Signatures of Environment-Induced Quantum Synchronization Transitions via Two-body Dissipator Engineering

Abstract

Metronome synchronization and the transition between the in-phase and anti-phase synchronization have been observed in classical systems. We demonstrate the quantum analog of this phenomenon in a two-qubit system coupled to a common environment. Tracing out the environment in the quantum collision model, we obtain an effective master equation with a two-body dissipator for two qubits. Quenching the two-body dissipator, we demonstrate controlled transitions from in-phase to anti-phase synchronization. This synchronization transition is robust against noise. Signatures of the transition are observed through Pearson correlation coefficient measurements obtained via quantum simulations on superconducting circuits. Future experiments employing qutrit systems are expected to yield a more pronounced effect.

Figures (4)

• Figure 1: (a) Schematics of classical synchronization transition with two metronomes coupled by a common movable platform. The transition from in-phase (I) to anti-phase (III) synchronization can be realized by tuning the movable platform (II). (b) Schematics of the quantum collision model. The two qubits $\varrho_{S,1(2)}$ interact stroboscopically with ancilla qutrits (environment). Different ancilla states lead to different effective dissipators for the qubits. Quantum synchronization transition is induced by quenching the ancilla state. (c) Schematics of the quantum circuit that simulates the quantum collision model.
• Figure 2: (a) The blue solid, red dashed, and green dotted lines show the order parameter $\langle\sigma^{x}_{1}\rangle$, $\langle\sigma^{x}_{2}\rangle$, and their Pearson correlation $C_{x_{1},x_{2}}$ as a function of the collision number $n$, respectively. As $n$ increases, ancilla state changes from $|\psi_{E}\rangle_{\text{I}}$ ( Phase I) to $|\psi_{E}\rangle_{\text{II}}$ ( Phase II) and $|\psi_{E}\rangle_{\text{III}}$ ( Phase III). (b) The circles and squares show mutual information $I(\varrho^{n}_{S})$ and entanglement $\pazocal{C}(\varrho^{n}_{S})$ as a function of $n$, respectively. The inset shows the zoom-in where mutual information and entanglement reach zero. Here $\omega\tau=0.01$, $g^{2}\tau=1$, sample length $\Delta n=140$, and the randomly selected initial state is $|\psi\rangle^{\text{ini}}_{S}=[0.8579 + 0.2631i,0.2774 + 0.3013i, 0.0222 - 0.1480i, 0.0428 - 0.0532i]^{\mathsf{T}}$ with $\mathsf{T}$ denotes the transpose.
• Figure 3: Comparison of two ancilla quench sequences under noise: Panel (a) and (b) are for the complete sequence ( Phase I $\to$II$\to$III) and the sequence without Phase II, respectively. Both panels display Pearson correlation $C_{x_{1},x_{2}}$ as a function of collision number $n$ and noise strength $\bar{\xi}$, with sample length $\Delta n=140$. The blue solid, red dashed, and green dotted lines in panels (b) and (e) show $\langle\sigma^{x}_{1}\rangle$, $\langle\sigma^{x}_{2}\rangle$, and $C_{x_{1},x_{2}}$ as a function of the collision number $n$ for $\bar{\xi}=0.21$ and $\bar{\xi}=0.49$, respectively, in the sequence without Phase II. The blue solid and red dashed lines in insets (d) and (f) show $\langle\sigma^{x}_{1}\rangle_{\text{traj}}$ and $\langle\sigma^{x}_{2}\rangle_{\text{traj}}$ along a single quantum trajectory, obtained from stochastic Schrödinger equation. The other parameters are the same as Fig. \ref{['Fig:CM']}.
• Figure 4: (a) The lines and squares show $\langle \sigma^{x}_{j}\rangle$ as a function of collision number $n$ for the quantum collision model (denoted by QCM) and ideal quantum circuits calculation (denoted by Ideal QC), respectively, with $\omega\tau=0.3$ and $g^{2}\tau = 1$. (b)-(c) The circles and triangles with error bar show $\langle\sigma^{x}_{j}\rangle$ as a function of $n$ computed via superconducting circuit simulation and noisy quantum circuits calculation, respectively, with $\omega\tau=0.8$ and $g^{2}\tau = 4$. (d) The blue circles, red squares, and yellow triangles show the Pearson correlation $C_{x_{1},x_{2}}$ as a function of $n$ computed via superconducting circuit simulation (Exp.), ideal quantum circuits calculation (Ideal QC), and noisy quantum circuits calculation (Noisy QC), respectively, with a sample length $\Delta n =4$.