Controllable Non-Hermitianity in Continuous-Variable Qubits

Abstract

Pure dephasing is the dominant leak mechanism in photonic cat qubits because its phase errors disrupt the parity protection, rendering the qubit vulnerable to energy relaxation. In this manuscript, we reveal that this dephasing mechanism conceals an interesting physical phenomenon: it induces \textit{asymmetric leakage} from the cat-state subspace, where even- and odd-parity cat states decay at different rates. This leak asymmetry enables the dynamics of the system to be described by a non-Hermitian Hamiltonian, thereby transforming the cat qubit into a platform with controllable gain and loss for probing non-Hermitian physics. Within this platform, we demonstrate the possibility to control the parity-time symmetry phase transition in a single cat qubit by adjusting its amplitude. Moreover, we couple two cat qubits to realize an entanglement phase transition induced by the exceptional point. Our work constructs a controllable non-Hermitian system simulator, overturning the conventional paradigm that treats dephasing as harmful noise.

Figures (4)

• Figure 1: (a) Energy spectrum of the Kerr parametric oscillator. The eigenstates separate into even- and odd-parity manifolds, with the cat-state subspace $\{\ket{\mathcal{C}_{\pm}}\}$ forming the ground states. The excited states appear at a lower energy because the Kerr nonlinearity is negative. The energy gap to the first excited states scales as $\omega_{\mathrm{gap}}\simeq4K\alpha^2$, providing protection against unwanted transitions. The purple and brown dashed arrows in (a) indicate the leakage from the cat-state subspace $\{\ket{\mathcal{C_{\pm}}}\}$ due to pure dephasing. (b) Bloch sphere of the cat qubit and the corresponding Wigner function representations.
• Figure 2: (a) Time evolution of the even cat state and the odd cat state governed by the effective master equation in Eq. (\ref{['eq9']}) (dashed curve) and the full master equation in Eq. (\ref{['eq3']}) (solid curve). Here, we choose $\alpha=1.5$. (b) Discrepancy in the population of the even cat state under the effective and full master equations, as a function of the cat state amplitude $\alpha$ and time. All simulations include a weak single-photon drive with amplitude $\Omega=0.01K$. Other parameters is $\kappa^{\phi}=0.001K$.
• Figure 3: (a) The loss/gain rate $\gamma$ (red solid) and the coherent coupling $\epsilon$ (blue solid) as functions of the cat amplitude $\alpha$. Their intersection at $\alpha = 1.5$ defines the EP. The white region indicates where the discrepancy between the effective and full models is below $1\%$, validating our approach. (b) Real and (c) imaginary parts of the eigenvalues $E_{1,2}$ of $\mathcal{H}$ versus $\alpha$, clearly showing the $\mathcal{P}\mathcal{T}$-symmetry breaking transition at the EP. Parameters: $\kappa^{\phi}=0.05K$, $\Omega = 0.0023K$.
• Figure 4: (a) Concurrence $C^{f,(s)}_{\pm}$ for the eigenstates $|\Phi^{f,(s)}_{\pm}\rangle$ as a function of $\beta$. Insets show the derivatives $dC^{f,(s)}_{\pm}/d\beta$ ($dC^{f,(s)}_{+}/d\beta$ are red and green dotted lines, respectively; $dC^{f,(s)}_{-}/d\beta$ are blue and purple solid lines, respectively), highlighting the critical behavior near the exceptional points. (b) Real and imaginary parts of the eigenvalues $E^{f,(s)}_{\pm}$ versus $\beta$, showing the coalescence of eigenvalues at the EPs. Parameters: $\alpha=2$, $\kappa^{\phi}_{1}=\kappa^{\phi}_{2}=0.05K_{1}$, $g=0.001K_{1}$, and $K_{2}=K_{1}$.