Phase-enhanced nonreciprocal photon-phonon conversion via coupled optomechanical cavities

Abstract: Nonreciprocity, characterized by direction-dependent signal propagation, is fundamental to technologies such as isolators, signal routing, and precision sensing. This letter theoretically demonstrates nonreciprocal phonon transport and the conversion between photon and acoustic phonon signals in coupled optomechanical cavities via phase-dependent driving. It is demonstrated that, in contrast to nonreciprocal phonon transport, which necessitates both dissipation and phase-induced violation of time reversal symmetry, the nonreciprocity in photon-phonon conversion can occur without violating time reversal symmetry. We demonstrate that such nonreciprocity arises due to the path-dependent asymmetry in photon-phonon conversion. Furthermore, we demonstrate that the nonreciprocity of photon-phonon conversion can be further enhanced, achieving isolation levels of up to 40 dB by suitably modifying the phase difference of the driving lasers.

• The paper demonstrates a novel method for tunable nonreciprocal photon-phonon conversion with phonon isolation reaching up to 60 dB.
• It employs coupled optomechanical cavities and synthetic flux to break time-reversal symmetry and achieve precise phase-controlled routing.
• The work uses linearized Hamiltonians and quantum Langevin equations to verify robust, magnet-free isolation for integrated photonic circuits.

Phase-Enhanced Nonreciprocal Photon-Phonon Conversion in Coupled Optomechanical Cavities

Introduction

Nonreciprocal signal transport, wherein the forward and backward transmission of excitations are asymmetric, is indispensable for the development of isolators and circulators in photonic, phononic, and hybrid quantum devices. Conventional nonreciprocity is achieved through magneto-optical effects, but such approaches lack full compatibility with on-chip integration and have reduced effectiveness at optical frequencies. Recent strategies exploit synthetic gauge fields, engineered interference, and dynamic modulation in cavity optomechanical systems for nonreciprocal routing without magnetic materials. This paper provides a theoretical analysis of nonreciprocal phonon transport and photon-phonon conversion in a pair of coupled optomechanical cavities, elucidating mechanisms that enable highly tunable, phase-controlled isolation and conversion efficiency.

System Architecture and Theoretical Model

The platform consists of two optomechanical cavities labeled as left (L) and right (R), each hosting a localized optical (photon) and mechanical (phonon) mode. The intra-cavity optical modes are coupled through photon hopping at rate $J$, while a parallel phononic hopping at rate $V$ hybridizes the mechanical modes. Enhanced optomechanical coupling $G_{j}$ is controlled by the drive amplitude and phase. Crucially, phase differences in the driving lasers impart a synthetic flux $\phi$, which can break TRS and mediate synthetic gauge fields conducive to nonreciprocity.

Figure 1: Schematic of two coupled optomechanical cavities, with photon hopping $J$, phonon hopping $V$, and optomechanical couplings $G_j$.

The system Hamiltonian accommodates optical/mechanical input fields and decay via coupling to external waveguides. The synthetic flux, given by the phase difference $\phi = \phi_L - \phi_R$, threads the four-mode network and is the central control parameter for the emergence and tuning of nonreciprocity.

Nonreciprocal Phonon Transport

Phonon isolation is determined by the ratio of forward to backward transport and is maximized when both the optical decay rates are nonzero and TRS is broken by the synthetic flux $\phi$. In the absence of cavity loss, even with nontrivial $\phi$, the system remains reciprocal. Optimal destructive interference parameters can yield phonon isolation up to 60 dB.

Figure 2: (a) Phonon isolation vs. frequency for three synthetic flux values. (b) Phonon isolation as a function of synthetic flux $V$0 and frequency $V$1.

Isolation drops to zero for $V$2 or integer multiples of $V$3, which correspond to TRS-preserving regimes. Full on/off reconfigurability of nonreciprocity is thus attainable simply by tuning the phase difference of driving lasers. This provides a robust pathway for phase-programmable phononic isolators in integrated circuits.

Nonreciprocal Photon-to-Phonon Conversion

The conversion of photonic signals to phononic excitations—and the associated isolation—is governed by asymmetric pathway interference, which persists even when TRS is not explicitly broken (i.e., for $V$4). The forward (L→R) and backward (R→L) conversion processes involve dissimilar indirect paths, and their constructive/destructive interference is highly sensitive to both $V$5 and coupling strengths.

Figure 3: (a) Isolation for photon-to-phonon conversion for various synthetic flux values. (b) Conversion isolation as a function of synthetic flux $V$6 and frequency $V$7.

Through tuning $V$8 and the effective interference, photon-to-phonon conversion isolation can reach up to 40 dB, while sign reversal of $V$9 can flip the directionality, allowing the system to preferentially transmit or suppress signals based on the phase configuration. Notably, this nonreciprocity is intrinsic to the path asymmetry and persists even in the absence of TRS breaking, distinguishing it from phonon transport isolation.

Nonreciprocal Phonon-to-Photon Conversion

The complement of the above scenario yields phonon-to-photon conversion, which similarly presents nonreciprocity due to pathway asymmetry and is highly tunable via phase control.

Figure 4: (a) Isolation for phonon-to-photon conversion for various synthetic flux values. (b) Conversion isolation as a function of synthetic flux $G_{j}$0 and frequency.

The system enables either forward or backward conversion to be preferentially enhanced or suppressed depending on the phase difference, allowing for integrated devices that can dynamically route or convert photons and phonons on demand.

Numerical Results and Experimental Feasibility

Simulations deploy experimentally realistic parameters, confirming the feasibility of achieving high phonon isolation (up to 60 dB) and photon-phonon isolation (up to 40 dB) through moderate tuning of laser phases and optomechanical coupling rates. Theoretical modeling leverages linearized Hamiltonians and full quantum Langevin equation analysis, with analytical expressions yielding explicit dependence of isolation and conversion ratios on system parameters and synthetic flux.

Implications and Outlook

The primary implication is the demonstration that robust, phase-controlled nonreciprocity in both phonon transport and photon-phonon interconversion is accessible in integrated optomechanical architectures without magnetic materials. This paradigm enables ultracompact, phase-programmable isolators and routers for quantum information processing, signal transduction, noise filtering, and thermal management. Future extensions may explore reconfigurable nonreciprocal quantum networks, nonclassical state manipulation, topologically protected quantum signal transfer, and hybrid interfaces for superconducting qubits via phononic or photonic links.

Conclusion

This work establishes that coupled optomechanical cavities driven with tunable phase differences exhibit highly configurable nonreciprocity in both phonon transport and photon-phonon conversion. While phonon isolation strictly requires TRS breaking via synthetic flux and finite optical decay, photon-phonon conversion nonreciprocity follows from intrinsic path asymmetry and persists even for $G_{j}$1. The reported isolation magnitudes (up to 60 dB for phonons and 40 dB for photon-phonon conversion) substantiate the practical value of this approach for advanced on-chip nonreciprocal devices, particularly relevant for scalable quantum information and integrated photonics applications.