Room-temperature plexcitonic strong coupling: Ultrafast dynamics for quantum applications

An optical cavity has the ability to confine electromagnetic waves and enhance light–matter interaction, facilitating rapid energy exchange between a quantum emitter and the optical field at the cavity resonance. When the energy exchange rate, traditionally defined by the coupling strength g, exceeds the total energy dissipation rate, the system reaches the strong coupling regime.^1,2 This effect is at the core of modern quantum technological applications such as single-qubit coherent control,³ universal quantum gates,⁴ and quantum sensing.⁵ However, strong light–matter coupling with a single emitter is extremely fragile and has so far mostly been realized at cryogenic temperatures, in systems such as trapped atoms in reflective mirror cavities,^6,7 trapped atoms in photonic crystal cavities,⁸ and solid-state qubits.⁹ In the past decade, tremendous progress has been made toward room-temperature single-emitter strong coupling by using nanoscale optical cavities formed by plasmonic resonances on metal nanostructures.^10–12 Although metals dissipate energy rapidly due to high Ohmic loss, plasmonic nanocavities are capable of confining and enhancing fields so intensely that this enhancement compensates for their dissipation and facilitates strong coupling.¹³ By realizing single-emitter strong coupling in an ambient environment,^14,15 the plasmonic platform opens up vast possibilities for applications and limitless opportunities for fundamental studies.

In addition to their extreme field confinement property, plasmonic nanocavities also possess several unique optical properties. First, plasmonic nanocavities facilitate significant spatiotemporal field variations¹⁶ such that different emitters placed in the proximity of the nanocavities may experience vastly different optical environments. Consequently, this leads to distinguishable optical properties of nearby quantum emitters and was exploited in a sensing application¹⁷ and multimode control of near-field plasmonic coupling.¹⁸ Second, plasmonic nanocavities also facilitate ultrafast energy exchange between quantum emitters in the timescale of a few tens of femtoseconds.^13,17–20 Such a rapid energy exchange is significantly faster than typical dephasing rates and makes a plexcitonic system an ideal platform for room-temperature quantum technologies. In this perspective, we first outline some key aspects related to strong coupling in nanoplasmonic cavities, highlighting, in particular, quasi-normal mode (QNM) theory (Sec. II), followed by a summary of current experimental state-of-the-art configurations of plasmonic nanocavities and quantum emitters (Sec. III) for strong coupling. We then discuss several theoretical studies that explore applications of plexcitonic strong coupling using a single emitter (Sec. IV A) and two or more emitters (Sec. IV B). Finally, we present an outline of future research directions of room-temperature strong coupling based on plexcitonic systems (Sec. V).

Resonances of a plasmonic nanostructure are characteristically non-conservative as their energy dissipates due to Ohmic losses and radiation to the (external) environment. Consequently, a plasmonic resonance is in terms of its photonic properties insufficiently captured by a simple real-frequency eigenmode. Generally, the photonics of a plasmonic resonance can be realistically described by taking Ohmic dissipation and radiation losses on board dynamically, such as within an appropriate finite-difference time-domain simulation¹³ or in terms of quasi-normal modes (QNM) with complex eigenfrequencies.^21–24 The QNM description is also useful for understanding interaction between plasmons and quantum emitters. In a non-dissipative optical cavity, the emission properties of quantum emitters are modified by a sum of positive contributions from each cavity mode. In a system composed of a lossy plasmonic nanocavity and quantum emitters, on the other hand, the emitters' emission properties are determined by coherent superposition of the QNMs.²³ Here, key properties of a plasmonic mode, i.e., the mode volume and quality factor, and its interaction with quantum emitters are outlined within the QNM framework. More comprehensive introductions and further background can also be found in recent works of Lalanne et al.²² and Kristensen et al.²⁵ 

Although significant progress has been made in treating dissipative electromagnetic systems with the QNM theory, most quantum mechanical analyses of lossy optical cavities, such as plasmonic systems, are implemented heuristically in terms of a dissipative Jaynes–Cummings (JC) model where optical and plasmonic losses are treated phenomenologically.²⁸ Franke et al. have recently introduced the QNM-JC model based on a symmetrization scheme for creation and annihilation operators.^23,29 In the QNM-JC model, the effective Hamiltonian that governs a plexcitonic system consists of three parts: $H = H p + H e + H I$⁠. (1) $H p = ℏ ∑ m n Ω m n a m † a n$ represents the quantized QNM fields that include the coupling between different symmetrized QNMs m and n with a coupling constant Ω_mn. $a m †$ (a_m) is the creation (annihilation) operator, obtained via a symmetrizing orthonormalization transformation; (2) $H e = ℏ ∑ e ω e σ + σ −$ describes the quantum emitters with different transition frequencies ω_e, where $σ +$ (⁠ $σ −$⁠) is the raising (lowering) operator for the emitters; (3) $H I = − i ℏ ∑ m g m σ + a m + H . a .$ is the interaction Hamiltonian in the symmetrized QNM basis, and $g m = ∑ n ( S 1 / 2 ) n m g ̃ n$ is the symmetrized coupling strength, where the symmetrizing matrix $( S ) m n$ characterizes the overlap/coupling between different QNMs m and n, and $g ̃ n = ω n 2 ε 0 ℏ μ · f ̃ n ( r 0 )$ denotes the overlap between the emitter dipole moment and the QNM eigenfunction $f ̃ n ( r 0 )$⁠.

The QNM-JC model provides a rigorous theoretical foundation for analyzing room-temperature plexcitonic strong coupling, including optical phenomena related to quantum fluctuation and high photon number. It does, however, not come without an extra cost. A fully quantized model requires computational resources that grow exponentially with the number of plasmonic modes and emitters' quantum states. This may present a challenge for plasmonic nanocavities that often involve a large collection of spectrally overlapping higher-order quasi-normal modes.²⁴ Alternatively, a dynamic semi-classical model, which treats emitters quantum mechanically and optical fields classically, could be employed to capture many relevant physical phenomena, especially those in the limit where the external pumping rate is smaller than the system's total decay rate.

This section outlines recent developments of different configurations of plasmonic nanocavities and representative quantum emitters that satisfy the criteria for room-temperature strong coupling.

Rapid progress in nanofabrication has, in the past 20 years, enabled nanoscale manipulation of plasmonic nanostructures. This has provided the foundation of nanoplasmonic room-temperature strong coupling, which has been studied with a wide range of configurations for plasmonic nanostructures, including (a) plasmonic nanoparticle (NP) arrays, (b) plasmonic NP arrays with microcavities, (c) single plasmonic NPs, (d) dimer plasmonic NPs, and (e) probe-like slit nanoresonators.

Since the coupling strength increases with the emitter number as $g ∝ N$⁠, strong coupling is more easily realized in a collective coupling setup involving a large number of emitters. Hence, early experiments on room-temperature strong coupling have been demonstrated between collective plasmons and ensembles of quantum emitters.¹⁰ A typical configuration includes NP arrays^31,38,39 [Fig. 1(a)] in which each NP collectively contributes to the coupling and forms collective lattice resonances. This constitutes a favorable platform for strong coupling studies, which alters the original interaction between single NPs and emitters.³⁹ 

The NP array configuration can also be optically improved by a sandwiching arrangement inside an external mesoscopic/microscopic cavity³² [Fig. 1(b)], where the plasmonic nanocavity is hybridized with a microcavity.^15,40,41 The sandwich configuration takes advantage of both ultraconfinement from the plasmonic nanocavities and a low dissipation rate from the external cavity, making strong coupling more easily reachable across a wide spectral range.

In the past decade, the attention has been shifted from exploiting collective plasmons in NP arrays to reducing the mode volume of single NPs to enhance the interaction with individual quantum emitters. Example configurations of single NPs include core–shell nanospheres^33,42 [Fig. 1(c)], nanoprisms^34,43–45 [Fig. 1(d)], and elongated nanorods^35,46,47 [Fig. 1(e)]. These configurations squeeze the plasmonic mode volume down to below ∼100 nm³ [Fig. 1(e)] and successfully facilitated room-temperature strong coupling at the single emitter limit.³⁵ 

The field confinement property of single NPs can be enhanced even further at extremely small gap widths of only a few nm between the two NPs. At such a nanogap, plasmonic modes of the two NPs hybridize and form dimer plasmonic modes with an extreme field confinement property. Dimer plasmonic configurations include bowtie³⁶ [Fig. 1(f)], nanosphere on mirror^11,48 [Fig. 1(g)], and nanocube on mirror^37,49,50 [Fig. 1(h)]. Among these configurations, the NP-on-mirror (NPoM) nanocavity^{11,37,48–50} was the first to demonstrate room-temperature strong coupling with single quantum emitters.¹¹ 

Although nanogaps can provide enormous field enhancement, fabrication is generally challenging. Positioning emitters at the hotspot inside the nanogap are even more challenging and rely on probabilistic techniques¹¹ or DNA origami. A probe-like slit nanoresonator [Fig. 1(i)] that can be freely moved, however, enables deterministic and tunable near-field (cavity-free) strong coupling with colloidal quantum dots at room temperature.¹² 

In practice, it still remains challenging to fabricate plasmonic NPs in perfect geometric shapes such as perfect spheres. In fact, NPs are always faceted and possess complex eigenmodes that are spectrally and spatially overlapping. As a result, an optical field incident on these nanostructures almost always excites multiple modes simultaneously, making it difficult to isolate individual modes and interpret near-field and far-field results.⁵¹ Hence, thorough theoretical and numerical investigations on eigenmodes of plasmonic nanocavities are essential for understanding their experimental behavior.^24,52 Such understanding could lead to designs for functional plasmonic devices, as demonstrated by a recent work on single-molecule nanoscopy.⁵³ 

So far, most studies have focused on plasmonic gap modes that are confined within a nanoscale space between metal surfaces. The gap modes arise from a hybridization of the plasmonic modes from the opposite sides of the gap and provide a more intense field enhancement and stronger interaction with quantum emitters.⁵⁴ However, these gap modes couple weakly to the far field, except for a few lower-order modes.²⁴ On the other hand, plasmonic antenna modes of single NPs couple often strongly to the far field, while providing much weaker field enhancement. By hybridizing gap modes with antenna modes, a mode with both large field enhancement and large radiation efficiency can be achieved,⁵⁵ enabling subwavelength manipulation of light and an interface to the far field. Alternatively, an antenna mode with high field enhancement can also be realized by simply coating the NP with a layer of dielectric^18,56 in a nanocube-on-mirror configuration.

Typical quantum emitters for realizing room-temperature strong coupling are summarized in Table I. This includes semiconductor quantum dots (QDs), dye molecules, and two-dimensional (2D) materials. At room temperature, quantum emitters experience large dephasing due to electron scattering, and plasmonic nanocavities are required to have a sufficiently small mode volume of $< 10 − 5 λ 3$⁠, in order for the systems to reach the strong coupling regime.

Semiconductor QDs, such as GaAs, often have a much larger dipole moment than other types of quantum emitters. However, the sizes of QDs are often larger than 2 nm and cannot fully exploit ultrasmall mode volumes of plasmonic nanocavities. Strong coupling with QDs has been demonstrated with, $e.g.$⁠, a bowtie³⁶ and slit nanoresonator,¹² as shown in Figs. 1(f) and 1(i). On the other hand, dye molecules are much smaller than QDs but often have a smaller dipole moment. For example, a dye molecule such as a methylene blue could fit into a 0.9 nm gap in an NPoM nanocavity and reach the strong coupling regime even though it has a dipole moment of 3.8 Debyes,¹¹ as shown in Fig. 1(g). Other promising candidate quantum emitters include defect color centers in hexagonal boron nitride (h-BN)⁵⁷ and nanodiamonds,^58,59 whose emission properties are shown to be drastically altered by plasmonic nanocavities.^60,61

Recently, 2D materials such as transition metal dichalcogenides (TMDCs) have emerged as alternative quantum emitters for room-temperature strong coupling. TMDCs allow for electrostatic doping and are capable of tuning the strong coupling processes. However, the dominant directions of TMDC's transition dipole moments are usually aligned in-plane. This results in inefficient coupling between TMDCs with plasmonic modes that are dominantly aligned out-of-plane in most plasmonic configurations. As a result, most experiments on strong coupling with TMDCs so far report relatively low Rabi splittings of below 200 meV.^48–50 The large dipole moment of TMDCs also arises from a collection of bound excitons that are delocalized throughout the TMDC sheets, and a direct analog to two-level atoms should be avoided while dealing with their excitonic excitation.³⁰ 

In recent years, a wide range of theoretical and experimental studies have been devoted to quantum plasmonics.^14,15,72 With the demonstration of single-emitter strong coupling in plexcitonic systems,^11,12,35 we can now explore applications of plexcitonic strong coupling. In this section, we focus on several theoretical studies that attempt to bring plexcitonic strong coupling to different application scenarios. Starting from a single emitter that strongly couples to a plasmonic nanocavity, quantum immunoassay sensing has been proven to be feasible (Sec. IV A). It serves as a biochemical sensing scheme that utilizes light–matter strong coupling to drastically enhance the sensitivity down to the single-molecule limit.¹⁷ With two or more emitters that strongly couple to the same plasmonic nanocavity, entangled qubits¹⁸ and reconfigurable single-photon sources⁷³ are achievable (Sec. IV B), which form the basic building blocks for quantum information processing. With the development of the concept of microcavity plasmonics,^15,19,40 we foresee a bright future of plexcitonic strong coupling in other areas as well, $e.g.$⁠, cavity-assisted ultrafast long-range periodic energy transfer between plasmonic nanoantennas.⁷⁴ 

The proposed schematic is illustrated in Fig. 2(a) consisting of four main components: (i) a hemisphere dimer plasmonic nanocavity that provides a light-enhancing plasmonic hotspot, (ii) an antigen as the “analyte” to be detected, (iii) two antibodies that are paired with the target antigen, and (iv) a quantum emitter label that is chemically linked with the antibody–antigen–antibody complex. The quantum emitter label (such as a quantum dot or a dye molecule) is initially positioned such that it is optimally located at or close to the plasmonic hotspot and such that it couples strongly with plasmons. Figure 2(b) demonstrates the sensing capability of the proposed strong-coupling immunoassay by comparing its extinction cross section spectrum with those of conventional plasmonic immunoassays. The spectra of a conventional plasmonic immunoassays show a characteristic shift of the optical resonance. In contrast, the strong-coupling immunoassay exhibits two split peaks, which is known as the characteristic Rabi splitting. This is in effect a bi-directional shift with higher sensitivity than those of conventional immunoassays.

In an emitter-labeled plasmonic immunoassay, the extinction spectrum originates from stimulated absorption and emission processes whose signals interfere with the background excitation light. Hence, the “splitting” manifested in the extinction spectrum is not definitive proof that the coupled system is in the strong coupling regime. To provide stronger evidence that the proposed immunoassay is indeed in the strong coupling regime, we calculate photoluminescence (PL) spectra of the emitter labels. Unlike extinction spectra, the PL reveals the spontaneous emission of the coupled system without the background excitation light.

Figure 2(c) compares the PL and extinction spectra for strong-coupling immunoassays with gap sizes of 2–6 nm and emitter labels placed at the plasmonic hotspots. The discrepancy between the PL and extinction spectra becomes more significant at large gap sizes (>4 nm) where splittings only appear in the extinction spectra. The single peak in the PL spectrum implies that the emitter and plasmons are, in fact, in the weak coupling regime. For smaller gap sizes (<4 nm), splittings can be observed in both the PL and extinction spectra, indicating a strong coupling regime.

Strong coupling is also evident in the time dynamics of the system. The polarization dynamics P(t) of the emitter is shown in Fig. 2(d) for gap sizes of 2–6 nm where P(t) is normalized by the incident field amplitude $ε 0 | E 0 |$⁠. For small gap sizes of <4 nm, the dynamics clearly shows ultrafast Rabi oscillations with a period of less than 40 fs. These oscillations arise from rapid energy exchange between the emitter and plasmons.

In a typical immunoassay measurement, multiple analytes are present in a liquid solution. To simulate more realistic experiments, let us consider an ensemble of emitter-labeled analyte complexes that are randomly scattered in the vicinity of a nanodimer, Fig. 2(a). In most cases, analyte-emitter complexes will be distributed around the nanodimer, and the emitters in these complexes couple weakly with plasmons. We define sensing in this scenario as sensing in the “classical” regime. However, there is a chance that a complex will be located optimally close to or within the gap between the two hemispheres, and the emitter label becomes strongly coupled with the nanodimer. Sensing in this case is defined as the “quantum” sensing regime. Figure 2(e) shows a statistical study on the extinction spectra of the nanodimer with different average surface densities of analyte–emitter complexes. At a large surface density, no boundary can be observed between the two regimes. However, the figure of merit (FoM) in the quantum regime remains roughly constant. This is because the spectrum in the quantum sensing is dominated by the dynamics of one emitter located at the plasmonic hotspot.

The results suggest that the proposed strong-coupling immunoassay protocol massively outperforms conventional shifting-type sensors. However, it is not without fabrication challenges related to the nanogap and alternative realizations such as such a plasmonic nanocube that provides sufficient field confinement at its corners is more accessible for biomolecules.³⁵ Another alternative protocol uses artificial proteins to capture an antigen between a plasmonic dimer without using much larger antibodies.^75–77 

An antenna mode in a coated nanocube-on-mirror (c-NCoM) nanocavity as depicted in Fig. 3 typically has multiple hotspots located at the upper corners of the nanocubes.¹⁸ These are relatively easy to access for enhancing various physical or chemical processes such as sensing.¹⁷ Remarkably, typical values of the field enhancement of the antenna mode in the c-NCoM geometry are comparable to the enhancement of the fields in coated nanosphere-on-mirror (c-NSoM) cavities. At the same time, due to the field confining effects of the dielectric coatings, the enhancement is much stronger than that in the case of the layered nanocube-on-mirror (l-NCoM) system.

The most attractive feature of the antenna mode lies in its multiple exterior hotspots. It is, therefore, possible to consider entanglement of two single emitters placed at the upper corners of the nanocube via the antenna mode within a single c-NCoM nanocavity, as illustrated in the inset of Fig. 3(d). For a system where two quantum emitters QE1 and QE2 are coupled to a nanocavity with a typical single-emitter coupling strength of $g 0 =$ 80 meV, we demonstrate the dynamics of the excited-state populations of QE1 and QE2 in Fig. 3(d). Clearly, there is an oscillatory exchange of excited state population between two of them. The concurrence C can be employed to systemically characterize the degree of entanglement between the two qubits.⁷⁸ It is found that the maximum concurrence of $C =$ 0.6 can be achieved in the strong coupling regime for a carefully designed off-resonant system with an emitter-cavity detuning of $Δ e , c >$ 0.2 eV. The dependence of the concurrence C on g₀ is exemplified in Fig. 3(e) in an off-resonant system with $Δ e , c =$ 0.3 eV. In the inset, we show the dynamics for a case study at g₀ = 80 meV, and a notable degree of entanglement $C ∼$ 0.4 can be achieved. It should be noted that plasmon-mediated qubit entanglement has also been studied in plasmonic nanowires^79–83 and metallic nanoparticles in the weak-to-intermediate coupling regime.⁸⁴ The work presented here¹⁸ extends the possibility to the strong coupling regime due to the remarkable three-dimensional field confinements provided by the antenna mode and reveals the dependence of the concurrence on the single-emitter coupling rate and the emitter-cavity detunings.

Single-emitter experiments such as summarized in Sec. III successfully propel active plasmonics into the quantum regime, typically characterized by an anharmonic energy structure as illustrated in Fig. 4(a), making the photon blockade (PB) highly feasible.⁸⁵ Meanwhile, an unconventional photon blockade (UPB) is also readily achievable in such a plexcitonic system by carefully engineering the quantum interference between different excitation pathways for multiple photons. With these concepts, we can now propose to operate a quantum plexcitonic system as a reconfigurable single-photon source⁷³ between the PB antibunched single photon beam and UPB antipaired photons with certain probability to emit bunched photons of three or more. It should be noted that for illustration purposes, a spherical Au nanoparticle is shown in Fig. 4(b). In practice, plasmonic nanocavities offering strong field localization as shown in Fig. 1 would be more feasible, e.g., a single nanoprism as shown in Figs. 4(c)–4(e).

To explain the concept of reconfiguration, we externally rotate the polarization angle α of the incident light in Figs. 4(c)–4(e) on a nanoprism-e₁ resonant plexcitonic system. The emitters coated around the nanoprism surface are now distinguished by their location, where we highlight the three apexes with strong plasmonic field enhancements: A, B, and C. Upon rotation of the polarization angle α from −30° to 150°, the electric fields at the three locations change periodically as shown in Fig. 4(d). These electric fields directly influence the local coupling rates³⁵ that can be approximated as $g A=85| cos α|, g B=85| cos (α−60°)|$⁠, and $g C=85| cos (α+60°)|$ and led to the calculated correlation functions $g ( 2 ) ( 0 )$ and $g ( 3 ) ( 0 )$ in Fig. 4(e). Evidently, we observe a repeating reconfiguration pattern of PB-UPB with tuning the polarization angle α.

In this perspective, we have focused on recent progress and applications of plasmonic nanocavities that facilitated room-temperature plexcitonic strong coupling. While room-temperature plexitonic strong coupling was initially realized with an ensemble of quantum emitters that respond collectively to plasmon excitation, advances in nanofabrication have provided sub-nanometer control over plasmonic nanostructures, bringing room-temperature plexcitonic strong coupling down to the single emitter limit. Of course, the natural next step is coherence control of a few quantum emitters and realization of multiple-emitter quantum operations at room temperature, and many more fascinating phenomena can be envisioned if advancing beyond the strong coupling into the ultrastrong coupling regime.^86,87

As particular examples, we have highlighted an immunoassay sensing scheme that employs strong coupling and quantum emitters as sensing labels.¹⁷ While a detailed statistical analysis with random positions of the analytes demonstrates that the proposed protocol works well and clearly serves as an important proof of principle for further designs of plasmonic immunoassay sensors, the concept could also be conceivably extended to detect other quantum objects such as electronic spins in nanodiamonds.⁸⁸ We have also deliberated on proposals for utilizing plexcitonic building blocks for quantum information processing, particularly for plasmon-mediated two-qubit entanglement and reconfigurable single-photon emission. These concepts build on designing multiple hotspots with deep sub-wavelength field localizations in a single plasmonic nanocavity, which make attached quantum emitters spatially distinguishable while still strongly coupled to the same plasmonic nanocavity. Collating a few or an array of such building blocks together in a systematic and controlled manner is certainly a promising route toward scalable room-temperature quantum networks.

While allowing strong coupling at room temperature, nanoplasmonic cavities also facilitate—as directly uncovered in our numerical simulations—plexcitonic dynamics on timescales shorter than 20 fs. Such ultrafast dynamics conceivably enables sub-picosecond quantum operations at room temperature and allows, for example, nearfield-induced dynamic bipartite quantum entanglement through a CNOT quantum operation⁸⁹ to be performed before decoherence effects become significant. Future research should investigate the potentials of plasmonic nanostructures as alternative or complementary platforms for noisy intermediate scale quantum (NISQ) technology.⁹⁰ Given the current pace of progress in the plasmonics community, we envision that room-temperature single- and multiple-qubit gates will soon be reliably realized in nanoplasmonic platforms, opening up a pathway toward room-temperature quantum technologies.

The Institute of High Performance Computing (IHPC) acknowledges financial support from National Research Foundation Singapore No. NRF2017-NRF-NSFC002–015. O.H. gratefully acknowledges funding from the Science Foundation Ireland (SFI) via Grant No. 18/RP/6236.

The data that support the findings of this study are available from the corresponding author upon reasonable request.