SyncLight: Dissipation-Induced Phase Locking

• SyncLight is a non-Hermitian optical synchronization method that drives multiple modes to equal intensities and a locked phase through engineered loss.
• It employs a programmable row-stochastic map via unitary dilation using thermal Mach–Zehnder interferometers on a silicon photonic chip.
• Experimental results demonstrate controlled convergence speed and independent throughput control, showcasing practical applications in dense photonic systems.

SyncLight denotes a non-Hermitian photonic synchronization scheme in which engineered loss on a programmable silicon photonic chip drives an arbitrary multimode coherent optical field toward one unique collective optical mode with equal modal intensities and a globally locked phase. In the reported realization, the synchronized quantities are the modal complex amplitudes, so both intensity and relative phase converge. The organizing mechanism is selective attenuation: dissipation suppresses all field components except one preferred collective mode, a process termed dissipation-induced phase synchronization (Xu et al., 14 May 2026).

1. Definition and physical content

SyncLight treats dissipation as the ordering resource. The synchronized state is not merely an equal-power distribution across channels. It is a state in which all output modes share the same complex amplitude structure: equal modal intensities and a common locked phase. In the three-mode experiment, this collective state is effectively the uniform mode $(1,1,1)^{\mathsf T}$, up to an overall complex scaling factor inherited from the input projection. The final field therefore retains only a global amplitude and phase, while initial mode-by-mode differences are erased (Xu et al., 14 May 2026).

This mechanism differs fundamentally from unitary linear optics. Ordinary Hermitian or unitary photonic transformations can mix amplitudes and phases, but they cannot make arbitrary inputs converge to a single state, because norm-preserving evolution does not destroy information about microscopic differences. SyncLight instead uses non-Hermitian evolution to make the desired collective mode the least lossy mode, ideally lossless relative to the others, while orthogonal or non-dominant directions in state space are dissipatively quenched. In that sense, synchronization is an eigenmode-selection process rather than a nonlinear locking transition.

A recurrent misconception is to identify the effect with conventional synchronization of oscillators, such as Kuramoto-type phase locking or laser injection locking. The reported mechanism is not based on nonlinear self-oscillation, frequency pulling, or gain competition. It is realized directly in the optical transport of an externally injected coherent field on a passive chip. The paper explicitly situates it closer in spirit to dissipative state engineering and reservoir engineering than to conventional laser synchronization (Xu et al., 14 May 2026).

2. Stochastic-matrix and non-Hermitian formulation

The central theoretical object is a row-stochastic matrix $F$, repurposed from Markov-chain theory to act on coherent optical amplitudes: $$F_{ij} \ge 0, \qquad \sum_j F_{ij}=1 \quad \text{for every row } i.$$ Because each row sums to one, the uniform vector

$v_0=(1,1,\dots,1)^{\mathsf T}$

is a right eigenvector with eigenvalue $\lambda_0=1$. For irreducible, aperiodic $F$, the Perron–Frobenius theorem guarantees that this eigenvalue is unique on the unit circle and that all other eigenvalues satisfy $|\lambda_j|<1$. Repeated application of $F$ therefore selects the uniform mode and damps all others. If the initial field is $a(0)$, the surviving asymptotic component has overall complex weight

$c_0=\pi^{\mathsf T}a(0),$

where $F$0 is the stationary distribution, i.e. the left eigenvector associated with eigenvalue $F$1 (Xu et al., 14 May 2026).

The synchronization rate is controlled by the second-largest eigenvalue modulus,

$F$2

and the spectral gap,

$F$3

Each application of $F$4 reduces the deviation from synchronization by at least a factor $F$5, so the characteristic number of steps scales as

$F$6

The paper also gives a continuous-time representation through the effective non-Hermitian Hamiltonian

$F$7

so that $F$8. In this picture, the synchronized mode has zero imaginary decay, while all other eigenmodes acquire negative imaginary parts and are exponentially damped (Xu et al., 14 May 2026).

For controlled speed programming, the implemented family is

$F$9

All matrices in this family share the same synchronized eigenvector, but the SLEM is exactly $$F_{ij} \ge 0, \qquad \sum_j F_{ij}=1 \quad \text{for every row } i.$$0, so $$F_{ij} \ge 0, \qquad \sum_j F_{ij}=1 \quad \text{for every row } i.$$1. Hence $$F_{ij} \ge 0, \qquad \sum_j F_{ij}=1 \quad \text{for every row } i.$$2 sets the convergence speed without changing the final synchronized state. The threshold synchronization time is given as

$$F_{ij} \ge 0, \qquad \sum_j F_{ij}=1 \quad \text{for every row } i.$$3

For general non-symmetric stochastic matrices, the paper gives the upper bound

$$F_{ij} \ge 0, \qquad \sum_j F_{ij}=1 \quad \text{for every row } i.$$4

where $$F_{ij} \ge 0, \qquad \sum_j F_{ij}=1 \quad \text{for every row } i.$$5 captures eigenvector non-orthogonality and non-normality. This is the reason the clean rate interpretation through $$F_{ij} \ge 0, \qquad \sum_j F_{ij}=1 \quad \text{for every row } i.$$6 applies most directly to the symmetric family used in the experiments.

The second programming knob is total optical throughput. Adding a uniform imaginary offset,

$$F_{ij} \ge 0, \qquad \sum_j F_{ij}=1 \quad \text{for every row } i.$$7

yields

$$F_{ij} \ge 0, \qquad \sum_j F_{ij}=1 \quad \text{for every row } i.$$8

The factor $$F_{ij} \ge 0, \qquad \sum_j F_{ij}=1 \quad \text{for every row } i.$$9 uniformly attenuates all modes, changing total transmitted power without affecting amplitude ratios or relative phases. Synchronization metrics are therefore unchanged while optical power throughput is set independently (Xu et al., 14 May 2026).

3. Silicon-photonic realization

The hardware problem is that a passive linear photonic circuit is unitary, whereas the target map $v_0=(1,1,\dots,1)^{\mathsf T}$0 is non-unitary. The implementation uses unitary dilation: a non-Hermitian operator $v_0=(1,1,\dots,1)^{\mathsf T}$1 is embedded into a larger unitary acting jointly on system and ancilla modes. With the singular value decomposition

$v_0=(1,1,\dots,1)^{\mathsf T}$2

the unitaries $v_0=(1,1,\dots,1)^{\mathsf T}$3 and $v_0=(1,1,\dots,1)^{\mathsf T}$4 are synthesized by interferometer meshes, while each singular value $v_0=(1,1,\dots,1)^{\mathsf T}$5 is realized by coupling a system mode to a vacuum ancilla through a beamsplitter with transmissivity $v_0=(1,1,\dots,1)^{\mathsf T}$6. Energy lost from the system exits through ancilla ports, and the reduced system dynamics implements the intended lossy transformation exactly (Xu et al., 14 May 2026).

The processor is a $v_0=(1,1,\dots,1)^{\mathsf T}$7 programmable silicon photonic mesh fabricated in a CMOS-compatible process. It contains 66 thermally tunable Mach–Zehnder interferometers, each formed by two multimode interference couplers and a phase-tunable arm, so that each MZI acts as a universal $v_0=(1,1,\dots,1)^{\mathsf T}$8 linear optical element. Optical excitation is provided by a 1550 nm pulsed diode laser. MEMS switches route the input to selected ports and sequentially direct outputs to a calibrated power meter, and each thermal phase shifter is electronically controlled with $v_0=(1,1,\dots,1)^{\mathsf T}$9A resolution.

Logically, the 12-mode chip is divided into three zones. The input preparation module uses three MZIs to distribute light from one laser input into three system modes with programmable amplitudes and phases. The synchronization module implements a $\lambda_0=1$0 non-Hermitian operator as part of a $\lambda_0=1$1 unitary dilation using ten MZIs; three modes are system channels and two are ancilla loss channels. The measurement module is reconfigurable between direct intensity readout and interferometric phase extraction. Thus the demonstrated synchronized subsystem is three-dimensional in signal space, even though the overall processor has 12 ports (Xu et al., 14 May 2026).

4. Experimental demonstrations

The reported experiments establish amplitude equalization, global phase locking, programmable convergence rate, and independent throughput control. Inputs are arbitrary three-mode coherent states prepared on chip. Outputs are measured either as modal intensities or, through pairwise interference, as relative phases (Xu et al., 14 May 2026).

Demonstration	Method	Reported outcome
Amplitude and phase synchronization	Initialize all power in Mode 2; repeated map application; pairwise interferometry	Intensities converge to equality; $\lambda_0=1$2 and $\lambda_0=1$3 become negligible
Programmable speed	Implement $\lambda_0=1$4 for different $\lambda_0=1$5	Faster decay for smaller $\lambda_0=1$6; $\lambda_0=1$7
Independent throughput control	Add uniform loss offset $\lambda_0=1$8	Total energy follows prescribed attenuation; synchronization trajectories collapse onto one master curve

In the first experiment, the measured intensity evolution shows power redistributing from the initially occupied channel into all three modes, converging to equal intensities. Phase synchronization is extracted from a two-channel interferometer by sweeping a controllable phase $\lambda_0=1$9 over 20 points from $F$0 to $F$1 and fitting the fringe

$F$2

This is done independently for adjacent mode pairs, yielding $F$3 and $F$4. The reported combined phase variance metric,

$F$5

collapses to zero at the synchronized steady state, directly verifying global phase locking rather than mere intensity equalization.

The speed-control experiment programs the family $F$6, so the target synchronized state is fixed while the spectral gap varies. The synchronization metric decays more rapidly for smaller $F$7, exactly as expected from the exponential $F$8 suppression of non-dominant modes. The throughput-control experiment implements several values of $F$9 in $|\lambda_j|<1$0. The measured total surviving optical energy follows the prescribed asymptotic attenuation level, while the synchronization metric follows the same master trajectory for all tested $|\lambda_j|<1$1, demonstrating decoupling between dissipative ordering and global loss.

The paper also includes simulation-based evidence beyond the three-mode subsystem. A 50-mode random simulation converges from random amplitudes and phases to a globally phase-locked equal-amplitude state. Across stochastic systems with $|\lambda_j|<1$2 to $|\lambda_j|<1$3, larger systems synchronize faster on average because the non-dominant eigenvalues are pushed further toward the origin, increasing the spectral gap (Xu et al., 14 May 2026).

5. Position within the broader synchronization literature

SyncLight belongs to a wider landscape of optical synchronization problems, but its target and mechanism are distinct. In quantum communication, synchronization often refers to making photons from distant sources arrive indistinguishably at a beamsplitter. One reported route is to synchronize an independently triggered pulsed diode laser to a master mode-locked laser over up to $|\lambda_j|<1$4 of fiber and to tolerate residual jitter by using photons with $|\lambda_j|<1$5 coherence time (Landry et al., 2010). That problem is about timing jitter and arrival-time indistinguishability. SyncLight, by contrast, operates directly on coherent multimode amplitudes inside a passive photonic processor.

A second nearby notion is phase-reference synchronization for optical Bell tests. In displacement-based Bell protocols implemented with Mach–Zehnder interferometers and strong coherent reference fields, the displacement settings are phase sensitive, and nonlocality cannot be detected if displacement phases are unknown. The protocol therefore requires a shared and stable phase frame between source and local lasers (Dastidar et al., 2022). SyncLight also enforces phase alignment, but it does so by dissipatively selecting a unique collective optical mode rather than by distributing a common measurement reference.

A third comparison is synchronization of synchrotron-radiation bursts in accelerator light sources. There, periodic RF modulation entrains the low-frequency bursting dynamics of coherent synchrotron radiation, producing 1:1, harmonic, and subharmonic locking, Arnold tongues, and phase slips near threshold (Evain et al., 6 Feb 2026). That phenomenon is a forced nonlinear oscillator problem at the level of burst envelopes. SyncLight is instead a programmable non-Hermitian linear-optical transport process.

These distinctions explain why the paper emphasizes that its mechanism is not a Kuramoto transition, not injection locking, and not exceptional-point physics. The dominant mathematical structure is Perron–Frobenius mode selection under programmable loss (Xu et al., 14 May 2026).

6. Applications, limitations, and open directions

The practical significance of SyncLight lies in the fact that the target non-Hermitian map is software-programmed into an MZI mesh, so both the collective state and the convergence properties can in principle be redesigned on demand. The authors explicitly frame possible applications in dense wavelength-division multiplexing, co-packaged optics, and quantum photonic networks, where maintaining stable phase relations across many channels is valuable. Because the underlying hardware is linear-optical and dissipation is engineered through ancillary modes, the framework is presented as relevant to both classical and quantum photonics, although the demonstrated experiments are entirely classical coherent-light experiments (Xu et al., 14 May 2026).

The principal limitations are also explicit. The on-chip demonstration is only for a three-mode synchronized subsystem; larger-$|\lambda_j|<1$6 advantages are numerical rather than experimental. The implementation is passive and therefore lossy by construction, so power efficiency must be balanced against convergence speed and fidelity. The simple relation between spectral gap and synchronization time applies most directly to the symmetric matrix family used experimentally; generic non-Hermitian, non-normal matrices can exhibit more complicated transient dynamics. The architecture is relevant to quantum photonics in principle, but the paper does not experimentally address nonclassical states, quantum coherence preservation, or noise added by practical imperfections. Scalability is described as promising but limited chiefly by thermal crosstalk in large MZI meshes, so active thermal compensation may be required. The paper also states that exceptional points are not a necessary mechanism in this setting.

As a result, SyncLight is best understood as a programmable dissipative-state-engineering primitive for integrated photonics: arbitrary coherent multimode inputs are driven to the unique equal-phase, equal-intensity Perron mode by a row-stochastic non-Hermitian map implemented through unitary dilation. A separate use of the name appears in computer vision as “SyncLight: Controllable and Consistent Multi-View Relighting” (Serrano-Lozano et al., 23 Jan 2026), but in the photonic sense defined here the term refers to dissipation-induced phase synchronization of light on a silicon photonic processor.