Dissipative Acousto-Mechanical Coupling

• Dissipative acousto-mechanical coupling is defined by acoustic or mechanical modes modulating dissipation channels via loss, radiation, or linewidth modulation rather than direct energy exchange.
• Key experimental platforms include magneto-mechanical crystals, SAW-coupled resonators, superconducting hybrid circuits, and nanophotonic devices demonstrating tunable dissipation and mode selectivity.
• Interplay between coherent and dissipative interactions, controlled by coupling phase, allows engineered spectral features and dissipation management in both quantum and classical regimes.

Dissipative acousto-mechanical coupling designates a family of interactions in which acoustic or mechanical degrees of freedom participate in loss channels, linewidth modulation, radiation damping, or common-reservoir decay, rather than only in conservative frequency shifts or direct energy exchange. In the literature considered here, the phrase covers several distinct but related mechanisms: magnon–phonon mixing through correlated decay in a magneto-mechanical crystal, surface-acoustic-wave-mediated modulation of resonator quality factors, cavity and acousto-optic systems in which displacement modulates $\kappa_{\rm ex}$, $\kappa_e$, or $\kappa_i$, fourth-sound modes that damp one another through turbulence-generated vortices, and structural acoustics in which thermal diffusion on a compliant interface is the sole dissipative pathway (Carrara et al., 2024, Kähler et al., 2020, Baraillon et al., 2020, Ji et al., 23 May 2026, Novotný et al., 2024, Avalos et al., 2017).

1. Conceptual scope and terminology

In a two-mode hybrid system, dissipative coupling is commonly distinguished from coherent coupling by the way the interaction enters the spectrum. In the magneto-mechanical crystal studied in "Coherent and dissipative coupling in a magneto-mechanical system" (Carrara et al., 2024), coherent coupling is direct energy exchange and produces the usual anti-crossing or frequency gap at resonance, whereas dissipative coupling arises from correlated decay into a common reservoir and tends to produce level attraction rather than repulsion. The paper parameterizes the balance by a coupling phase $\Phi$ in

$$\mathcal{H}/\hbar = \tilde{\omega}_A a^\dagger a + \tilde{\omega}_B b^\dagger b + g\left(a^\dagger b + e^{i\Phi}ab^\dagger\right),$$

with $\tilde{\omega}_i=\omega_i-i\gamma_i$. In that formulation, $\Phi=0$ is pure coherent coupling, $\Phi=\pi$ is pure dissipative coupling, and intermediate $\Phi$ gives mixed coupling.

In cavity and acousto-optic platforms, the same adjective usually means that motion modulates a decay rate instead of, or in addition to, a resonance frequency. The general linearized framework of "Linear analytical approach to dispersive, external and intrinsic dissipative couplings in optomechanical systems" (Baraillon et al., 2020) separates three first-order couplings,

$$\omega_c(u_m)=\omega_{c0}+g_{\rm om}u_m,\qquad \kappa_e(u_m)=\kappa_{e0}+\kappa_{\rm om}^e u_m,\qquad \kappa_i(u_m)=\kappa_{i0}+\kappa_{\rm om}^i u_m,$$

thereby distinguishing dispersive coupling from external and intrinsic dissipative coupling. The HBAR–membrane system of "Dissipative acousto-mechanical parametric interface between high-overtone acoustics and flexural phonons" (Ji et al., 23 May 2026) uses the same distinction in single-phonon form,

$\kappa_e$0

In substrate-mediated mechanical systems, dissipative coupling may appear as a complex retarded interaction. "Surface acoustic wave coupling between micromechanical resonators" (Kähler et al., 2020) shows that the SAW-mediated force acquires a phase $\kappa_e$1, so the effective coupling has a real part $\kappa_e$2 that shifts $\kappa_e$3 and an imaginary part $\kappa_e$4 that shifts $\kappa_e$5. In that setting, dissipation is not an added phenomenological term; it is the quadrature component of a propagating interaction.

The term is therefore not monolithic. In the literature surveyed here, it consistently marks coupling through decay, leakage, radiation, or damping channels, but the underlying microscopic origin differs substantially from one platform to another.

2. Physical realizations

A direct experimental realization of mixed coherent–dissipative hybridization is the one-dimensional magneto-mechanical crystal of rectangular bilayer nanostripes on Si(001), each stripe consisting of Fe $\kappa_e$6 nm and Permalloy $\kappa_e$7 nm, with stripe width $\kappa_e$8 nm, inter-stripe gap $\kappa_e$9 nm, and period $\kappa_i$0 nm (Carrara et al., 2024). The array is simultaneously a magnonic crystal, through dipolar coupling between neighboring stripes, and a phononic crystal, through standing surface acoustic waves and localized acoustic breathing modes. In that device, ultrafast optical pumping excites both thermoelastic expansion and magnetization precession, enabling direct time-domain access to phonon–magnon mixing.

A second line of work places dissipative phenomena inside hybrid quantum circuits. "Strong dispersive coupling between a mechanical resonator and a fluxonium superconducting qubit" (Lee et al., 2023) uses a flip-chip hybrid circuit composed of a light-fluxonium superconducting qubit, a lithium niobate phononic-crystal mechanical resonator, and a microwave readout resonator. The target defect mode is a sub-GHz mechanical mode at $\kappa_i$1, and the fitted resonant qubit–mechanics coupling is $\kappa_i$2. In that paper, dissipative acousto-mechanical coupling is the interaction used not only for phonon number-resolved measurements but also for extracting the resonator’s dissipation and dephasing through the qubit’s dispersive response.

A third realization makes dissipative coupling the dominant interaction channel. The HBAR–membrane interface of (Ji et al., 23 May 2026) combines a GHz HBAR on a $\kappa_i$3-$\kappa_i$4m-thick sapphire substrate, with a $\kappa_i$5-nm Mo bottom electrode and a $\kappa_i$6-$\kappa_i$7m AlN piezoelectric layer, and a suspended $\kappa_i$8-nm-thick LPCVD SiN membrane with a $\kappa_i$9 window coated by $\Phi$0 nm Al. The membrane displacement changes the capacitance and loading at the HBAR port, thereby modulating $\Phi$1. A representative acoustic mode lies at $\Phi$2, while the membrane fundamental is at $\Phi$3.

Integrated nanophotonic realizations engineer the same principle optically. "Dissipative Optomechanics in High-Frequency Nanomechanical Resonators" (Primo et al., 2022) uses two silicon photonic-crystal nanobeams with co-localized optical and mechanical defect modes, coupled optically but mechanically isolated by a phononic mirror. Because only one optical cavity is directly coupled to the bus waveguide, mechanical motion changes the hybridization of the optical supermodes and produces motion-dependent external loss. The device operates with $\Phi$4, optical linewidths $\Phi$5, and photon tunneling rate $\Phi$6.

The concept also extends outside solid-state electromechanics. In the nano-superfluidic acoustic resonator of (Novotný et al., 2024), fourth-sound modes in strongly confined He II couple to mechanically compliant walls and, in the nonlinear regime, to localized clusters of quantized vortices. The resulting multimode interaction is dissipative and strongly asymmetric. In the structural acoustics PDE model of (Avalos et al., 2017), an acoustic wave in a three-dimensional chamber is coupled through a flexible interface $\Phi$7 to a thermoelastic plate or beam, and the only true dissipation is the heat equation on that interface.

3. Experimental signatures and metrology

The most explicit experimental separation of coherent and dissipative contributions appears in the magneto-mechanical crystal of (Carrara et al., 2024). Time-resolved MOKE reveals two nearly field-independent modes, MEC1 and MEC2, and one field-dispersive magnonic mode PM. Time-resolved reflectivity identifies MEC1 as a Rayleigh surface acoustic wave with $\Phi$8 and $\Phi$9, and MEC2 as a localized stripe breathing mode with $$\mathcal{H}/\hbar = \tilde{\omega}_A a^\dagger a + \tilde{\omega}_B b^\dagger b + g\left(a^\dagger b + e^{i\Phi}ab^\dagger\right),$$0 and $$\mathcal{H}/\hbar = \tilde{\omega}_A a^\dagger a + \tilde{\omega}_B b^\dagger b + g\left(a^\dagger b + e^{i\Phi}ab^\dagger\right),$$1. The PM branch is independently confirmed by BLS and micromagnetics. In the PM–MEC1 crossing region, the decisive signature of mixed coupling is an offset between the field at which the frequencies coincide and the field at which the dampings coincide. The fitted values are $$\mathcal{H}/\hbar = \tilde{\omega}_A a^\dagger a + \tilde{\omega}_B b^\dagger b + g\left(a^\dagger b + e^{i\Phi}ab^\dagger\right),$$2 and $$\mathcal{H}/\hbar = \tilde{\omega}_A a^\dagger a + \tilde{\omega}_B b^\dagger b + g\left(a^\dagger b + e^{i\Phi}ab^\dagger\right),$$3, placing the device in the weak-coupling regime with coherent and dissipative contributions of comparable weight.

In SAW-coupled resonator pairs, the diagnostic is a joint modulation of frequency and quality factor. The model of (Kähler et al., 2020) predicts that the oscillations of $$\mathcal{H}/\hbar = \tilde{\omega}_A a^\dagger a + \tilde{\omega}_B b^\dagger b + g\left(a^\dagger b + e^{i\Phi}ab^\dagger\right),$$4 and $$\mathcal{H}/\hbar = \tilde{\omega}_A a^\dagger a + \tilde{\omega}_B b^\dagger b + g\left(a^\dagger b + e^{i\Phi}ab^\dagger\right),$$5 are out of phase by $$\mathcal{H}/\hbar = \tilde{\omega}_A a^\dagger a + \tilde{\omega}_B b^\dagger b + g\left(a^\dagger b + e^{i\Phi}ab^\dagger\right),$$6. FEM simulations confirm this directly. In the $$\mathcal{H}/\hbar = \tilde{\omega}_A a^\dagger a + \tilde{\omega}_B b^\dagger b + g\left(a^\dagger b + e^{i\Phi}ab^\dagger\right),$$7 limit, the antisymmetric mode becomes nonradiating with $$\mathcal{H}/\hbar = \tilde{\omega}_A a^\dagger a + \tilde{\omega}_B b^\dagger b + g\left(a^\dagger b + e^{i\Phi}ab^\dagger\right),$$8, while the symmetric mode reaches $$\mathcal{H}/\hbar = \tilde{\omega}_A a^\dagger a + \tilde{\omega}_B b^\dagger b + g\left(a^\dagger b + e^{i\Phi}ab^\dagger\right),$$9. For the SAW-coupled pillars at $\tilde{\omega}_i=\omega_i-i\gamma_i$0, the antisymmetric mode reaches $\tilde{\omega}_i=\omega_i-i\gamma_i$1, compared with the single-resonator value $\tilde{\omega}_i=\omega_i-i\gamma_i$2.

In superconducting cQAD, dissipative behavior is diagnosed through number-resolved spectroscopy and time-domain coherence measurements. In (Lee et al., 2023), the dispersive shifts $\tilde{\omega}_i=\omega_i-i\gamma_i$3 and $\tilde{\omega}_i=\omega_i-i\gamma_i$4 exceed the relevant linewidths, allowing phonon-number peaks to be resolved up to about $\tilde{\omega}_i=\omega_i-i\gamma_i$5 in post-processed data. The same dispersive interaction then exposes multichannel mechanical decay: $\tilde{\omega}_i=\omega_i-i\gamma_i$6, $\tilde{\omega}_i=\omega_i-i\gamma_i$7, $\tilde{\omega}_i=\omega_i-i\gamma_i$8, $\tilde{\omega}_i=\omega_i-i\gamma_i$9, and $\Phi=0$0. The energy-relaxation curve is explicitly multi-exponential, which the paper interprets as evidence for nontrivial dissipation channels.

The HBAR–membrane platform of (Ji et al., 23 May 2026) diagnoses dissipative dominance by red-sideband transparency and amplification. Under red-sideband pumping, the reflection spectrum shows acousto-mechanically induced transparency, steep phase dispersion, and at stronger drive a peak above the background. At $\Phi=0$1 dBm the group delay reaches about $\Phi=0$2. At $\Phi=0$3 dBm, $\Phi=0$4, so the effective dissipative coupling is about $\Phi=0$5 times stronger than the dispersive coupling, and $\Phi=0$6 is observed under red-sideband driving.

In the high-frequency nanobeam system of (Primo et al., 2022), dissipative signatures appear in both thermomechanical spectra and coherent OMIT/OMIA spectroscopy. The extracted vacuum couplings satisfy $\Phi=0$7, yet the interference between dissipative and dispersive scattering strongly reshapes backaction. The dissipative coupling is summarized as $\Phi=0$8, described there as a tenfold increase over previous dissipative optomechanics.

In superfluid acoustics, the signature is modal asymmetry rather than avoided crossings. The pump–probe experiments of (Novotný et al., 2024) show that when $\Phi=0$9 or $\Phi=\pi$0 pumps the system into turbulence, the $\Phi=\pi$1 probe can be attenuated strongly; in the $\Phi=\pi$2–$\Phi=\pi$3 case the attenuation reaches nearly $\Phi=\pi$4 at the highest drive. Reversing pump and probe produces only weak attenuation or essentially none, demonstrating asymmetric dissipative coupling.

4. Theoretical descriptions

A common theoretical pattern is the use of non-Hermitian normal-mode theory. In (Carrara et al., 2024), the eigenvalues

$\Phi=\pi$5

encode both frequency hybridization and damping hybridization. The real part gives the oscillation frequencies and the imaginary part the damping. The paper proposes the mismatch between the zero-detuning point and the damping-crossing point as a practical experimental marker of mixed coupling.

Wave-mediated mechanical coupling admits an equivalent complex description. The SAW model of (Kähler et al., 2020) yields

$\Phi=\pi$6

$\Phi=\pi$7

These expressions make the distinction exact: the in-phase component of the retarded interaction shifts the eigenfrequencies, while the quadrature component shifts the quality factors.

For cavity-mediated systems, input–output theory is the natural language. The generalized optical equation of (Baraillon et al., 2020),

$\Phi=\pi$8

provides a unified linear description once $\Phi=\pi$9, $\Phi$0, and $\Phi$1 are made displacement-dependent. The paper then decomposes both the optical spring and the optomechanical damping into pure dispersive, pure external dissipative, pure intrinsic dissipative, and mixed interference terms. That decomposition is important because it shows that the backaction is not merely a sum of independent channels.

Circuit acousto-dynamics adds a qubit-mediated dispersive description. In (Lee et al., 2023), the interaction Hamiltonian is

$\Phi$2

and, in the strong dispersive regime, the effective Hamiltonian becomes

$\Phi$3

That model does not encode dissipative coupling as linewidth modulation; rather, it turns the qubit into a spectroscopic sensor of the mechanical resonator’s dissipation and dephasing.

The superfluid model of (Novotný et al., 2024) uses coupled hydrodynamic and elastic field equations,

$\Phi$4

together with the plate equation. Dissipative coupling then emerges only after the system crosses into a turbulent regime with vortex nucleation. This suggests that, in some systems, dissipation is not a small linear perturbation but a nonlinear state of the driven medium.

5. Regimes, functionality, and engineered consequences

The surveyed literature spans weak coupling, strong dispersive coupling, resolved-sideband dissipative coupling, and deliberately mixed regimes. The magneto-mechanical crystal of (Carrara et al., 2024) is explicitly weakly coupled because $\Phi$5 is smaller than the intrinsic damping rates. By contrast, the fluxonium device of (Lee et al., 2023) is in the strong dispersive regime with $\Phi$6, $\Phi$7, and $\Phi$8, so the dispersive interaction exceeds the decoherence rates even though the qubit and mechanics remain far off resonance. Both regimes are informative: the former isolates mixed damping–frequency hybridization, while the latter allows dissipation and dephasing to be measured at the single-phonon level.

Dissipative coupling can also be the dominant resource for room-temperature control. In (Ji et al., 23 May 2026), the system enters the resolved-sideband regime at room temperature, and dominant dissipative coupling produces AMIT, red-sideband amplification, tunable Kerr nonlinearity, and coherent HBAR frequency combs. In (Primo et al., 2022), dissipative coupling in the sideband-resolved regime reshapes both mechanical and optical spectra and permits mode-selective cooling, heating, and lasing through interference between dissipative and dispersive scattering amplitudes.

A recurrent outcome is dissipation engineering rather than dissipation avoidance. The SAW work (Kähler et al., 2020) exploits destructive interference of radiation losses to realize high-$\Phi$9 phonon cavities without phononic crystals or acoustic shielding. Several optomechanical papers make the same point in another language. "Strong-coupling effects in dissipatively coupled optomechanical systems" (Weiss et al., 2012) shows that purely dissipative coupling gives a Fano force spectrum, two cooling regions, two amplification regions, and optomechanically induced transparency. "Stable Optical Rigidity Based on Dissipative Coupling" (Nazmiev et al., 2018) shows that a Fabry–Perot cavity with dissipative coupling and detuned pump can realize stable optical rigidity when

$$\omega_c(u_m)=\omega_{c0}+g_{\rm om}u_m,\qquad \kappa_e(u_m)=\kappa_{e0}+\kappa_{\rm om}^e u_m,\qquad \kappa_i(u_m)=\kappa_{i0}+\kappa_{\rm om}^i u_m,$$0

and can then be used for sub-SQL force sensing. "Combination of dissipative and dispersive coupling in the cavity optomechanical systems" (Karpenko et al., 2022) and "Dissipative coupling, dispersive coupling and its combination in simplest opto-mechanical systems" (Karpenko et al., 2020) further show that mixed coupling produces optical rigidity even on resonant pump or with a single pump, and that variational measurement can exploit the resulting noise correlations.

At the same time, the consequences are regime-dependent rather than universal. "Dissipative vs dispersive coupling in quantum opto-mechanics: squeezing ability and stability" (Tagantsev et al., 2018) analyzes the bad-cavity limit and finds that purely dissipative coupling suppresses backaction and strongly suppresses squeezing ability because the two routes by which vacuum noise reaches the mechanics interfere destructively. That result does not negate the functionality found in sideband-resolved systems; it indicates that the utility of dissipative coupling depends strongly on spectral hierarchy and readout architecture.

6. Interpretive issues and current directions

One interpretive issue is terminological breadth. In some papers, dissipative coupling is a microscopic modulation of linewidth; in others, it is a common-reservoir interaction, a radiation-loss interference effect, a turbulence-enabled damping channel, or an indirect thermoelastic path. The fluxonium work (Lee et al., 2023) is a clear example of a broader usage: the interaction is fundamentally dispersive during readout, but the same platform is used to resolve dissipative, multi-channel phonon decay. Conversely, "Influence of thermal effects on the optomechanical coupling rate in acousto-optic cavities" (Ortiz et al., 2024) shows a loss-mediated thermal pathway,

$$\omega_c(u_m)=\omega_{c0}+g_{\rm om}u_m,\qquad \kappa_e(u_m)=\kappa_{e0}+\kappa_{\rm om}^e u_m,\qquad \kappa_i(u_m)=\kappa_{i0}+\kappa_{\rm om}^i u_m,$$1

where optical absorption, thermo-optic response, and thermal expansion renormalize the canonical coupling rate. That paper does not formulate a separate dissipative Hamiltonian; it treats dissipation as a photothermal correction to $$\omega_c(u_m)=\omega_{c0}+g_{\rm om}u_m,\qquad \kappa_e(u_m)=\kappa_{e0}+\kappa_{\rm om}^e u_m,\qquad \kappa_i(u_m)=\kappa_{i0}+\kappa_{\rm om}^i u_m,$$2.

A second issue is that dissipation is not equivalent to simple degradation. The data repeatedly contradict that simplification. In (Carrara et al., 2024), dissipative coupling is a measurable part of magnon–phonon hybridization. In (Kähler et al., 2020), it is the mechanism by which radiation losses are suppressed. In (Ji et al., 23 May 2026) and (Primo et al., 2022), it enables transparency, amplification, and mode-selective spectral control. In (Novotný et al., 2024), it provides a controllable asymmetry between acoustic modes. This suggests that dissipation, when spatially or spectrally structured, is a design variable rather than merely a parasitic term.

A third direction is explicit tunability between dissipation-dominated and dispersion-dominated limits. "Optomechanical system with tunable dissipative and dispersive couplings" (Wang et al., 9 Jun 2026) reports experimental dissipative-to-dispersive ratios of $$\omega_c(u_m)=\omega_{c0}+g_{\rm om}u_m,\qquad \kappa_e(u_m)=\kappa_{e0}+\kappa_{\rm om}^e u_m,\qquad \kappa_i(u_m)=\kappa_{i0}+\kappa_{\rm om}^i u_m,$$3 and $$\omega_c(u_m)=\omega_{c0}+g_{\rm om}u_m,\qquad \kappa_e(u_m)=\kappa_{e0}+\kappa_{\rm om}^e u_m,\qquad \kappa_i(u_m)=\kappa_{i0}+\kappa_{\rm om}^i u_m,$$4 using two mechanical resonators, and a theoretical tuning range from $$\omega_c(u_m)=\omega_{c0}+g_{\rm om}u_m,\qquad \kappa_e(u_m)=\kappa_{e0}+\kappa_{\rm om}^e u_m,\qquad \kappa_i(u_m)=\kappa_{i0}+\kappa_{\rm om}^i u_m,$$5 to $$\omega_c(u_m)=\omega_{c0}+g_{\rm om}u_m,\qquad \kappa_e(u_m)=\kappa_{e0}+\kappa_{\rm om}^e u_m,\qquad \kappa_i(u_m)=\kappa_{i0}+\kappa_{\rm om}^i u_m,$$6 by optimizing resonator diameter and material. " $$\omega_c(u_m)=\omega_{c0}+g_{\rm om}u_m,\qquad \kappa_e(u_m)=\kappa_{e0}+\kappa_{\rm om}^e u_m,\qquad \kappa_i(u_m)=\kappa_{i0}+\kappa_{\rm om}^i u_m,$$7-symmetry and chaos control via dissipative optomechanical coupling" (Tchounda et al., 2023) adds that dissipative coupling can lower the threshold for the exceptional point, enhance energy exchange in the unbroken-$$\omega_c(u_m)=\omega_{c0}+g_{\rm om}u_m,\qquad \kappa_e(u_m)=\kappa_{e0}+\kappa_{\rm om}^e u_m,\qquad \kappa_i(u_m)=\kappa_{i0}+\kappa_{\rm om}^i u_m,$$8 phase, and suppress chaotic beats-like behavior in the nonlinear regime. A plausible implication is that the most consequential future use of dissipative acousto-mechanical coupling will be in architectures where the dissipative-to-dispersive balance is itself an actively engineered degree of freedom.

Across these literatures, the field has therefore shifted from treating dissipation as an unwanted correction to treating it as a spectroscopically identifiable, quantitatively modelable, and often useful coupling channel.