment and the simulations for the relative positions of the fringes on the two outputs A and B (section S4). Although losses are detrimental for some quantum effects such as the visibility of the Hong-OuMandel experiment (20, 27), they can be used as a resource for manipulating plasmonic interferences, even in the deep quantum regime involving one- or two-plasmon states (31).

DISCUSSION Here, we have developed a platform to manipulate SPPs in a controlled way using directional plasmonic couplers, large-slit decouplers, and a two-groove BS. On the one hand, we have measured the intensity correlation function of heralded SPPs and observed single SPP antibunching in the low-intensity pump regime of the source. This is evidence of a particle-like behavior. On the other hand, we observed fringes by making those single SPPs interfere in an MZ interferometer, therefore showing their wavelike nature. We found that the interferences produced by the plasmonic chip differ from the photonic case. The observed phase difference has been attributed to the subtle role 3 of 5

RESEARCH ARTICLE of losses in the interferometer. Despite the losses, the quantum properties of the SPP statistics have been preserved. We thus demonstrated the wave-particle duality of nonguided, freely propagating SPPs.

MATERIALS AND METHODS Sample fabrication We used 300-nm-thick gold films deposited on clean glass substrates by e-beam evaporation (ME300 Plassys system) at a pressure of 2 × 10−6 mbar and at a rate of 0.5 nm/s. Their root mean square roughness is 1 nm. They were then loaded in a crossbeam Zeiss Auriga system and milled by a focused ion beam at low current (20 pA), except for the large slits used to decouple plasmons for propagating light that were milled at 600 pA. Experimental method The single-photon source was based on parametric down-conversion in a potassium titanyl phosphate crystal (KTP crystal from Raicol). It generated pairs of 806-nm degenerate photons. The combination of the pair source with the heralded detection of one photon of the pair formed the single-photon source. A tunable laser diode (Toptica) with an extended cavity was focused by a 300-mm focal-length planoconvex lens on a periodically poled KTP crystal at 38 mW with a 60-mm waist. We used the laser diode at 403 nm to emit degenerate pairs at 806 nm, and the laser diode’s temperature was maintained at 32.5°C. The waist in the crystal was conjugated to infinity with a 100-mm focal-length plano-convex lens, and the red photons emerging from the crystal were separated in polarization by a PBS cube (Fichou Optics). We eliminated the remaining pumping signal with an interferometer filter from AHF (FF01-810/10). The photons were coupled to polarization-maintaining monomode fibers (P1-780PM-FC) via collimators (F220FC-780, Thorlabs). Each photon was outcoupled via Long Working Distance M Plan Semi-Apochromat microscope objectives (LMPLFLN-20× BD, Olympus) and sent to two different outputs of a PBS (Fichou Optics) with orthogonal polarizations. They left the cube by the same output port and were focused with a 10× microscope objective (Olympus) on the plasmonic sample. The plasmonic sample was mounted on a solid immersion lens. The surface plasmons propagating on the chip left the sample by two different output slits. The conversion of the SPP back to photons via the slits led to two different directions of light in free space. The photons from the output ports could be collected from the rear side of the sample using mirrors and a 75-mm focal-length lens for each output. The output modes were then conjugated to multimode fibers via a 10× microscope objective (Olympus), which were connected to singlephoton counting modules (SPCMs). Detection method All the photons in these experiments were sent to SPCMs, which deliver transistor-transistor logic pulses. APDs A and B are PerkinElmer modules (SPCM AQRH-14), and APD C is a Laser Component SPCM (Count-100C-FC). To count the correlations between the heralding signal and the APD A and B pulses, we used a PXI Express system from National Instruments (NI). The NI system is composed of a PXIe-1073 chassis on which NI FlexRIO materials are plugged: a fieldprogrammable gate array (FPGA) chip (NI PXIe-7961R) and an adapter module at 100 MHz (NI 6581). The FPGA technology allows changing Dheur et al. Sci. Adv. 2016; 2 : e1501574

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the setting of the acquisition by simply programming the FPGA chip to whatever set of experiments we want to conduct. A rising edge from APD C triggers the detection of another rising edge on channel A or B or both at specific delays. Counting rates and correlations of heralded coincidences between channels A and B are registered. The resolution of the detection system is mainly ruled by the acquisition board frequency clock at 100 MHz, which corresponds to a time resolution of 10 ns.

SUPPLEMENTARY MATERIALS Supplementary material for this article is available at http://advances.sciencemag.org/cgi/ content/full/2/3/e1501574/DC1 Section S1. Characterization of the single-photon source. Section S2. Characterization of the plasmonic chip. Section S3. Fit function for HBT experiments. Section S4. The lossy BS influence on the MZ interferences. Fig. S1. Single-photon source antibunching. Fig. S2. Schematic of the lossless-lossy MZ interferometer. Fig. S3. Reflection and transmission coefficients of the plasmonic BS as a function of the incidence angle. Fig. S4. Comparison between experimental data and numerical simulation of the plasmonic MZ outputs. References (32, 33)

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31. J. Jeffers, Interference and the lossless lossy beam splitter. J. Mod. Opt. 47, 1819–1824 (2000). 32. A. Fedrizzi, T. Herbst, A. Poppe, T. Jennewein, A. Zeilinger, A wavelength-tunable fibercoupled source of narrowband entangled photons. Opt. Express 15, 15377–15386 (2007). 33. O. Alibart, D. B. Ostrowsky, P. Baldi, S. Tanzilli, High-performance guided-wave asynchronous heralded single-photon source. Opt. Lett. 30, 1539–1541 (2005). Acknowledgments: We acknowledge E. Rousseau, F. Cadiz, and N. Schilder for their help in the beginning of this study, as well as L. Jacubowiez, A. Browaeys, and P. Grangier for fruitful discussions. Funding: The research was supported by a DGA-MRIS (Direction Générale de l’Armement– Mission Recherche et Innovation Scientifique) scholarship, by RTRA (Réseau Thématique de Recherche Avancée) Triangle de la Physique, and by a public grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (reference: ANR-10-LABX-0035, Labex NanoSaclay). J.-J.G. is a senior member of Institut Universitaire de France. Author contributions: P.L., G.M., F.M., and J.-J.G. initiated the project. The plasmonic chip design and multiphoton characterization were supervised by P.L. J.-C.R. and J.-P.H. designed the chip, which was fabricated by E.D. and T.W.E. and characterized by A.B. and M.-C.D. M.-C.D. built the setup and performed all quantum experiments under the supervision of G.M. and F.M. M.-C.D., F.M., G.M., and J.-J.G. wrote the paper. All authors discussed the results. Competing interests: The authors declare that they have no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from F.M. (francois.marquier@ institutoptique.fr). Submitted 4 November 2015 Accepted 7 January 2016 Published 11 March 2016 10.1126/sciadv.1501574 Citation: M.-C. Dheur, E. Devaux, T. W. Ebbesen, A. Baron, J.-C. Rodier, J.-P. Hugonin, P. Lalanne, J.-J. Greffet, G. Messin, F. Marquier, Single-plasmon interferences. Sci. Adv. 2, e1501574 (2016).

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SUPPLEMENTARY MATERIALS

S1.  Characterization  of  the  single  photon  source   The  single  photon  source  (Fig.  S1(A))  is  based  on  parametric  down-­‐conversion  in  a  25  mm-­‐long  type  II  Periodically-­‐ Poled  Potassium  Titanyl  Phosphate  crystal  (PPKTP,  Raicol)  pumped  by  a  continuous-­‐wave  laser  diode  extended  cavity   (λp  =  403  nm,   Toptica)   (32).   Consequently,   the   two   generated   photons   are   orthogonally   polarized   (horizontal   and   vertical)   and   their   frequencies   are   defined   by   phase   matching   which   can   be   adjusted   with   the   crystal   temperature   placed   in   a   tunable   oven   (Covesion).   In   the   following,   we   chose   to   work   with   degenerate   photons   at   806  nm.   After   the   crystal,  the  remaining  pump  signal  is  next  removed  with  a  10nm-­‐narrow-­‐band  filter  centered  at  λ  =  805  nm.  The  pairs   are   then   separated   with   a   polarizing   beam   splitter   and   the   vertically-­‐polarized   photon   of   the   pair   is   directed   to   a   fibered  single  photon  counting  module  (a  silicon  Avalanche  PhotoDiode  used  in  the  Geiger  mode)  denoted  APD  C.  This   detector  delivers  an  electronic  pulse  heralding  the  arrival  of  the  horizontally-­‐polarized  photon.  The  detection  of  the   heralding   photon   eliminates   the   probability   of   measuring   vacuum   states   in   the   heralded-­‐photons   statistics   and   the   heralded-­‐photon  state  is  then  close  to  a  single-­‐photon  Fock  state  in  the  low  intensity  regime.  To  assess  the  quantum   nature  of  this  state,  we  measured  the  stationary  intensity  correlation  function:    

g(2)(0) =

ˆ )I(t ˆ + τ ): : I(t



ˆ ) I(t

 

(1)  

2

at  zero  delay  (τ  =  0)  using  an  Hanbury  Brown  and  Twiss  (HBT)  setup  (Fig.  S1(A)).  The  heralded  single  photon  is  sent   into  a  polarization  maintaining  single-­‐mode  fiber  splitter  whose  outputs  are  connected  to  APDs  A  and  B.  The  detected   signals  from  APD  A,  B  and  C  are  sent  to  a  programmable  chip  (FPGA  module,  National  Instrument)  that  post-­‐processed   the  data  in  order  to  only  select  the  clicks  from  APD  A  and  B  heralded  by  APD  C  within  the  resolution  gate   ΔT=10  ns.   The  number  of  coincidences  between  A  and  B  conditioned  by  a  detection  of  C  is  also  recorded.  We  then  extract  the   averaged  g(2)(0)  over  the  gate  ΔT  :      

g(2)(0) =

PAB/C PA/C PB/C

 

(2)  

where   the   probabilities   derive   from   the   measured   count   rates   as   follows:   PA|C  =  RA|C  /  RC,   PB|C  =  RB|C  /  RC,   and   PAB|C  =  RAB|C  /  RC.   RC   is   the   count   rate   on   detector   C.   RA|C,   RB|C,   and   RAB|C   are   the   rates   on   APDs   A   and   B   and   the   coincidence  rate  triggered  by  a  click  on  APD  C.     The  characterization  of  the  single  photon  source  is  shown  in  Fig.  S1(B).  We  plotted  the  dependency  of  the  g(2)(0)   on   the   mean   photon   number   (µ  ΔT)   in   the   gate   resolution   while   varying   the   pumping   laser   power   on   the   PPKTP   crystal.   The   data   are   fitted   with   the   theory   developed   in   references   (33)   and   (2)   (see   Supplementary   Section   3   for   more   details).   Since   g(2)(0)  <  1,   the   photon   source   is   clearly   sub-­‐Poissonian   and   therefore   generates   non-­‐classical   photon  states  (1).  As  the  pump  power  decreases,  g(2)(0)  approaches  close  to  zero  values  (g(2)(0)  =  0.03  ±  0.07)  which   indicates  that  the  state  is  close  to  a  perfect  single  photon  Fock  state.    

S2.  Characterization  of  the  plasmonic  chip   The   plasmonic   chip   is   composed   of   two   SPP   launchers,   one   plasmonic   BS   and   two   slits.   The   as-­‐fabricated   BS   characteristics   were   measured   with   an   Atomic   Force   Microscope   (AFM)   and   found   to   be   550  ±  5  nm   for   the   width,   102  ±  5  nm   for   the   spacing   and   we   measured   two   different   depths   for   the   grooves   102  ±  10nm   and   91nm±10nm.   The   variations  from  the  designed  characteristics  come  from  the  Focused  Ion  Beam  (FIB)  etching  technique  that  produces   rounded-­‐angled   grooves   instead   of   right-­‐angled   grooves.   The   AFM   values   given   here   correspond   to   the   dimensions   of   the  upper  part  of  the  structure,  but  the  lower  part  dimensions  are  very  similar  to  the  design  ones.   In   this   paragraph,   we   summarize   the   different   contributions   to   the   losses   encountered   on   the   plasmonic   experimental   part   of   the   setup.   Firstly,   we   measured   the   SPP   propagation   length   on   the   sputtered   gold   film:   lSPP  =  13  ±  2  µm.  Then,  we  took  into  account  the  SPP-­‐photon  coupler  efficiency   ηcoup,  the  attenuation   ηprop(10µm)  due   to   the   SPP   propagation   over   10  µm,   the   BS   losses   ηBS,   the   propagation   attenuation   ηprop(10µm)   again   and   the   decoupling  efficiency  of  the  slits   ηslit,  and  we  found  that  the  overall  attenuation  undergone  by  the  photons  between   the  input  of  the  sample  to  the  output  was   ηsample  =   ηcoup  ηprop(10µm)  ηBS  ηprop(10µm)  ηslit  =  2.5%.  Adding  to  that  all  the   losses  due  to  the  manipulation  of  the  photons  in  optical  elements  (fibers,  objectives,  PBS)  to  couple  the  photons  on  the   chip   and   to   collect   them   from   the   slit   to   the   detectors,   we   got   the   overall   transmission   efficiency   ηoverall  =  ηsample  ηoptics  =  0.21%.  We  did  not  account  here  for  the  quantum  efficiencies  of  the  detector  (ηdetector  ≈  40%).    

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S3.  Fit  function  for  Hanbury  Brown  and  Twiss  experiments   In   this   section,   we   give   more   details   about   the   fit   functions   for   the   photon   antibunching   and   for   the   SPP   antibunching.   The   intensity   correlation   functions   at   zero   delay   were   measured   using   Hanbury   Brown   and   Twiss   configuration   setups.  Both  setups  are  based  on  photon  pairs  generated  by  parametric  down  conversion  issued  from  a  PPKTP  crystal.   We   denote   µ   the   emission   rate   of   the   pairs   produced   by   the   crystal.   The   photon   pairs   are   separated   so   that   the   heralding  photon  goes  on  APD  C.  We  neglect  the  dark  count  of  APD  C  (100  counts  per  second)  which  is  several  orders   of   magnitude   lower   than   the   heralding   count   rate   RC  ≥  25  kHz.   We   denote   ηC  =  RC  /  µ   the   detection   efficiency   of   the   photons   on   the   heralding   port  C.   ηC   includes   all   the   optical   losses   (fiber   coupling   and   lenses   transmissions)   as   well   as   the   quantum   efficiency   of   APD   C.   Depending   on   whether   we   test   antibunching   on   photons   or   on   SPPs,   we   send   the   heralded  photon  to  two  different  setups.  But  in  both  cases,  determining  g(2)(0)  requires  to  split  the  flux  of  photons  (or   SPPs)  and  to  measure  heralded  correlations  after  the  splitting  with  a  detector  on  each  output:  APD  A  and  APD  B.  We   can  therefore  define  the  detection  efficiencies   ηA  =  RA  /  µ  and   ηB  =  RB  /  µ  where  RA  and  RB  are  the  count  rates  detected   on  ports  A  and  B.  We  denote  the  overall  detection  efficiency  as  ηA+B  =  ηA  +  ηB.     For   the   photon   antibunching   case,   the   heralded   photon   is   sent   to   a   monomode   polarization   maintaining   fused   fiber   splitter.   Therefore,   ηherald   includes   all   the   losses   through   the   optical   elements   (fiber   BS   coupling,   lens   transmissions)   and   the   quantum   efficiency   of   the   detectors.   Note   that   in   all   the   experiments   RC  ΔT   ≪ 1   where   ΔT  =  10  ns  is  the  resolution  gate  time.  Hence  we  find  g(2)(0)  writes  (33,  2):    

g(2)(0) =

2

2µ ΔT

(1+ (1− 2η ) µ ΔT )

2

=

A+B



RC ΔT ηC

⎛ ⎞ RC ⎜ 1+ 1− 2η A+B η ΔT ⎟ ⎝ ⎠ C

(

)

 

(3)  

2

In  the  set  of  data  of  Fig.  1(B)  of  the  article,  one  can  note  the  saturation  of  the   g(2)(0)  towards  the  Poissonian  limit   for  high   µ.  To  observe  this  behavior,  it  was  necessary  to  reach  high  values  of  pump  power  without  damaging  APD  C.   Therefore   we   have   attenuated   the   heralding   photons   rate   by   a   factor   7.   We   find   an   excellent   agreement   with   the   experimental   data   with   ΔT  =  10  ns   and   ηC  =  0.0197  ±  0.0002   and   ηA+B  =  0.219  ±  0.002.   This   is   consistent   with   our   observations.   For   the   plasmonic   HBT   measurement,   the   heralded   photons   are   sent   to   the   plasmonic   chip   where   they   are   converted  to  SPPs.  The  antibunching  of  SPPs  is  tested  with  the  plasmonic  BS.  The  new  detection  efficiencies  ηA  and  ηB   related  to  the  plasmonic  case  are  significantly  decreased  (by  a  factor  of about  ηoverall  =  0.21%)  due  to  the  important   losses  on  the  plasmonic  device.  This  allows  restoring  the  maximum  collection  efficiency  on  APD  C  for  the  plasmonic   HBT   experiment,   which   increases   the   number   of   triggering   pulse,   and   thus   increases   the   probability   of   detecting   simultaneous  counts  on  APD  A  or  B.  Nevertheless,  since  we  are  essentially  interested  in  the  sub-­‐Poissonian  regime,  we   keep  µ   ΔT ≪  1.  Then,  Eq.  (3)  simplifies  to:      

g(2)(0) ≈ 2µ ΔT = 2

RC

ηC

ΔT  

(4)  

We   see   that   under   these   conditions,   g(2)(0)   is   proportional   to   the   mean   photon   pairs   number   during   ΔT.   The   linear  

dependency   is   in   perfect   agreement   with   our   experimental   results.   Fig.   3(C)   of   the   article   was   obtained   for   ηc  =  0.150  ±  0.007  which  is  consistent  with  the  APD  datasheet  and  the  previous  experimental  characterizations.    

S4.  The  lossy  beamsplitter  influence  on  the  Mach-­‐Zehnder  interferences     We  study  here  the  variations  in  amplitude  and  phase  of  the  transmission  and  reflection  coefficients  of  the  plasmonic   beam   splitter   (BS)   with   a   misalignment   of   the   setup.   In   Fig.   S2,   one   can   find   the   sketch   of   the   MZ   interferometer   used   in  our  experiment.  In  this  interferometer,  the  first  BS  is  lossless  and  the  second  one  is  lossy.  The  first  BS  is  assumed  to   be  symmetric  and  balanced  so  that  it  can  be  described  by  the  following  matrix:      

1 ⎛ 1 i ⎞   TBS = ⎜ ⎟ 1 2⎝ i 1 ⎠

(5)  

The  lossy  BS  is  a  4-­‐ports  device  with  two  input  ports  (1  and  2)  and  two  output  ports  (3  and  4).  The  incident  light  on   the   MZ   interferometer   is   first   separated   in   two   photonic   modes:   mode   a   and   mode   b.   In   our   experiment,   the   photonic   modes  are  converted  to  plasmonic  modes  c  and  d.  They  are  sent  to  the  lossy  beamsplitter  that  recombines  them  into  

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two   output   modes   e   and   f.   The   path   difference   δ   between   the   MZ   arms   can   be   tuned   thus   revealing   fringes   in   each   output  port  of  the  MZ  interferometer  (25).  We  denote  rk  =  |rk|  exp(iφk)  the  complex  reflection  factor  of  the  lossy  BS  for   an   incident   field   on   port   k   (k  =  1,  2)   where   |rk|   and   φk   are   the   amplitude   and   phase   reflection   factor.   Similarly,   we   denote  tk  =  |tk|  exp(iϕk)    the  complex  transmission  factor  of  the  lossy  BS  for  an  incident  field  on  port  k  (k  =  1,  2)  where   |tk|  and   ϕk  are  the  amplitude  and  phase  of  the  transmission  factor.  The  creation  of  one  photon  in  each  output  port  of   the  lossy  BS  is  respectively  described  by  the  operators  â3†  and  â4†,  so  that  the  mean  photon  numbers  of  the  MZ  output   3  and  4  for  a  single  photon  state  entering  the  interferometer  on  port  in1  are  given  by:  

⎛ 2t r 2 1⎛ 2 ⎞ N3 = aˆ aˆ 3 = t1 + r2 ⎜ 1− 2 1 2 2 sin δ + ϕ1 − φ2 ⎝ ⎠ 2 ⎜ t1 + r2 ⎝

( (

† 3

 

))

⎛ 2r t 2 2 1 N4 = aˆ 4† aˆ 4 = ⎛ t 2 + r1 ⎞ ⎜ 1− 2 1 2 2 sin δ − ϕ 2 − φ1 ⎠⎜ 2⎝ t 2 + r1 ⎝

( (

⎞ ⎟ ⎟ ⎠

 

(6)  

⎞ ⎟ ⎟ ⎠

))

From  these  equations,  it  is  clear  that  the  phase  difference  between  the  transmission  and  the  reflection  coefficients   of  the  BS  is  responsible  for  the  phase  shift  between  the  two  outputs  of  the  MZ  interfermoter.  In  the  case  of  the  lossless   symmetric  balanced  beamsplitter  (t1  =  t2  =  1/√2  and  r1  =  r2  =  i/√2),  the  phase  shift  between  the  outputs  is  equal  to   π,   which  is  the  very  well-­‐known  result  for  the  phase  shift  at  the  reflection  for  a  lossless  BS.   The   visibility   of   the   fringes   is   given   by   the   factor   in   front   of   the   sine   function   V  =  2|ri||tj|/(|ri|2+|tj|2).   This   factor   depends  on  the  modes  impinging  on  each  input  ports.  In  the  ideal  case,  modes  c  and  d  are  identical  but  in  practice  this   requirement  is  difficult  to  achieve,  as  it  is  very  sensitive  to  the  free  space  mode  alignment  of  each  arm  and  on  the  SPP   launcher  dimensions.  But,  more  critically  in  our  setup,  the  collection  of  each  of  the  two  output  signals  from  the  chip  is   not  identical.  Indeed,  the  two  modes  leaving  the  slits  are  propagating  in  different  directions:  one  output  is  emitted  in  a   vertical  plane  and  the  other  one  is  emitted  in  a  horizontal  plane.  The  collection  of  the  vertical  mode  is  more  delicate   and   in   the   actual   setup   we   partially   cut   the   output   beam.   By   doing   so,   we   select   a   part   of   the   mode   and   we   change   the   mode   overlap   involved   in   the   interference.   Consequently,   the   visibility   of   the   fringes   on   the   vertical   mode   (corresponding   to   the   counting   rate   RA   in   our   experiment)   is   deteriorated.   The   visibilities   of   both   MZ   output   rates   differ  from  each  other  because  they  do  not  imply  the  same  mode  overlap.  We  also  note  that  the  visibility  depends  on   the  beamsplitter  features.  In  our  case,  the  grooves  depths  are  not  exactly  the  same  and  this  asymmetry  leads  to  r1  ≠  r2   and   t1  ≠  t2,   therefore   the   visibility   of   each   output   port   must   be   affected   by   the   unbalanced   factors.   However,   simulations  show  little  impact  on  the  visibility  difference  for  such  slight  differences  of  depths.   Since   the   interference   contrast   degradation   has   multiple   origins,   it   is   delicate   to   give   an   exact   model   that   reproduces  our  experimental  results,  as  we  do  not  know  the  contribution  of  each  parameter.  To  have  an  idea  of  the   influence   of   the   mode   selection   on   the   reflection   and   transmission   coefficients,   we   ran   numerical   calculations   to   evaluate   the   influence   of   the   incident   angle   on   the   BS   on   the   reflection   and   transmission   factors   (amplitude   and   phase)  in  Fig.  S3.  In  the  experiment  a  Gaussian  beam  is  focused  on  the  device.  Since  the  chip  dimensions  are  smaller   than   the   Rayleigh   range   (dR  =  π  wo2/λ  ≈  97µm  >  20µm),   the   divergence   of   the   beam   is   weak   and   we   assume   that   we   can  treat  the  problem  with  plane  waves.  We  show  the  amplitude  of  the  reflection  and  transmission  for  a  plane  wave   impinging  with  an  angle  θ  on  the  beamsplitter  in  the  upper  graph  of  Fig.  S3.  To  simulate  the  BS,  we  chose  intermediate   BS   dimensions   between   the   AFM   and   the   designed   ones   (to   account   for   the   rounded-­‐angled   grooves)   that   provide   the   same   averaged   BS   splitting   ratios   (R/(R+T)   and   T/(T+R))   as   the   one   measured   experimentally.   We   found:   430  nm   for   the   width,   160  nm   for   the   spacing   and   two   different   depths   for   the   grooves   102  nm   and   90  nm.   We   assumed   symmetrical   r   and   t   factors   (for   simplicity),   which   means   that   reflection   and   transmission   coefficients   of   the   BS   for   identical   modes   on   port   1   and   2   are   equal   (r1  =  r2  =  r   and   t1  =  t2  =  t).   We   note   that   both   reflection   and   transmission   factors  show  strong  variations  with  the  illumination  conditions.  The  second  graph  of  Fig.  S4  represents  the  phase  shift   between   the   MZ   outputs   under   the   symmetric   BS   assumption,   which   is   simply   2(ϕ  -­‐  φ).   The   phase   difference   varies   strongly  with  θ  for  this  given  structure  and  is  generally  not  equal  to  p,  contrary  to  the  lossless  beamsplitter  case.   The   numerical   simulations   are   now   used   to   reproduce   the   interferences   we   experimentally   observe   on   both   outputs  A  and  B.  To  account  for  the  visibility  difference  in  the  two  channels,  we  introduce  a  difference  in  the  incidence   angle   between   the   two   SPPs.   As   the   reflection   and   transmission   factors   of   the   beamsplitter   depend   on   the   angle   of   incidence,  this  difference  breaks  the  symmetry  between  the  two  output  channels.  We  show  the  results  in  Fig.  S4.  The   dots  with  the  error  bars  are  the  normalized  experimental  count  rates  RA|C  and  RB|C.  The  solid  and  dashed  black  lines   are  the  simulated  normalized  MZ  outputs.  We  find  a  qualitative  agreement  of  the  phase  difference  (120°)  between  the  

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experiment   and   the   simulations.   Here,   the   role   of   the   BS   losses   appears   in   the   phase   shift   between   the   MZ   output   rates.  

Figures    

Fig.   S1.   Single   photon   source   antibunching.   (A)   HBT   setup   for   testing   the   photon   statistics   of   the   heralded   single  photon  source.  The  source  is  a  PPKTP  crystal  pumped  by  a  403  nm  laser  diode,  producing  twin  photons   of  orthogonal  polarizations  at  806  nm.  The  detection  of  one  of  them  heralds  the  other  one.  PBS:  Polarizing   beam  splitter.  IF:  pump  blocking  interference  filter.  The  intensity  correlation  function  of  the  heralded  photons   is   obtained   by   measuring   the   heralded   detection   events   at   the   outputs   of   a   50:50   fiber   beamsplitter   during   a   time  window   ΔT.  For  the  experiment,  the  counting  rate  RC  and  the  heralded  counts  RA|C,  RB|C  and  RAB|C  are   (2) recorded.   (B)   Intensity   correlation   function   at   zero   delay   g (0)   as   a   function   of   the   mean   photon   number   (2) produced   in   the   resolution   window   ΔT  =  10  ns.   g (0)   vanishing   to   zero   (0.03  ±  0.07)   is   a   clear   signature   of   single  photon  emission  

  Fig.   S2.   Schematic   of   the   lossless-­‐lossy   Mach-­‐Zehnder   interferometer.   The   first   BS   is   a   classical   photonic   beamsplitter  and  is  considered  lossless.  Photons  in  mode  a  and  mode  b  are  then  converted  into  plasmons  in   mode   d   and   mode   c,   that   enter   port   1   and   2   of   the   second   BS,   which   is   a   plasmonic   beamsplitter   and   is   considered  lossy.  

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      Fig.  S3.  Reflection  and  transmission  coefficients  of  the  plasmonic  beamsplitter  as  a  function  of  the  incidence   angle.   The   plasmonic   beamsplitter   is   considered   lossy,   but   symmetric   for   simplicity:   r1  =  r2  =  r   and   t1  =  t2  =  t.   Upper   graph:   reflection   and   transmission   amplitude   dependency   with   the   incidence   angle   θ.   Lower   graph:   evolution  of  the  MZ  outputs  phase  shift  2(ϕ  -­‐  φ)  with  θ,  where  ϕ  =  arg(t)  and  φ  =  arg(r).  

      Fig.  S4.  Comparison  between  experimental  data  and  numerical  simulation  of  the  plasmonic  MZ  outputs.  As   compared  to  the  photon  case,  the  SPP  interferences  on  the  two  output  channels  present  a  visibility  difference   and  a  phase  shift  different  from  π.  Normalized  experimental  output  rates  of  the  MZ  interferometer  are  plotted:   normalized   RA|C   (red   circled   dots)   and   RB|C   (blue   squared   dots).   The   solid   and   dashed   black   lines   are   the   simulated  normalized  MZ  outputs  for  which  we  accounted  for  the  asymmetry  of  the  interferometer  leading  to   different  visibilities  by  picking  two  different  incident  angles  of  the  SPP  on  the  BS  for  each  output  of  the  MZ.  We   clearly   see   that   experiment   and   the   simulations   are   in   fair   agreement   and   lead   to   a   very   similar   phase   difference  of  about  120°.  

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