Strong coupling of a quantum emitter to a broadband cavity enabled by a nanoantenna
The strong-coupling regime of the interaction between a single emitter and a resonant photonic structure has been restricted to the use of optical cavities with high quality factors or metallic nanoparticles with extremely small mode volumes. In this work, we explore a system that allows us to reach strong coupling between an emitter and an optical mode that results from the coupling of a broadband Fabry-Perot microcavity and an off-resonant plasmonic nanoantenna. We identify the interference mechanism that creates the necessary enhancement factors and bandwidths and show that quenching, commonly thought as an intrinsic property of a metallic nanostructure, can be externally modified by a cavity. Our results provide new possibilities for improving the efficiency of solid-state emitters and accessing extreme regimes of photophysics with hybrid structures that can be fabricated using existing technologies.
The most conventional approach for enhancing photon-atom interactions uses Fabry-Perot (FP) cavities with highly reflective boundaries to circulate a photon across an atom by a large number of times. One of the consequences of the resulting enhanced coupling is to induce faster atomic transitions. This so-called Purcell effect Purcell (1946) can be attributed to an increase in the local density of states (LDOS) proportional to , where is the cavity quality factor and denotes its mode volume. If the cavity photon storage time is long enough, the rate of atom-photon interaction may become so large that it dominates both the cavity loss rate () and the coupling rate of the atom to other competing spatial modes. In this scenario, photonic and emitter excitations are coherently exchanged and the system enters the strong coupling regime (SCR) Haroche and Raimond (2006). This extreme type of interaction is of broad interest as reflected in reports on a wide range of phenomena such as strong single-photon nonlinearities Imamoglu et al. (1997), nonclassical communications Cirac et al. (1997) and simulations Cirac and Zoller (1995), Bose-Einstein condensation Kasprzak et al. (2006), unobserved effects in optomechanics Aspelmeyer et al. (2014), and rare photo-induced chemical reactions Hutchison et al. (2012); Galego et al. (2016).
The pioneering optical demonstrations of strong coupling for single quantum emitters have used different resonator designs but always with high s Hood et al. (1998); Vahala (2003); Reithmaier et al. (2004); Yoshie et al. (2004). This approach is not suitable for solid-state platforms at room temperature, where the emitter linewidths exceed by several orders of magnitude Grange et al. (2015). Furthermore, high- cavities pose technical challenges on both their fabrication design and frequency stabilization Kelkar et al. (2015); Wang et al. (2017). An alternative strategy for accessing the SCR is to use plasmonic nanoantennas Törmä and Barnes (2015). These structures support resonances with tiny s Trügler and Hohenester (2008); Savasta et al. (2010); Hümmer et al. (2013), reaching sizable Purcell factors Sauvan et al. (2013); Agio and Martin-Cano (2013) and allowing them to overcome their very broad resonances and low s. The first reports of this phenomenon have emerged very recently Santhosh et al. (2016); Chikkaraddy et al. (2016) for emitters at extremely close distances to metallic antennas, where nonradiative decay channels have significant contributions.
In this Letter, we investigate a hybrid nanoantenna-cavity configuration with two distinctive features that emerge as a result of the radiative coupling of a detuned nanoantenna and a broadband cavity. We find that an emitter coupled to the hybrid compound resonance can enter SCR in configurations, where neither the isolated nanoantenna nor the cavity alone would provide access to this regime. Furthermore, we show that the cavity coupling can counteract quenching effects by competing with nonradiative channels in the near field of the metallic nanoantenna.
Figure 1 sketches an example of the proposed configuration, where a dipolar emitter is placed close to a metallic nanocone antenna Mohammadi et al. (2010) embedded in a confocal FP microcavity that is tunable by its length . To investigate the influence of the hybrid cavity-antenna structure on the emitter, we examine the LDOS. This electromagnetic quantity is connected to the imaginary part of the Green’s tensor and thus to the power dissipated by a dipole, which we calculate by means of full-wave computations with COMSOL Multiphysics Bai et al. (2013). Figure 2 displays the normalized LDOS for a broadband FP-nanocone system (black squares) as a function of the emission wavelength for an emitter that lies at ten nanometers from the nanocone close to the antinode of the FP microcavity [see Fig. 1(b)]. We can identify two main regions of enhanced LDOS in Fig. 2: a double-peaked feature with a very broad linewidth at nm and a narrower resonance around 820 nm.
It is instructive to compare the normalized LDOS to the same configurations of a bare microcavity (blue circles) and an isolated nanocone (green triangles) in Fig. 2. The outcome indicates that the broadband plasmon modes of the nanoantenna and two transverse cavity modes with narrower linewidths interfere constructively to yield to two general scenarios: a double-peaked structure for resonant modes coupling and a shifted cavity resonance for off-resonant interaction. The latter frequency change at longer wavelengths is attributed to the common cavity red shifts reported for small plasmonic nanoparticles Kelkar et al. (2015). Notice that the maximum LDOS values () for the off-resonant mode has been enhanced by one order of magnitude with respect to the bare cavity mode and by a factor of three with respect to the isolated nanocone over a fairly narrow bandwidth (). These features make the detuned hybrid mode very attractive for strong coupling as shown below. Furthermore, the combination of the nanoantenna and cavity modes also leads to dips in the LDOS values, which result from destructive interference events known from Fano phenomena Luk’yanchuk et al. (2010) for two resonant systems with antithetic bandwidths (, ).
An important and attractive aspect of the broadband hybrid cavity is that the enhancement effect can be tuned to different frequencies over a very large spectral range by simply adjusting the cavity length (see inset in Fig. 2). In fact, it is remarkable that the LDOS is enhanced to such a degree at over hundred nanometers wavelength detuning from the antenna plasmon resonance, which in this case was set close to 750 nm. Intuitively, the circulation of the optical energy in the microcavity compensates for the lower plasmonic enhancement of the LDOS at a large detuning. We note that this phenomenon provides a unique and novel means for external and selective manipulation of the emitter coupling to plasmonic antennas.
To obtain a deeper insight into the different participating resonant modes and to evaluate semianalytical expressions of the Green’s tensor, we also made use of a quasinormal mode (QNM) approach Bai et al. (2013) and determined the Purcell factor for single QNMs Sauvan et al. (2013); Agio and Martin-Cano (2013). The red lines in Fig. 2 represent the contribution from several QNMs, showing an excellent agreement for the hybrid full-wave response, whereas additional non-resonant modes would be necessary for describing the suppressed LDOS values with respect to free space (cf. values below 1 for the blue circles). The double-peaked LDOS arises as a result of the interference of two nearly resonant QNMs, consisting of a plasmonic-like mode and an FP-like one with positive and negative values, respectively. Negative contributions are common features of nearly resonant QNMs Sauvan et al. (2013), with the total sum remaining positive and thus physical (cf. red line). On the other hand, the detuned peak is mainly described by a single FP-nanoantenna QNM [cf. its intensity distribution in Fig. 1(b)], whereas the broader off-resonant QNMs contribute to the destructive interference dip.
A severe general limitation of plasmonic nanoantennas concerns quenching of emission at very small distances caused by the coupling to nonradiative and absorptive modes Rogobete et al. (2007); Delga et al. (2014). To study the quenching behavior of the detuned hybrid mode, we calculated the fraction of the LDOS that is dissipated () in the metallic nanostructure given by as a direct measure for quenching, where LDOS, and is the imaginary part of the permittivity of the metal. Figure 3(a)-(b) displays versus the antenna-emitter distance at the Fano peak (a) and dip (b) of the far-detuned hybrid mode shown in Fig. 2, while Fig. 3(c)-(d) presents both the radiative and nonradiative components of the LDOS, together with the bare nanocone results for comparison.
At the Fano peak [cf Fig. 3(a)], we find that is stronger than the case of a bare nanocone for nm and has a nearly constant value. This anomalous trend is in marked contrast to the quenching behavior for a bare nanoantenna (green triangles), which commonly increases in a monotonous fashion for smaller Rogobete et al. (2007). We attribute these findings to the concentration of the field in the metallic structure [see left inset of Fig. 3(a)] caused by the constructive interference of the nanoantenna and cavity modes, thus, resulting in an enhanced absorption. The right inset in Fig. 3(a) shows that the circulation of the optical energy in the microcavity can extend this effect even to separations comparable to a FWHM of the cavity mode profile (blue curve), where quenching by a bare nanocone becomes negligible. We note that, nevertheless, the structure keeps an overall good radiation efficiency of over a large spatial range while the LDOS is enhanced by ten times with respect to the bare cone [see Fig. 3(c)]. This radiative emission can be mostly collected by a FP mode with an overlap of about 81% [see Fig. 1(b)].
Another impressive phenomenon occurs at the Fano dip, as presented in Fig. 3(b). Here, acquires lower values than that of the bare nanocone case, exhibiting suppression of quenching. The inset in Fig. 3(b) illustrates that in this case, the destructive interference of the plasmonic and cavity modes lead to an intensity minimum inside the nanocone. This effect makes the emitter highly efficient over a large distance range, e.g. at nm. Figure 3(d) shows in more detail the involved competition between the radiative and nonradiative rates of the hybrid structure at different emitter-antenna separations compared to the bare nanoantenna case. The balance between emission enhancements and quenching can be adjusted smoothly between the Fano dip and peak by varying the FP cavity length or by changing the emitter-antenna separation. For example, the general quenching behaviors are reversed for nm due to the cavity radiative competition against quasistatic contributions González-Tudela et al. (2014); Delga et al. (2014).
We now present an example of an antenna-FP geometry that can even enter the SCR for a single quantum emitter. Here, we consider a bowtie antenna Kinkhabwala et al. (2009); Santhosh et al. (2016) compatible with fabrication on a flat cavity mirror [see Fig. 4(a)] and an organic molecule with a typical natural linewidth of MHz at cryogenic temperatures. We chose the antenna parameters (see caption of Fig. 4) to place its resonance at nm and tune a moderately low-Q cavity resonance (=3400) at nm in order to obtain an enhancing hybrid mode as discussed in Fig. 2. Figure 4(b) displays the LDOS enhancement on the Fano peak of the resulting hybrid mode at nm, whereas the red line shows the excellent single QNM approximation near resonance that relates directly to the Purcell factor Sauvan et al. (2013), reaching .
Next, we evaluate the resonance fluorescence spectrum of the composite system Vogel and Welsch (2006); Delga et al. (2014) within the single QNM approximation and using its Green’s tensor with component Collin (1990), where denotes the normalized field parallel to the orientation of the dipole at its position Bai et al. (2013), is the QNM resonance real frequency, and denotes its fullwidth at half-maximum. Figure 4(c) shows the spectrum outcome, which reveals a large peak splitting characteristic of strong coupling. Using a single Lorentzian model Vogel and Welsch (2006), we can estimate and understand the coupling rate and the condition for entering in SCRs. In the case of the bare cavity, , and lead to and , i.e. outside the SCR. Similarly, in the case of a bare nanoantenna, the very small mode volume of , and lead to while remains well below unity. It is the cooperative-enhanced ratio of large and fairly low of the detuned FP hybrid mode (, ) that allows surpassing the strong coupling threshold to , while keeping a very efficient coupling of to radiative modes.
The features of FP-antenna hybrids studied in this work are quite general Benson (2011); Xiao et al. (2012); Dezfouli et al. (2016); Doeleman et al. (2016) and can be realized in different cavity geometries Benson (2011); Xiao et al. (2012); Dezfouli et al. (2016); Doeleman et al. (2016); Kelkar et al. (2015); Wang et al. (2017) and different nanoantenna structures Santhosh et al. (2016); Chikkaraddy et al. (2016), opening new avenues in diverse research areas such as sensing, surface-enhanced Raman scattering, solid-state spectroscopy Benson (2011); Orrit et al. (2014), and quantum optics Tame et al. (2013). The resulting Fano resonances at tunable frequencies can be used to improve the emission efficiency of solid-state emitters such as organic molecules or color centers by selective enhancement of their zero-phonon transitions Grange et al. (2015); Wang et al. (2017). The strong radiative enhancement also ushers in new studies of single-emitter coherent interactions at ambient temperatures, where . Here, accounts for the pure dephasing rate Cui and Raymer (2006) caused by phononic excitations, which typically ranges from to for solid-state emitters Grange et al. (2015). The high coupling rates ( THz) and large bandwidths ( THz) of the hybrid structure could then bring diverse solid-state emitters at room temperatures into the strong coupling regime (e.g. for a SiV Grange et al. (2015), MHz and THz, or for a molecule, MHz and THz). Another prominent attribute of the hybrid cavity-nanoantenna system is the possibility to tune the near-field quenching and enhancement caused by plasmonic nanoantennas and to extend these interactions to longer length scales of the order of several hundred nanometers. This feature opens important doors for coupling a large number of emitters to the same hybrid mode, facilitating investigations of collective effects such as nonclassical correlations Carmichael et al. (1991) with enhanced dipole-dipole interactions Haakh and Martin-Cano (2015) and in collective strong coupling phenomena González-Tudela et al. (2013) that take place on femtosecond scales at room temperature Santhosh et al. (2016); Chikkaraddy et al. (2016). Here, the tunability of the cavity-antenna system can be particularly useful for modifying in-situ collective interactions of mesoscopic systems of emitters Hutchison et al. (2012); González-Tudela et al. (2013); Delga et al. (2014); Törmä and Barnes (2015); Galego et al. (2016).
Acknowledgements.This work was supported by the Max Planck Society and the European Research Council (Advanced Grant SINGLEION). V. acknowledges the support from the Alexander von Humboldt Professorship. The authors thank Claudiu Genes for reading and providing constructive comments of the manuscript.
- E. Purcell, Phys. Rev. 69, 681 (1946).
- S. Haroche and J. M. Raimond, Exploring the quantum (Oxford, 2006).
- A. Imamoglu, H. Schmidt, G. Woods, and M. Deutsch, Phys. Rev. Lett. 79, 1467 (1997).
- J.I Cirac, P. Zoller, H.J. Kimble, and H. Mabuchi, Phys. Rev. Lett. 78, 3221 (1997).
- J. I. Cirac and P. Zoller, Phys. Rev. Lett. 74, 4091 (1995).
- J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J. Keeling, F. Marchetti, M. Szymańska, R. Andre, J. Staehli, et al., Nature 443, 409 (2006).
- M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys. 86, 1391 (2014).
- J. A. Hutchison, T. Schwartz, C. Genet, E. Devaux, and T. W. Ebbesen, Angewandte Chemie International Edition 51, 1592 (2012).
- J. Galego, F. J. Garcia-Vidal, and J. Feist, Nat. Comm. 7 (2016).
- C.J. Hood, M.S. Chapman, T.W. Lynn, and H.J. Kimble, Phys. Rev. Lett. 80, 4157 (1998).
- K. J. Vahala, Nature 424, 839 (2003).
- J. Reithmaier, G. Sęk, A. Löffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. Keldysh, V. Kulakovskii, T. Reinecke, and A. Forchel, Nature 432, 197 (2004).
- T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. Gibbs, G. Rupper, C. Ell, O. Shchekin, and D. Deppe, Nature 432, 200 (2004).
- T. Grange, G. Hornecker, D. Hunger, J.-P. Poizat, J.-M. Gérard, P. Senellart, and A. Auffèves, Phys. Rev. Lett. 114, 193601 (2015).
- H. Kelkar, D. Wang, D. Martín-Cano, B. Hoffmann, S. Christiansen, S. Götzinger, and V. Sandoghdar, Phys. Rev. Appl. 4, 054010 (2015).
- D. Wang, H. Kelkar, D. Martin-Cano, T. Utikal, S. Götzinger, and V. Sandoghdar, Phys. Rev. X 7, 021014 (2017).
- P. Törmä and W. L. Barnes, Rep. on Prog. in Phys. 78, 013901 (2015).
- A. Trügler and U. Hohenester, Phys. Rev. B 77, 115403 (2008).
- S. Savasta, R. Saija, A. Ridolfo, O. Di Stefano, P. Denti, and F. Borghese, ACS Nano 4, 6369 (2010).
- T. Hümmer, F.J. García-Vidal, L. Martín-Moreno, and D. Zueco, Phys. Rev. B 87, 115419 (2013).
- C. Sauvan, J.-P. Hugonin, I.S. Maksymov, and P. Lalanne, Phys. Rev. Lett. 110, 237401 (2013).
- M. Agio and D. Martin-Cano, Nature Phot. 7, 674 (2013).
- K. Santhosh, O. Bitton, L. Chuntonov, and G. Haran, Nat. Comm. 7 (2016).
- R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, Nature 535, 127 (2016).
- A. Mohammadi, F. Kaminski, V. Sandoghdar, and M. Agio, J. Phys. Chem. C 114, 7372 (2010).
- Q. Bai, M. Perrin, C. Sauvan, J.-P. Hugonin, and P. Lalanne, Opt. Express 21, 27371 (2013).
- B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, Nature Mat. 9, 707 (2010).
- L. Rogobete, F. Kaminski, M. Agio, and V. Sandoghdar, Opt. Lett. 32, 1623 (2007).
- A. Delga, J. Feist, J. Bravo-Abad, and F.J. Garcia-Vidal, Phys. Rev. Lett. 112, 253601 (2014).
- A. González-Tudela, P.A. Huidobro, L. Martín-Moreno, C. Tejedor, and F.J. García-Vidal, Phys. Rev. B 89, 041402 (2014).
- A. Kinkhabwala, Z. Yu, S. Fan, Y. Avlasevich, K. Müllen, and W. E. Moerner, Nat. Photon. 3, 654 (2009).
- W. Vogel and D.-G. Welsch, Quantum optics (WILEY-VCH Verlag, Weinheim, 2006).
- R. E. Collin, Field theory of guided waves, 2nd ed., edited by D. G.Dudley (Wiley-IEEE Press Series on Electromagnetic Wave Theory, 1990).
- O. Benson, Nature 480, 193 (2011).
- Y.-F. Xiao, Y.-C. Liu, B.-B. Li, Y.-L. Chen, Y. Li, and Q. Gong, Phys. Rev. A 85, 031805 (2012).
- M. K. Dezfouli, R. Gordon, and S. Hughes, arXiv preprint arXiv:1606.05874 (2016).
- H. M. Doeleman, E. Verhagen, and A. F. Koenderink, ACS Phot. 3, 1943 (2016).
- M. Orrit, T. Ha, and V. Sandoghdar, Chemical Society Reviews 43, 973 (2014).
- M. Tame, K. McEnery, Ş. Özdemir, J. Lee, S. Maier, and M. Kim, Nature Phys. 9, 329 (2013).
- G. Cui and M.G. Raymer, Phys. Rev. A 73, 053807 (2006).
- H. Carmichael, R. Brecha, and P. Rice, Opt. Comm. 82, 73 (1991).
- H. R. Haakh and D. Martin-Cano, ACS Phot. 2, 1686 (2015).
- A. González-Tudela, P.A. Huidobro, L. Martín-Moreno, C. Tejedor, and F.J. García-Vidal, Phys. Rev Lett. 110, 126801 (2013).