Editorial for special issue on nano-optomechanics

The long-standing quest to measure displacements with ever greater precision using electromagnetic fields [1, 2] and the related drive to harness radiation pressure forces [3–5] have spawned the field of optomechanics, which aims to control the motional state of mechanical resonators via optical or microwave electromagnetic fields [6, 7]. Typical optomechanical setups are equivalent to a Fabry–Perot optical cavity where one of the end mirrors is mechanically compliant so that its motion is coupled to the intra-cavity field via radiation pressure. Analogously, microwave electromechanical setups usually involve a resonant superconducting circuit with a compliant capacitor electrode. The motivation for this pursuit is twofold. On the one hand, these systems offer a host of applications in high precision measurements (e.g. mass, displacement and force sensing) or in signal processing (e.g. quantum-coherent frequency-conversion and non-reciprocal on-chip optical devices). These applications have ramifications that range all the way from sensing at the single particle scale [8] and quantum information processing (QIP) devices [9, 10] to black-hole astrophysics [11]. Accordingly, optomechanical systems span many orders of magnitude in mass and frequency, ranging from photonic–phononic crystal nanostructures and resonators made from atomically thin 1D and 2D materials, to kilogram-scale, kilometres-long gravitational wave detectors. On the other hand, these mechanical systems provide an ideal testbed for the study of quantum foundations: given their macroscopic massive nature, their now-accessible quantum regime enables experiments to elucidate how our macroscopic 'classical world'—wherein quantum superpositions seem to be absent—emerges from the underlying microscopic quantum physics.

The last decade has witnessed impressive progress in this field enabled by the nanoscale engineering of the optical and/or mechanical systems involved [6, 7]. This is exemplified by the following milestones: laser cooling close to the mechanical ground state [12–17], resolving the zero-point motion [18–21] and observing phonon 'vacuum Rabi' oscillations [22], resolving radiation-pressure shot noise [23], optomechanical squeezing of light [24–26] and mechanical motion [27–29], mechanical Q-enhancement through optical trapping [30], mechanically mediated signal conversion between dramatically different carrier photon wavelengths [31–35], and coherent state-transfer [36], generation of entanglement [37] and measurement of single-quanta non-classical correlations [38], between light and mechanical motion. Within this stimulating context, this special issue offers a cross-section of recent accomplishments, focusing in particular on 'nano-optomechanical' systems in which light and/or the mechanical elements are confined to the nanoscale. The benefits of the latter are twofold. Firstly, owing to the reduced 'round trip time' between subsequent 'bounces', light naturally exerts a stronger force per quanta upon the boundaries of a nanoscale cavity, and this force can be further enhanced using near-field effects associated with sub-wavelength structures. In turn, mechanical systems of nanoscale dimensions are significantly lighter than their micro (and macro) counterparts so that a given radiation pressure force has a stronger influence on their motion. In what follows, we briefly introduce the contributions to this special issue in relation to the field's development and present challenges.

Ever since the seminal work of Braginsky and others four decades ago, a key influence on the development of optomechanics has been the search for force metrology strategies that eliminate the ubiquitous quantum backaction noise [1, 2]. Kurt Jacobs et al elaborate on more recent efforts to find quantum noise cancellation schemes that are practical and broadband (i.e. where the bandwidth is not limited by the frequency of the probe oscillator) [39, 40]. In particular, they explore interesting alternatives afforded by using two identical mechanical oscillators to probe the signal force. An important realisation that has also shaped the field is that such quantum-limited displacement measurements can also be used to cool the mechanical oscillator. More precisely, cooling can be induced through dynamical backaction [12–16, 41, 42] or, alternatively, using active feedback [17, 43]. Habibi et al provide further insight into the limits of quantum-feedback cooling in the fast-feedback regime where the measurement rate overwhelms the mechanical decoherence rate [44]. The phase of the local oscillator is optimised in a way that can be nicely interpreted in terms of the Gedanken experiment on the Heisenberg microscope. Their outlook underscores how open problems in the theory of quantum feedback are coming to the forefront as a result of cutting-edge quantum optomechanics experiments [17]. A related leitmotif in this research area is the idea of generating squeezed light through optomechanical interactions [24–26]. Kilda et al revisit this theme for the alternative scenario of dissipative optomechanics where the mechanical displacement also modulates the cavity decay rate [45]. They find that, in contrast to the standard dispersive optomechanics case, strong squeezing can coexist with ground state cooling.

A further aspect of these systems, also enabled by driving the nonlinearity afforded by radiation forces, is the occurrence of phonon or mechanical 'lasing', where optical pumping leads to self-sustained coherent mechanical oscillations. Navarro-Urrios et al review various optomechanical mechanisms that can induce this useful behaviour: phonon-analogue of conventional lasing, dynamical back-action, forward stimulated Brillouin scattering and self-pulsing [46]. Beyond 'phonon lasing' an interesting question is the emergence, at low temperatures, of quantum signatures in the optomechanical self-oscillations. Various proposals to access subpoissonian phonon statistics exploit the nonlinear fluctuations of the optomechanical interaction. By contrast, Grimm et al analyse the scenario where such quantum behaviour is induced via the intrinsic Duffing nonlinearity of the mechanical oscillator [47]. They elucidate the conditions to achieve a non-classical Fano factor in the realistic regime where the single-quanta nonlinearity is weak.

Ultimately the desiderata to fully explore the quantum regime of mechanical systems using cavity optomechanics, is to realise the single-photon strong coupling regime, where the shift of the cavity resonance induced by a single phonon g exceeds the photon and phonon decay rates. Li et al analyse an interesting alternative to achieve this goal based on placing two high-reflectivity dielectric-membrane resonators separated by a small distance inside a high-Finesse Fabry–Perot cavity [48]. Expanding upon previous work on multi-membrane systems [49], they find that for certain modes, that match a resonance of the inner cavity formed by the two membranes, the relative motion couples with a g determined by the small separation between the membranes while the cavity decay rate κ is still set by the length of the external Fabry–Perot cavity. State-of-the-art parameters could then allow to reach the strong coupling condition $g/\kappa \sim 1$.

Most experiments in optomechanics have so far involved a single electromagnetic mode coupled to a single mechanical mode. A natural extension is to explore collective phenomena involving several mechanical and/or optical modes. Damskägg et al study a system where two separate mechanical oscillators couple to the same electromagnetic cavity mode [50]. Previous work by this same group, at Aalto University, has shown that when the two mechanical modes have similar frequencies (i.e. differing by much less than the cavity bandwidth κ) and in the regime where a strong single-tone (red-detuned) pump leads to hybrid optomechanical modes, there is a collective dark mode that decouples from the electromagnetic field [16]. Damskägg et al demonstrate with a microwave optomechanical device how a two-tone pump can be used to dynamically generate an analogous tripartite resonance starting from off-resonant mechanical oscillators. The resulting dark mode could be useful to create narrowband filters for signal processing or to store quantum information.

An important limit of optomechanical multimode effects is when the relevant optical and mechanical modes form a continuum. The exploration of such scenarios bridges optomechanics with Brillouin scattering, and is spawning the sub-field of waveguide nano-optomechanics that promises broadband functionality. Following upon recent observations of stimulated Brillouin scattering in nanoscale silicon waveguides, Van Laer et al report the first observation in these systems of thermal Brillouin scattering driven by the Brownian motion of gigahertz acoustic modes [51].

In spite of the aforementioned efforts to boost the ratio $g/\kappa$, realising the single-photon strong coupling regime of cavity-optomechanics remains elusive. This poses a substantial limitation to the use of these systems in QIP devices and in studies of quantum foundations, since such strong-coupling condition is a prerequisite for the deterministic generation of non-Gaussian motional states using classical electromagnetic fields. Additionally, in the optical domain the role played by the cavity places stringent requirements on the design through the micron-sized photon wavelength. Within this context, an interesting alternative is to realise hybrid systems where the mechanical resonator directly couples to a two-level-system (TLS). In turn, when the latter affords a qubit, the mechanical mode could then be used in QIP devices as a quantum bus, via phonon-mediated qubit–qubit interactions [9], or as a quantum interface between disparate qubits [10]. Hybrid mechanical-resonator-TLS systems have already been realised with various TLSs, namely, superconducting circuits, ultracold atoms, quantum dots, and solid-state spins and defects. The corresponding interaction mechanisms include capacitive coupling, radiation pressure, magnetic forces and crystal-strain-induced coupling. Lee et al review recent progress on a particularly promising candidate: diamond-based hybrid quantum systems in which the spin and orbital dynamics of single nitrogen-vacancy colour centres (NV) couple to a mechanical resonator [52]. Their review underscores the potential of these systems for QIP applications, quantum sensing and fundamental studies of quantum mechanics. A crucial limitation within these contexts is the NV spin decoherence time T₂ which is typically dominated by low-frequency noise. Teissier et al demonstrate a novel way to overcome this hurdle based on a concatenated continuous dynamical decoupling scheme that exploits the parametric coupling of the NV spin to the strain field of a high-Q diamond mechanical oscillator in which the NV is embedded [53]. A first degree of decoupling is afforded by resonant microwave driving of the spin transition. Subsequently, matching the corresponding microwave Rabi frequency to the frequency of the mechanical oscillator and forcing the latter resonantly so that it parametrically drives the spin via its strain field, provides a second degree of decoupling that locks the spin Rabi oscillations to the mechanical frequency in a physics analogous to the resonance fluorescence of a two-level atom. It is then found that this configuration results in a remarkable boost, by two orders of magnitude, to the T₂ of the relevant photon–phonon dressed spin states relative to the T₂ of the bare spin. Central to this remarkable noise suppression is the role of the mechanical resonator's narrow bandwidth in reducing the fluctuations of the parametric drive.

Indeed, mechanical dissipation emerges as a key limitation in most applications of optomechanics. This has spurred the search for optomechanical setups featuring ultra-low dissipation mechanical elements [7, 54]. An interesting alternative is the use of optically levitated nanoparticles where the phonon-radiation losses, that are unavoidable in any suspended (or supported) system, are absent and the centre-of-mass degree of freedom can be largely decoupled from internal losses, leading to mechanical quality-factors $Q\sim {10}^{10}\mbox{--}{10}^{11}$. Additionally, these systems promise a fruitful interface between optomechanics and matter-wave interferometry techniques. Within this context, the hybrid setup combining a Paul trap with an optical cavity developed by the group at University College London, has allowed the demonstration of cavity cooling of a levitated nanosphere in vacuum [55]. In this special issue, this same group (Aranas et al) further analyses distinctive features that emerge in the output spectrum of this system, in particular, a peculiar splitting of the sidebands, and elucidate their impact on sideband thermometry [56].

Finally, another intriguing path toward optomechanics with ultra-low dissipation mechanical oscillators is to use as the mechanical element superfluid helium, so that internal losses are strongly suppressed at cryogenic temperatures. Several groups are currently investigating optomechanical setups where an electromagnetic resonator is filled with (or immersed in) superfluid helium and thereby couples to vibrational modes of the superfluid. Kashkanova et al analyse such a device consisting of a filled fibre-based optical cavity [57]. They complement their recent work on the electrostrictive coupling to the paraxial acoustic mode inside the cavity [58], by analysing instead the optomechanical signatures of modes associated with the helium surrounding the cavity. The coupling is found to be mostly photothermal and the underlying microscopic mechanisms are elucidated.

With this special issue, we hope to highlight some of the recent progress that has been made in optomechanics and to show just how bright and vibrant this field currently is.