Cavity polaritonics and cavity optomechanics. Microcavity exciton-polariton Bose-Einstein-like condensates (BECs), a quantum state of matter formed by strongly coupled quantum well (QW) excitons and photons in semiconductor microcavities (MCs), constitute a hybrid system [1] that displays a plethora of interesting properties [2]. These include, in addition to the Bose-Einstein condensation nature [3], superfluidity [4] and Josephson-like oscillations in coupled condensates [5,6]. A polariton condensate is also characterised by a spinor degree of freedom, which involves both the exciton spins and the MC photons and results in the polarisation of the light emitted from the MC [7]. The latter can be used to probe as well as to efficiently control the BEC state. In this context, rich physics including self-induced Larmor precession of the spinor under non-resonant excitation [8], bistability [9], and spin switching [10], have been reported. While these polariton fluids bear some similarities with more standard quantum phases in interacting equilibrium systems, there are several peculiar aspects that arise from their driven-dissipative, non-equilibrium nature that makes them specially interesting, even more nowadays with fresh new ideas emerging in the field of non-hermitian dynamics [2]. The recent blooming of polariton-related research has been strongly supported by the high degree of maturity achieved in engineering controllably coupled polariton BEC traps, either in pairs [5,6] or forming arrays of different geometries and dimensionalities [11–15]. These have allowed, for instance, the implementation of quantum simulators [16–19] and the exploitation of the topological properties of different lattice models [20] by profiting from the experimental possibility of accessing excited states and/or controlling interactions among polaritons.

In parallel, another consolidated area is that of cavity optomechanics, which employs hybrid structures to bridge the optical domain and acoustics [21–24]. Optomechanical resonators and optomechanical crystals exploit the co-localisation of mechanical and optical modes to enhance their mutual interaction and, eventually, induce collective phenomena. Non-linearities arising in this context due to dynamical backaction [23] have been exploited, e.g., for the optical cooling of mechanical oscillators down to the quantum ground state [25–28] and for mechanical self-oscillation conceptually similar to phonon lasing [29,30]. These optomechanical non-linearities are accesible at the single-photon level when the optomechanical cooperativity $C_0=4g_0^2/\kappa \Gamma >1$, where $g_0$ is the single-photon optomechanical coupling factor, and $\kappa$ and $\Gamma$ are the optical and mechanical dissipation rates, respectively [23]. For the multiple-photon case, the optomechanical coupling is amplified as $g_\mathrm {eff}=g_\mathrm {0} \sqrt {N_\mathrm {p}}$, with $N_\mathrm {p}$ the photon number [23]. The optomechanical strong-coupling regime defined by $g_\mathrm {eff} > \kappa,\Gamma$ [23,31–33] requires a large $g_0$ and small $\kappa$ and $\Gamma$, but can also be enforced by increasing ${N_\mathrm {p}}$ via a strong optical pumping. The potentials of new physics in merging cavity polaritons with cavity optomechanics were quite early identified [34–36], but only recently started to find experimental realization.

Polariton-mediated optomechanical coupling factor and cooperativity. Typically, cavity-optomechanical systems rely on radiation-pressure (RP) forces [37]. This mechanism is relatively weak [38] and, thus, optomechanical non-linearities demand ultra-long photon and phonon lifetimes [24,39]. Semiconductor materials provide an alternative strategy through the access to exciton-mediated electrostrictive forces (based on deformation potential interaction, DP), which can be strongly enhanced at electronic resonances [40,41]. Cavity optomechanics becomes naturally connected with the physics of exciton-polariton fluids in semiconductor microcavities by the fact that the same GaAs/AlAs-based planar MCs with distributed Bragg reflectors (DBRs) required for polaritons are also ideally suited to confine hypersound in the GHz range [42,43]. The fundamental confined acoustic mode with frequency of around $\Omega ^0_\mathrm {m}/2\pi \sim 20$ GHz for microcavities operating in the near-infrared range corresponds to a breathing of the cavity spacer along the growth direction, which has overtones at $\Omega ^n_\mathrm {m} =(1+2n) \Omega ^0_\mathrm {m}$. The wavelength of the fundamental confined mode, which is determined by the cavity spacer thickness, is the same as for the confined photons. The frequency ratio between tens of GHz for the phonons and hundreds of THz for the photons just bears the relation between their respective wave speeds.

Phonons interact with polaritons via their excitonic component through the DP interaction as well as via their photonic component through RP. The DP contribution arises from the effects of the strain $s=\partial u/\partial z$ on the excitons’ energies, which can be included as $\tilde {\omega }_{l} = \omega _{l} - \Xi _{l} \times s$, where $\Xi _{hh (lh)}$ is the hh (lh) DP coefficient for the electron-heavy hole (electron-light hole) exciton states. RP corresponds to the change of the polariton energies induced by the movement of the interfaces within the MC structure due to the mechanical displacement $u(z)$. The polariton optomechanical coupling factor can, hence, be expressed as $g_{0}=S_c\,g_{0}^{RP} + S_{x}\,g_{0}^{DP}$, where $S_c$ ($S_x$) is the photon (exciton) Hopfield coefficient [44,45].

Theoretical [45] and experimental [46] studies have shown that the coupling $g_0^{DP}$ mediated by excitons in the QWs embedded in a polariton MC can exceed RP by two orders of magnitude. Recalling that $C_0 \propto g_0^2$, it follows by this token that $C_0$ can be amplified by up to four orders of magnitude. Benefiting from the co-localization of both sound and light, it can be shown that $g_0 \propto 1/L$, with $L$ the lateral size of a microstructured cavity [47,48]. This implies that single-polariton coupling on the order of magnitude of $g_0/2\pi \sim 20$ MHz can be achieved in microstructured MCs with lateral dimensions of around $\sim 1\mu$m [45,46]. These microresonators can have a bare photonic lifetime of around 50 ps (photonic Q-factor$\sim 10^5$, implying a decay rate $\kappa$ of a few GHz), and a phonon lifetime of 100’s of ns (decay rate $\Gamma$ of a fraction of a MHz). Both features, which are accessible with current technologies, could allow single-polariton cooperativities $C_0>1$, something that still needs to be experimentally demonstrated. We note here that the hybrid polariton-phonon MCs require an optimized positioning of the QWs within the MC spacer layer, which differs from the standard choice that maximizes the confined electromagnetic field $E$ at the QW position. Indeed, the confined phonon strain $s$ vanishes at these positions, thus resulting in a small DP coupling. Designs for the hybrid phonon-polariton MCs rather optimize the product $s \times |E|^2$ at the QW positions. One natural concern is whether such premium performances can indeed be attained in real structures, in view of the fact that the same QW excitons that enhance the optomechanical coupling can also lead to residual absorption and inhomogeneous-broadening-related dephasing (i.e., to a reduction of $\kappa$). In fact, the previously cited polariton decay rates are based on existent devices. In addition, it turns out that such high finesses for polaritons partially arises from the dephasing protection induced by the strong exciton-photon coupling [46].

Polariton platforms. Polariton optomechanics can be implemented in planar MCs with DBRs [34,49,50] but, as mentioned before, the optomechanical coupling $g_0$ greatly benefits from lateral confinement. Lateral microstructuring for optomechanical applications can be realized using pillar resonators fabricated by deep etching [6,47,51], created by micro-structuring the MC spacer [12,13,44], or using laser-induced effective potentials [52,53]. In the latter case, however, while the polaritons are laterally confined, the phonons are not. With all the mentioned technologies polaritons can be confined into single traps, pairs of traps, or in arrays of different geometries determined by design. Similar to polaritons, phonon states can also be engineered as, e.g., molecular-like levels in double-structures or to form tailored engineered phonon bands in lattices [54,55]. We note that this brings-in the concept of polaromechanical metamaterials [55], different from optomechanical crystals [22] not only because polaritons are involved, but also because both the lattice geometry and the internal energy structure of the sites making the network are the determinant for the system properties. We would also like to stress another major difference between optomechanics and polaromechanics, specifically the active character of the latter. That is, the fact that non-resonantly pumped polaritons are an internal light source with self-attained coherence. This self-established condensed state collectively responds generating and being affected by the mechanical fields.

All the above polariton platforms have been implemented for optomechanical applications, to the best of our knowledge, exclusively based in the GaAs/AlAs family of materials. II-VI materials could in principle be implemented with similar strategies, with the benefit of relatively larger Rabi gaps and consequently operation at higher temperature and excitation powers [3]. Larger Rabi gaps also are characteristic of microcavities with perovskite [56] and 2D-materials [57–59], for which cavity polaritons have been already reported. Exciton-phonon interactions are also expected to be particularly strong in the latter case, potentially opening the path to the ultra-strong optomechanical coupling regime ($g_{eff} > \Omega _m$). Electrical biasing could be implemented in 2D-materials, providing both efficient electrical driving of the vibrations, and an additional knob to tune cavity optomechanics. Such electrical tuning is also possible with liquid crystal cavities [60]. Clearly, there is a huge fertile and still unexplored ground for the investigation of the crossroad between cavity electrodynamical and optomechanical concepts in resonant devices.

Coherent phonons. Piezoelectrically excited surface acoustic waves (SAWs) can be injected to modulate microcavity polaritons using interdigitated transducers (IDTs) [50,61]. Due to technological limitations associated with the IDT microfabrication, this technology is limited to frequencies up to a few GHz. In addition, the reduced penetration depth of high-frequency SAWs sets a limit to the thickness of the top DBR of the MC and, thus, to the minimum photon decay-rate $\kappa$ of the resonator. These limitations can be overcome by the use of piezoelectric bulk acoustic wave (BAW) transducers [62], which, as recently demonstrated, can resonantly excite 20 GHz confined acoustic modes. Hybrid MCs can also be designed to guide GHz acoustic modes along their spacer [63], an in-plane configuration that ensures strong interaction with polaritons while overcoming the frequency limitation of conventional SAWs. The upper frequency limit for piezoelectric generation of acoustic fields can be substantially extended: in fact, the feasibility of acoustic waves excitation up to 60 GHz using piezoelectric thin films has already been established [64]. Broad-band BAWs can also be impulsively generated by ultrafast laser pulses impinging on a thin metal layer deposited at the back surface of the sample [49]. A similar pump-and-probe technique based on ps-lasers can be used to resonantly generate, probe, and control confined acoustic vibrations [65–68]. These last technique can be used in DBR-based MCs to generate both the $\sim 20$ GHz fundamental cavity confined mode as well as its first overtones. With proper positioning of the QWs within the MC spacer, it has been shown that one can push the phonon frequency limit up to $\sim 180$ GHz [69]. By increasing the working frequency the passage from adiabatic ($\Omega _m < \kappa$) to non-adiabatic ($\Omega _m > \kappa$) mechanical modulation of polariton condensates has recently been demonstrated [70].

In the situations mentioned above, the coherent phonons used to modulate the polaritons are generated externally either piezoelectrically or using laser pulses. Based on the advances established in the domain of cavity optomechanics [29,30], it has been recently shown that confined mechanical waves with GHz frequencies can also be self-induced in polariton MCs by a continuous and non-resonant optical excitation [44,70,71]. Self-induced phonon excitation has been reported both for single polariton traps [70] and for coupled traps [44,71], in which a pair of polariton energy levels are set to double-resonantly couple to the confined vibrations. Interestingly, in the latter case, and for rather separated traps, the dominating optomechanical coupling mechanism becomes quadratic in the phonon displacement, thus opening the path for the parametric generation of squeezed phonon states [71]. Once generated, the phonons imprint coherent information on the light field through the modulation of its intensity or the generation of spectral sidebands. In such a way, bidirectional optical-to-microwave transduction has been recently demonstrated in the GHz range using GaAs/AlAs microcavities at low temperatures [70]. Interestingly, this was shown to involve phonoritons, that is, optomechanical quasi-particles consisting of strongly coupled polariton and mechanical fields. It remains to be demonstrated if such a technology can be pushed to operate at higher temperatures.

Optomechanics and Synchronization. Polariton condensates, i.e., the many-body state constituted by coherently coupled polaritons, are also particularly interesting due to their long coherence time as compared to the decay time of individual polaritons. Based on the condensate coherence time, determined to be in the range of a few ns in state-of-the-art devices [44], it can be shown that only as few as $10^3$ condensed polaritons are required to attain the above mentioned regime of strong optomechanical coupling with $g_\mathrm {eff} = g_\mathrm {0} \sqrt {N_\mathrm {p}} > \kappa _{LP},\Gamma _m$.

The physics involved in systems with coupled polariton condensates naturally connects with that of synchronization and Josephson oscillations in non-Hermitian systems [52,72–75]. According to the present understanding of synchronization phenomena in the context of polariton condensates, the Coulomb repulsion, together with residual disorder, and the inter-trap coupling $J$, determine the local energies (and thus, the dynamics) of polaritons in traps. When polariton traps are coupled via a large $J$, the Josephson particle flow equalizes the frequency and locks the phase of the condensates (synchronization) [72–74]. If the potential difference between the traps (determined, e.g., by local disorder [52,75] of by an inhomogeneous Coulomb interaction with an exciton reservoir) exceeds a certain critical value (limit of small $J$), the Josephson flow cannot reach a steady state and the condensates cannot synchronize. By allowing the adjustment of frequencies, the non-linearities inherent to polariton condensates facilitate synchronization.

Optomechanics adds a time-dependent inter-level coupling [$J(t)$] to the above picture. As a consequence, it has been shown that striking signatures can emerge in coupled traps for polariton condensates when mechanical self-oscillation sets-in under a continuous, non-resonant optical excitation, i.e., in the phonon lasing regime [44]. The coherently excited phonons, in this case, back-act so that the two trapped polariton condensates asynchronously lock at energies differing by integer multiples of the phonon energy [55]. That is, a self-induced modulation $J(t)$ sets-in that synchronizes the relative energy of the coupled condensates to the phonon energy. In these experiments, the mechanical motion is self-induced, but it can also be externally excited (e.g., using BAW resonators) to imprint a time dependence to $J$ with a well-defined phase [70].

We note that dissipation and polariton non-linearities are prerequisites for the reported synchronization phenomenon. The latter is just one of the peculiar features emerging in cavity optomechanics in the presence of inter-particle Coulomb interactions [45,76], a novel regime that has remained so far vastly unexplored. Moreover, we note that so far we have made reference to synchronization of coupled polariton condensates. However, exactly the same physics applies when the two involved states correspond to two internal spinor degrees of freedom of a single condensate (the so-called internal Josephson effect). Only very recently evidences for synchronization, asynchronous locking, and control of the spinor degrees of freedom using externally injected and self-induced mechanical fields, have been reported [70]. In this context the possibility to operate with so-called dissipative coupling between the involved polariton states becomes particularly attractive due to the rich dynamics that can induce [77,78].

Optomechanically induced non-reciprocal phenomena. The above brings us to the subject of spatio-temporal modulation of photonic networks [79,80]. A series of publications has reviewed the subject from different perspectives and emphasized its potential for the implementation of compact, low-power integrated non-reciprocal devices [81–83]. Broadly speaking, the idea is to generate a synthetic magnetic field to break the time-reversal symmetry via the temporal modulation of network links with a spatially-dependent controlled phase ($J_{i,j}(t,\phi )$). From this perspective, the optomechanical interactions described in the previous section emerge as a highly attractive alternative to break reciprocity in compact systems.

It has been theoretically shown that mechanically mediated transfer between two optical modes can be made non-reciprocal by controlling the optical driving [84,85]. The necessary conditions for the generation of such synthetic magnetism have been described, with applications, for instance, in directional optical amplification [86–88]. Quite interesting proposals have been introduced for the general case of a network of optical cavities subjected exclusively to laser excitation with arbitrary phase patterns, making the connection between non-reciprocal light flow and topological systems [89]. The latter includes the identification of a strong coupling regime between photons and phonons, resulting in the appearance of a diversity of topological phases. Also, by matching coherent interactions with their corresponding dissipative counterparts, a connection was highlighted with the concepts of parity-time (PT) symmetries and the so-called exceptional points [90].

The above mentioned theoretical approaches have extended the idea of synthetic gauge fields in optomechanical networks to the concept of self-consistent dynamic fields. That is, on one hand the phases of the self-induced mechanical fields determine the effective magnetic fields for the photons. On the other hand, once these phases are allowed to evolve, they respond through a dynamic feedback and in-turn affect the mechanical modes [91]. Similar ideas have arisen great interest recently for the implementation of quantum simulators of dynamic gauge theories, such as quantum electrodynamics and quantum chromodynamics [92,93]. In the proposed optomechanical systems, only phonon-assisted photon tunneling processes are required, which are generated as a consequence of basic optomechanical interactions. Interestingly, precisely this kind of self-induced spatio-temporal $J(t)$ appears in lattices of polariton condensates [55]. It remains to be experimentally demonstrated how these optomechanical schemes can be applied to induce non-reciprocal polariton propagation and, in the long run, polariton simulators of dynamical gauge theories. Theoretical developments would also be required to take into account the large $g_0$, the large coherence times, and the inter-particle interactions (non-linearities), all features peculiar of polariton condensates.

Pseudo-radiofrequency modulation. The modulation of polaritons at the super and extreme high-frequency range (20-200 GHz) is just at its beginning. Very recently, it has been shown that detuned lasers can be used to simulate the equivalent of a radio-frequency field to control the Larmor precession of polariton pseudospins [94]. It would clearly be a major achievement to demonstrate an analog of magnetic resonance based on polariton spinors pumped by radio-frequency resonant mechanical fields. While these fields introduce non-diagonal, time-dependent terms in the hamiltonian, a similar approach can also be implemented via the mechanical modulation of the diagonal energies in coupled states, which could be applied to demonstrate state-preparation through Landau-Zener-Stückelberg dynamics [95,96]. More generally, these phenomena relate to the coherent control of quantum systems using periodic driving, i.e., Floquet state engineering [97] a topic that, to the best of our knowledge, remains elusive in the domain of polaritonics.

Conclusions and prospects. We have reviewed recent achievements in polaritonics and optomechanics, two fields that have evolved so far almost contactless notwithstanding the various unexplored opportunities that exist by bridging the gap between them to create the new area of polaromechanics. Among the most important developments, one finds the technology for the generation and detection of coherent mechanical oscillations at frequencies up to 10s of GHz by piezoelectric excitation and beyond 100 GHz by optical excitation. In addition, one now has access to the regime of mechanical self-oscillations as well as to novel synchronization regimes enabling the locking of polariton states to mechanically determined detunings. The experimental developments are based on theoretical advances that describe the inter-particle interactions relevant to the physics of coupled polariton condensates under external or self-excited mechanical fields. These developments open vast opportunities in the search for non-reciprocal transport of polaritons, and the possibility to use mechanical fields in the 10s-100s of GHz range in ways similar to the way electromagnetic fields are presently used in electronics and magnetism. They also provide a solid basis to address several challenges, including the access to single-particle optomechanical non-linearities as well as to the optomechanical strong and ultra-strong coupling regimes, and the exploitation of alternative MC polariton-based optomechanical platforms using new materials, e.g., 2D materials.

Quantum polaromechanics is another relevant field which we have, however, mostly left out of this prospective analysis. Here, reaching single-particle optomechanical cooperativities $C_0>1$ in polariton systems will be clearly a major milestone which, as argued here, should be feasible. Cooling of the mechanical ground state to the quantum limit has so far not yet been demonstrated in this domain, but we believe there are no major barriers to it. Indeed, the involved mechanical frequencies are so high that, e.g., even at 5 K the occupation $n$ of the 20 GHz mechanical ground state mode is already of only $n \sim 4$. Furthermore, laser cooling to $n<1$ in a system with well-defined side-bands should represent an accessible task. However, to be fully “quantum”, polaromechanics must deal with single polariton states. Reaching this regime (as e.g., through quantum blockade) remains an important challenge for the whole field of polaritonics. Both in the classical and in the quantum domain, it is clear that many new and interesting things occur when polaritonics meets optomechanics.