Squeezed Phonon Laser

• Squeezed phonon lasing is a regime where a vibrational mode achieves self-sustained coherent oscillation while one quadrature’s noise is reduced below the quantum limit.
• Multiple platforms including Dirac-vortex nanoelectromechanics, Floquet-engineered defect systems, trapped ions, and nonreciprocal optomechanics demonstrate distinct mechanisms for realizing squeezed phonon lasers.
• These techniques enhance sensing, phase-sensitive amplification, and topologically protected single-mode phonon generation, with significant implications for quantum metrology and phononic information processing.

Searching arXiv for the cited squeezed phonon laser and related papers to ground the article with current literature. {"query":"(Xi et al., 2021) squeezed phonon laser Dirac-vortex parametric phonon laser (Molinares et al., 3 Jun 2026, Lee et al., 9 Jan 2026, Lu et al., 2023)","max_results":10} {"query":"squeezed phonon laser","max_results":10} Squeezed phonon lasing denotes a regime in which a vibrational mode undergoes self-sustained, coherent oscillation while quadrature fluctuations are modified by squeezing, so that gain, threshold behavior, linewidth narrowing, and phase coherence are treated together with reduced noise in a selected quadrature. In the recent literature, the term encompasses experimentally realized topological parametric phonon lasing in nonlinear nanoelectromechanical Dirac-vortex cavities, Floquet-engineered squeezed phonon lasing in solid-state defect platforms, bath-free squeezed lasing via intrinsic ion–phonon coupling in trapped ions, and nonreciprocal phonon lasing induced by directional optical squeezing in compound optomechanical systems (Xi et al., 2021, Molinares et al., 3 Jun 2026, Lee et al., 9 Jan 2026, Lu et al., 2023).

1. Definition and distinguishing characteristics

Phonon lasing—the acoustic analogue of an optical laser—occurs when driven gain overcomes mechanical damping, and a vibrational mode enters a regime of self-sustained, coherent oscillation. Generating squeezed phonon states—where one quadrature’s noise is suppressed below the zero-point level—opens the door to measurements below the standard quantum limit, offering enhanced force, mass or field sensing in nanomechanical platforms (Molinares et al., 3 Jun 2026).

Within this framework, a squeezed phonon laser is not merely a phonon laser with large amplitude, and it is not merely a squeezed mechanical state. The defining feature is the coexistence of lasing-type gain and threshold behavior with quadrature-selective noise control. In the experimental topological realization, the squeezed-bosonic interaction provides phase-sensitive gain or deamplification depending on pump phase, and below threshold the quadrature ellipse narrows along one axis with a 40% reduction in noise variance; above threshold, a sharp peak at $\omega_0=\tfrac12\cdot \text{pump}$ appears once $V_{\rm pump}>2.09\ {\rm V}$ (Xi et al., 2021).

The literature also makes clear that squeezed phonon lasing is not tied to a single mechanism. One proposal enables a continuous transition from conventional lasing to phase-locked squeezed phonon lasing by Floquet engineering in a color-center platform (Molinares et al., 3 Jun 2026). Another realizes squeezed lasing in a trapped-ion system without relying on engineered baths or tailored dissipative reservoirs (Lee et al., 9 Jan 2026). A distinct line of work uses directional optical squeezing to generate directional mechanical gain, leading to nonreciprocal phonon lasing with a well-tunable directional power threshold (Lu et al., 2023).

2. Dynamical mechanisms and threshold conditions

The principal mechanisms reported in the literature can be organized by the effective interaction that generates gain and by the form of the threshold condition.

Platform	Effective interaction	Threshold condition
Dirac-vortex nanoelectromechanics	$(\hat a^{\dagger 2}+\hat a^2)$ squeezing term	$g=\gamma/2$
Floquet-controlled solid-state defects	$B\equiv u\,b+v\,b^\dagger$ squeezed-mode coupling	$g_{\rm eff}^2/\gamma'_m>\gamma_m$
Trapped ions	dual red- and blue-sideband ion–phonon coupling	$A_{\rm th}=B$
Nonreciprocal optomechanics	directional optical squeezing modifies mechanical gain $G$	$G=\gamma_m$

In the topological nanoelectromechanical system, the rotating-frame Hamiltonian of the Dirac-vortex mode is

$$\hat H = \hbar\omega_0\,\hat a^\dagger\hat a +\frac{\hbar B}{2}\,\hat a^\dagger\hat a^\dagger \hat a\,\hat a +\frac{\hbar\,\alpha\,V_{\rm dc}\,V_{\rm pump}}{2}\,\Bigl(\hat a^{\dagger2} + \hat a^2\Bigr),$$

with $V_{\rm pump}>2.09\ {\rm V}$0. The Heisenberg–Langevin analysis yields eigenvalues $V_{\rm pump}>2.09\ {\rm V}$1, so the onset of parametric instability and phonon lasing occurs when $V_{\rm pump}>2.09\ {\rm V}$2, equivalently

$V_{\rm pump}>2.09\ {\rm V}$3

The experiment finds $V_{\rm pump}>2.09\ {\rm V}$4 for coherent pumping at optimal detuning $V_{\rm pump}>2.09\ {\rm V}$5 (Xi et al., 2021).

In the Floquet-controlled solid-state-defect proposal, periodic modulation at the primary red sideband resonance $V_{\rm pump}>2.09\ {\rm V}$6, $V_{\rm pump}>2.09\ {\rm V}$7 produces

$V_{\rm pump}>2.09\ {\rm V}$8

where $V_{\rm pump}>2.09\ {\rm V}$9, $(\hat a^{\dagger 2}+\hat a^2)$0, $(\hat a^{\dagger 2}+\hat a^2)$1, and $(\hat a^{\dagger 2}+\hat a^2)$2. After elimination of the ancilla sector, the semi-classical occupation obeys

$(\hat a^{\dagger 2}+\hat a^2)$3

leading to the threshold

$(\hat a^{\dagger 2}+\hat a^2)$4

Above threshold, $(\hat a^{\dagger 2}+\hat a^2)$5 (Molinares et al., 3 Jun 2026).

In the trapped-ion proposal, adiabatic elimination of the internal states yields an effective phonon-mode master equation

$(\hat a^{\dagger 2}+\hat a^2)$6

with

$(\hat a^{\dagger 2}+\hat a^2)$7

and the threshold is reached when

$(\hat a^{\dagger 2}+\hat a^2)$8

This formulation keeps the gain–loss balance explicit while moving the squeezing into a unitary basis change (Lee et al., 9 Jan 2026).

In the nonreciprocal optomechanical scheme, the phonon-laser threshold is reached when $(\hat a^{\dagger 2}+\hat a^2)$9, and the emitted-phonon number is $g=\gamma/2$0, so $g=\gamma/2$1 at threshold. The forward threshold power is

$g=\gamma/2$2

whereas in the backward direction one replaces $g=\gamma/2$3 and $g=\gamma/2$4 (Lu et al., 2023).

3. Topological Dirac-vortex parametric phonon laser

The experimentally realized topological platform is a 2D nanomechanical crystal that implements the Jackiw–Rossi model by imposing a vortex in the local Kekulé distortion, $g=\gamma/2$5. The Dirac-vortex mode is a zero mode bound to the vortex core with spinor envelope

$g=\gamma/2$6

where $g=\gamma/2$7 is the Bloch profile in each unit cell and $g=\gamma/2$8 sets the modal area $g=\gamma/2$9. The device consists of a 2D hexagonal lattice of suspended silicon-nitride membranes of thickness $B\equiv u\,b+v\,b^\dagger$0 and $B\equiv u\,b+v\,b^\dagger$1, patterned with two radii of holes in each unit cell to implement a Kekulé modulation; after Al metallization ($B\equiv u\,b+v\,b^\dagger$2), the membrane array sits above a Si substrate that serves as ground (Xi et al., 2021).

In the $B\equiv u\,b+v\,b^\dagger$3 device, the bare resonant frequency is $B\equiv u\,b+v\,b^\dagger$4. The Kerr coefficient is $B\equiv u\,b+v\,b^\dagger$5, the electromechanical tuning coefficient is $B\equiv u\,b+v\,b^\dagger$6, and the damping rate is $B\equiv u\,b+v\,b^\dagger$7. A combined bias $B\equiv u\,b+v\,b^\dagger$8 and parametric pump $B\equiv u\,b+v\,b^\dagger$9 are applied between the Al electrode and substrate. The electrostatic force $g_{\rm eff}^2/\gamma'_m>\gamma_m$0 couples to the Dirac-vortex deflection $g_{\rm eff}^2/\gamma'_m>\gamma_m$1, yielding both a linear tuning of $g_{\rm eff}^2/\gamma'_m>\gamma_m$2 and the two-phonon interaction (Xi et al., 2021).

The topological properties reported for this cavity differ sharply from those of conventional cavities. Unlike conventional cavities whose fundamental frequency shifts with size, with $g_{\rm eff}^2/\gamma'_m>\gamma_m$3, the Dirac-vortex frequency is topologically pinned to the bulk Dirac point. In measurements from $g_{\rm eff}^2/\gamma'_m>\gamma_m$4, $g_{\rm eff}^2/\gamma'_m>\gamma_m$5 stays within $g_{\rm eff}^2/\gamma'_m>\gamma_m$6 even though $g_{\rm eff}^2/\gamma'_m>\gamma_m$7 increases by over an order of magnitude. The spacing between the zero mode and its first excited bound state remains nearly constant, with $g_{\rm eff}^2/\gamma'_m>\gamma_m$8 for $g_{\rm eff}^2/\gamma'_m>\gamma_m$9 from $A_{\rm th}=B$0 to $A_{\rm th}=B$1, defying the $A_{\rm th}=B$2 law. The mode profile decays algebraically as $A_{\rm th}=B$3 rather than as a simple Gaussian or sine-mode, and the sideband modes correspond to excited Jackiw–Rossi bound states rather than higher longitudinal or transverse Fabry–Pérot orders (Xi et al., 2021).

Experimentally, the quadratures were recorded via a laser interferometer or via the electrode readout demodulated at $A_{\rm th}=B$4. With $A_{\rm th}=B$5 below threshold, the quadrature ellipse narrows along one axis, with a 40% reduction in noise variance, directly evidencing squeezed vacuum fluctuations. Under a coherent pump with bandwidth $A_{\rm th}=B$6, a sharp peak at $A_{\rm th}=B$7 appears once $A_{\rm th}=B$8, and the spectrum linewidth narrows from $A_{\rm th}=B$9 down to $G$0. Under an incoherent white-noise pump with bandwidth $G$1, lasing still occurs but with a slightly higher threshold, $G$2, due to reduced spectral density near $G$3 (Xi et al., 2021).

These results were summarized in the source as the first squeezed, topological phonon laser, combining a Jackiw–Rossi Dirac-vortex cavity, strong second-order electromechanical nonlinearity, and observation of phonon lasing above threshold, phase-sensitive amplification, vacuum squeezing, and linewidth narrowing in a single integrated platform. A plausible implication is that the combination of frequency pinning and nearly constant mode spacing directly addresses the large-area single-mode problem in bosonic cavities.

4. Floquet-engineered squeezed phonon lasing in solid-state defects

A distinct route uses a single mechanical mode of frequency $G$4 coupled dispersively to a principal pair of two-level defects embedded in a suspended hBN membrane, while an identical ancilla pair provides engineered dissipation. The time-dependent Hamiltonian is

$G$5

plus analogous primed terms for the ancilla spins. Under periodic driving and in the regime $G$6, a Magnus/Floquet expansion yields the effective squeezed-mode coupling of the principal sector and, under a different sideband resonance for the ancilla, an engineered squeezed-mode decay rate $G$7 (Molinares et al., 3 Jun 2026).

The squeezed character is encoded by the Bogoliubov relation $G$8, which identifies

$G$9

as a squeezed-mode operator. Above threshold, the Wigner function of the mechanical mode in the squeezed basis $G=\gamma_m$0 becomes a ring of radius $G=\gamma_m$1 with reduced width along one quadrature. For canonical quadratures

$G=\gamma_m$2

the steady-state variances satisfy

$G=\gamma_m$3

with squeezing parameter

$G=\gamma_m$4

The same study analyzes the emission spectrum

$G=\gamma_m$5

and the zero-delay second-order correlation

$G=\gamma_m$6

The latter evolves from thermal values $G=\gamma_m$7 below threshold to Poissonian $G=\gamma_m$8 for conventional lasing at $G=\gamma_m$9, and to super-Poissonian $$\hat H = \hbar\omega_0\,\hat a^\dagger\hat a +\frac{\hbar B}{2}\,\hat a^\dagger\hat a^\dagger \hat a\,\hat a +\frac{\hbar\,\alpha\,V_{\rm dc}\,V_{\rm pump}}{2}\,\Bigl(\hat a^{\dagger2} + \hat a^2\Bigr),$$0 in the squeezed-lasing regime at $$\hat H = \hbar\omega_0\,\hat a^\dagger\hat a +\frac{\hbar B}{2}\,\hat a^\dagger\hat a^\dagger \hat a\,\hat a +\frac{\hbar\,\alpha\,V_{\rm dc}\,V_{\rm pump}}{2}\,\Bigl(\hat a^{\dagger2} + \hat a^2\Bigr),$$1 (Molinares et al., 3 Jun 2026).

The Floquet control protocol also distinguishes conventional, squeezed, and phase-locked squeezed lasing. At $$\hat H = \hbar\omega_0\,\hat a^\dagger\hat a +\frac{\hbar B}{2}\,\hat a^\dagger\hat a^\dagger \hat a\,\hat a +\frac{\hbar\,\alpha\,V_{\rm dc}\,V_{\rm pump}}{2}\,\Bigl(\hat a^{\dagger2} + \hat a^2\Bigr),$$2, one realizes squeezed amplification into $$\hat H = \hbar\omega_0\,\hat a^\dagger\hat a +\frac{\hbar B}{2}\,\hat a^\dagger\hat a^\dagger \hat a\,\hat a +\frac{\hbar\,\alpha\,V_{\rm dc}\,V_{\rm pump}}{2}\,\Bigl(\hat a^{\dagger2} + \hat a^2\Bigr),$$3; for $$\hat H = \hbar\omega_0\,\hat a^\dagger\hat a +\frac{\hbar B}{2}\,\hat a^\dagger\hat a^\dagger \hat a\,\hat a +\frac{\hbar\,\alpha\,V_{\rm dc}\,V_{\rm pump}}{2}\,\Bigl(\hat a^{\dagger2} + \hat a^2\Bigr),$$4, the usual beam-splitter-type coupling recovers a standard phonon laser. The dimensionless drive amplitude $$\hat H = \hbar\omega_0\,\hat a^\dagger\hat a +\frac{\hbar B}{2}\,\hat a^\dagger\hat a^\dagger \hat a\,\hat a +\frac{\hbar\,\alpha\,V_{\rm dc}\,V_{\rm pump}}{2}\,\Bigl(\hat a^{\dagger2} + \hat a^2\Bigr),$$5 controls the balance between the Stokes and anti-Stokes sidebands and tunes the squeezing strength continuously from zero to moderate values. Furthermore, choosing $$\hat H = \hbar\omega_0\,\hat a^\dagger\hat a +\frac{\hbar B}{2}\,\hat a^\dagger\hat a^\dagger \hat a\,\hat a +\frac{\hbar\,\alpha\,V_{\rm dc}\,V_{\rm pump}}{2}\,\Bigl(\hat a^{\dagger2} + \hat a^2\Bigr),$$6 and $$\hat H = \hbar\omega_0\,\hat a^\dagger\hat a +\frac{\hbar B}{2}\,\hat a^\dagger\hat a^\dagger \hat a\,\hat a +\frac{\hbar\,\alpha\,V_{\rm dc}\,V_{\rm pump}}{2}\,\Bigl(\hat a^{\dagger2} + \hat a^2\Bigr),$$7 yields an extra term proportional to $$\hat H = \hbar\omega_0\,\hat a^\dagger\hat a +\frac{\hbar B}{2}\,\hat a^\dagger\hat a^\dagger \hat a\,\hat a +\frac{\hbar\,\alpha\,V_{\rm dc}\,V_{\rm pump}}{2}\,\Bigl(\hat a^{\dagger2} + \hat a^2\Bigr),$$8 that explicitly breaks the $$\hat H = \hbar\omega_0\,\hat a^\dagger\hat a +\frac{\hbar B}{2}\,\hat a^\dagger\hat a^\dagger \hat a\,\hat a +\frac{\hbar\,\alpha\,V_{\rm dc}\,V_{\rm pump}}{2}\,\Bigl(\hat a^{\dagger2} + \hat a^2\Bigr),$$9 phase symmetry, leading to phase-locked squeezed lasing without any external injection tone (Molinares et al., 3 Jun 2026).

The feasible parameter set used in the numerical simulations is given, in units of $V_{\rm pump}>2.09\ {\rm V}$00, by $V_{\rm pump}>2.09\ {\rm V}$01, $V_{\rm pump}>2.09\ {\rm V}$02–$V_{\rm pump}>2.09\ {\rm V}$03, $V_{\rm pump}>2.09\ {\rm V}$04, $V_{\rm pump}>2.09\ {\rm V}$05, $V_{\rm pump}>2.09\ {\rm V}$06, $V_{\rm pump}>2.09\ {\rm V}$07, and $V_{\rm pump}>2.09\ {\rm V}$08. These values correspond to hBN membranes of radius $V_{\rm pump}>2.09\ {\rm V}$09, $V_{\rm pump}>2.09\ {\rm V}$10, mechanical $V_{\rm pump}>2.09\ {\rm V}$11, and magnetic field gradients $V_{\rm pump}>2.09\ {\rm V}$12 that yield $V_{\rm pump}>2.09\ {\rm V}$13. The proposal states that a steady-state squeezed phonon laser enables force or mass sensors whose sensitivity improves by a factor $V_{\rm pump}>2.09\ {\rm V}$14 over the standard quantum limit and that one expects a $V_{\rm pump}>2.09\ {\rm V}$15 enhancement in signal-to-noise ratio (Molinares et al., 3 Jun 2026).

5. Bath-free squeezed phonon lasing in trapped ions

The trapped-ion realization uses two effective two-level ions coupled to a single common vibrational mode of frequency $V_{\rm pump}>2.09\ {\rm V}$16, with each ion driven simultaneously on its red- and blue-sidebands. Under the Lamb–Dicke and rotating-wave approximations, the interaction Hamiltonian is

$V_{\rm pump}>2.09\ {\rm V}$17

Each ion undergoes spontaneous decay at rate $V_{\rm pump}>2.09\ {\rm V}$18 into an auxiliary level, and in the regime $V_{\rm pump}>2.09\ {\rm V}$19 the internal states can be adiabatically eliminated, yielding the effective phonon-mode master equation quoted above (Lee et al., 9 Jan 2026).

The squeezing is encoded through the unitary operator

$V_{\rm pump}>2.09\ {\rm V}$20

If the ratio of red and blue couplings satisfies

$V_{\rm pump}>2.09\ {\rm V}$21

then with $V_{\rm pump}>2.09\ {\rm V}$22 the Hamiltonian takes the standard phonon-laser form in the squeezed frame,

$V_{\rm pump}>2.09\ {\rm V}$23

The source explicitly characterizes this as a “bath-free” approach, because it uses only coherent sideband drives and standard optical pumping, embeds all squeezing into a unitary basis change, and avoids the technical overhead and extra noise of engineered squeezed reservoirs (Lee et al., 9 Jan 2026).

Well above threshold, the phonon mode reaches a displaced squeezed coherent state. Denoting by $V_{\rm pump}>2.09\ {\rm V}$24 the coherent amplitude, the laboratory-mode average phonon number is

$V_{\rm pump}>2.09\ {\rm V}$25

The second-order correlation is given analytically by

$V_{\rm pump}>2.09\ {\rm V}$26

with the full expression reported in the source, and the quadrature variances for

$V_{\rm pump}>2.09\ {\rm V}$27

satisfy

$V_{\rm pump}>2.09\ {\rm V}$28

The minimum variance is therefore $V_{\rm pump}>2.09\ {\rm V}$29 (Lee et al., 9 Jan 2026).

Above threshold the lasing mode has a free, uniformly random phase, and the proposal introduces a weak resonant force

$V_{\rm pump}>2.09\ {\rm V}$30

to lock it. Without the drive, the phase-diffusion rate is

$V_{\rm pump}>2.09\ {\rm V}$31

where $V_{\rm pump}>2.09\ {\rm V}$32 is the small decay above threshold. With the drive, the effective phase diffusion is suppressed as

$V_{\rm pump}>2.09\ {\rm V}$33

The locked quadrature $V_{\rm pump}>2.09\ {\rm V}$34 is squeezed by roughly the same factor $V_{\rm pump}>2.09\ {\rm V}$35 (Lee et al., 9 Jan 2026).

The proposal gives realistic mixed-species ion-chain parameters: trap axial frequency $V_{\rm pump}>2.09\ {\rm V}$36–$V_{\rm pump}>2.09\ {\rm V}$37, Lamb–Dicke parameter $V_{\rm pump}>2.09\ {\rm V}$38–$V_{\rm pump}>2.09\ {\rm V}$39, sideband Rabi rates $V_{\rm pump}>2.09\ {\rm V}$40–$V_{\rm pump}>2.09\ {\rm V}$41, and optical pumping rates $V_{\rm pump}>2.09\ {\rm V}$42–$V_{\rm pump}>2.09\ {\rm V}$43. The example above threshold yields $V_{\rm pump}>2.09\ {\rm V}$44, $V_{\rm pump}>2.09\ {\rm V}$45, squeezing parameter $V_{\rm pump}>2.09\ {\rm V}$46, expected $V_{\rm pump}>2.09\ {\rm V}$47–$V_{\rm pump}>2.09\ {\rm V}$48, $V_{\rm pump}>2.09\ {\rm V}$49–$V_{\rm pump}>2.09\ {\rm V}$50, and quadrature-noise reduction to $V_{\rm pump}>2.09\ {\rm V}$51 (Lee et al., 9 Jan 2026).

6. Directionality, phase locking, and application domains

The nonreciprocal variant is implemented with two evanescently coupled whispering-gallery-mode microresonators and two tapered waveguides. One resonator is a standard optomechanical resonator supporting an optical mode and a mechanical breathing mode coupled by radiation pressure. The other is a purely optical resonator made of a $V_{\rm pump}>2.09\ {\rm V}$52 medium and pumped by a strong laser at $V_{\rm pump}>2.09\ {\rm V}$53, phase-matched so that only the counter-clockwise optical mode is squeezed. In the forward case, the optomechanical resonator couples to the squeezed mode; in the backward case, it couples to the unsqueezed mode. This asymmetry produces direction-dependent mechanical gain and hence nonreciprocal phonon lasing (Lu et al., 2023).

The squeezed frame is introduced by the Bogoliubov transformation

$V_{\rm pump}>2.09\ {\rm V}$54

with

$V_{\rm pump}>2.09\ {\rm V}$55

leading, under the rotating-wave approximation, to an effective forward Hamiltonian with renormalized parameters

$V_{\rm pump}>2.09\ {\rm V}$56

By varying the pump power $V_{\rm pump}>2.09\ {\rm V}$57, which sets

$V_{\rm pump}>2.09\ {\rm V}$58

one tunes $V_{\rm pump}>2.09\ {\rm V}$59, $V_{\rm pump}>2.09\ {\rm V}$60, and $V_{\rm pump}>2.09\ {\rm V}$61, so the forward threshold can be shifted over orders of magnitude while the backward threshold remains unchanged. The isolation parameter is

$V_{\rm pump}>2.09\ {\rm V}$62

The reported applications are nonreciprocal acoustic amplification, one-way phononic network elements, and back-scattering-immune force or sound sensing (Lu et al., 2023).

Across platforms, phase locking appears in more than one form. In the Floquet hBN proposal, explicit breaking of the $V_{\rm pump}>2.09\ {\rm V}$63 phase symmetry produces phase-locked squeezed lasing without any external injection tone (Molinares et al., 3 Jun 2026). In the trapped-ion proposal, phase coherence is stabilized by an external coherent drive that suppresses phase diffusion while preserving the squeezed quadrature structure (Lee et al., 9 Jan 2026). In the topological nanoelectromechanical platform, phase-sensitive amplification arises directly from the $V_{\rm pump}>2.09\ {\rm V}$64 interaction under $V_{\rm pump}>2.09\ {\rm V}$65 pumping (Xi et al., 2021).

A common misconception is that squeezed phonon lasing is synonymous with a single parametric-cavity architecture. The available results instead span topological Dirac-vortex cavities, Floquet-controlled solid-state defects, trapped ions driven on red- and blue-sidebands, and compound optomechanical systems with directional optical squeezing. Another common misconception is that squeezing and lasing are necessarily competing regimes. The reported models and measurements treat them jointly: one quadrature can be squeezed while the mode still exhibits threshold behavior, linewidth narrowing, and coherent emission (Xi et al., 2021, Molinares et al., 3 Jun 2026).

The application space reported in these works includes large-area single-mode phonon and photon lasers with minimal sensitivity to fabrication imperfections, testbeds for nonlinear and non-Hermitian topological physics, topologically protected phononic logic circuits, sub-standard-quantum-limit sensing in solid-state devices, quantum metrology, phononic information processing, directional acoustic amplifiers, and one-way phononic networks (Xi et al., 2021, Molinares et al., 3 Jun 2026, Lu et al., 2023). A plausible implication is that squeezed phonon lasing has become less a single device concept than a family of gain-and-squeezing protocols whose unifying theme is the controlled coexistence of coherent phonon generation and quadrature engineering.