Quantum nonreciprocity from qubits coupled by Dzyaloshinskii-Moriya interaction

TL;DR

The paper addresses quantum nonreciprocity in a bidirectional waveguide QED system by introducing a Dzyaloshinskii-Moriya–type antisymmetric exchange between two qubits, formalized as a complex exchange $\\mathcal{J}=J e^{i\\theta}$. Using the full quantum master equation and input–output theory, the authors show that the DMI phase $\\theta$ and propagation phase $\\phi$ produce strong nonreciprocity in both coherent and incoherent transmission, even without chiral waveguides, and enable phase-programmable, power-independent perfect transparency at phase-matched spacings $\\phi=n\\pi$ when detunings are symmetrically or antisymmetrically set. They further reveal nonreciprocal steady-state entanglement with analytic expressions at pure-state points and demonstrate redistribution of two-photon correlations between transmission and reflection (superbunching) controlled by $J$ and $\\theta$. Overall, the work highlights DMI as a versatile resource to engineer nonreciprocity, transparency, entanglement, and photon statistics in waveguide QED, with potential applications in isolators, routers, and quantum light sources without relying on chiral waveguides.

Abstract

We present a theoretical study of quantum nonreciprocity induced via a Dzyaloshinskii-Moriya interaction (DMI) in an otherwise achiral, waveguide quantum electrodynamics. Using the full quantum master equation and input-output formalism for two-level systems coupled to a one-dimensional waveguide and driven by a coherent field, we show that an engineered DMI enables strong nonreciprocity in an otherwise reciprocal system, with tunable behavior governed by driving strength, detunings, and phase of the DMI. Using it not only demonstrates nonreciprocal transmission but also demonstrates nonreciprocal quantum entanglement and photon bunching. The system can end up in a pure state as certain decohering channels do not participate. The pure state leads to power-independent perfect transparency. Conditions are derived and depend on the propagation phase, the relative detuning of the two qubits, and the exchange interaction. At these pure-state points, the steady-state entanglement is reciprocal and admits a closed-form expression; away from them, phase control generates strong entanglement nonreciprocity. The DMI also reshapes photon statistics, redistributing two-photon correlations and shifting superbunching from transmission (no DMI) to reflection at finite DMI. These results establish DMI as a versatile resource for engineering nonreciprocity, transparency, entanglement, and photon correlations in waveguide QED, enabling isolators, routers, and superbunching light sources without requiring chiral waveguides.

Figures (8)

• Figure 1: Two qubits $a,b$ separated by $x_{ab}$ along a bidirectional 1D waveguide. Each qubit couples to the waveguide at rate $\Gamma$ and to other loss channels at rate $\gamma$. The inter-qubit exchange is complex, $\mathcal{J}=J e^{i\theta}$, whose DMI part $J\sin\theta$ produces an $i(S_a^+S_b^--S_b^+S_a^-)$ coupling. A coherent drive at frequency $\omega_d$ is injected from the left (port 1, right-going) or from the right (port 2, left-going) with amplitudes $\varepsilon_{1\rightarrow}$ and $\varepsilon_{2\leftarrow}$. Propagation between the qubits adds a phase $\phi = \omega_d x_{ab}/v_p$, with $v_p$ denoting the phase velocity of the drive. Quantum vacuum input fields are $(a_{\rm in\rightarrow},a_{\rm in\leftarrow})$.
• Figure 2: Forward (F, solid) and backward (B, dashed) transmission under single-sided driving (the counterpropagating input is zero). Panels: (a) coherent component $T_{\mathrm c}$, (b) incoherent component $T_{\mathrm inc}$, and (c) total transmission $T=T_{\mathrm c}+T_{\mathrm inc}$ versus drive power $p/\Gamma$. Curves compare a reciprocal reference ($\mathcal{J}=0$) with a complex exchange ($\mathcal{J}=\Gamma e^{18i\pi/25}$). Parameters: $\Delta_a=\Delta_b=0.5\,\Gamma$, $\phi=9\pi/25$. These phases are chosen to produce pronounced nonreciprocity. All curves show steady-state quantities obtained by numerically solving the master equation [Eq. (\ref{['master']})]. Unless stated otherwise, since our normalized quantities are divided by the input power $p$, we start the $p$-axis at $p=10^{-3}\Gamma$.
• Figure 3: Forward (F, solid) and backward (B, dashed) coherent transmission versus drive power $p/\Gamma$ under single-sided driving (the counterpropagating input is zero). Curves compare with or without DMI ($\theta=\pi,3\pi/4$). Parameters: $\Delta_a=\Delta_b=0.5\,\Gamma$, $\phi=\pi/4$, $|J|=\Gamma$.
• Figure 4: The Purity $\mathrm{Tr}[\rho^2]$ as a function of phase $\phi$ and $\theta$, with (a) anti-symmetry detuning $\Delta_a = -\Delta_b = 0.5J$ and (b) symmetry detuning $\Delta_a = \Delta_b = 0.5J$. The other parameters used are $p=\Gamma=J$.
• Figure 5: The transmission $T$ as a function of symmetry detuning $\Delta = \Delta_a = \Delta_b$ with different exchanges, $\mathcal{J}=0,J e^{3i\pi/2}, J e^{2i\pi/3}$. The other parameters used are $\phi=\pi$, $p=\Gamma=J$.