Quantum nonreciprocity from qubits coupled by Dzyaloshinskii-Moriya interaction

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.

💡 Research Summary

This paper presents a comprehensive theoretical investigation of quantum nonreciprocity generated by an engineered Dzyaloshinskii‑Moriya interaction (DMI) between two two‑level emitters (qubits) coupled to an otherwise symmetric one‑dimensional waveguide. The authors start by situating their work within the broader context of nonreciprocal photonic devices, noting that traditional approaches rely on magnetic bias, spatiotemporal modulation, synthetic gauge fields, or intrinsic chirality of the waveguide. In contrast, they demonstrate that a purely antisymmetric exchange term—embodied by a complex inter‑qubit coupling J e^{iθ}—can break left‑right symmetry even when the waveguide itself is non‑chiral.

The model consists of two qubits separated by a distance x_ab along the waveguide, each coupled to the guided mode with rate Γ and to ancillary loss channels with rates γ_a, γ_b. A coherent drive of frequency ω_d is injected from either side, and the propagation phase between the qubits is ϕ = ω_d x_ab/v_p. The Hamiltonian includes the qubit detunings Δ_a, Δ_b, the complex exchange term (J e^{iθ} S⁺_a S⁻_b + J e^{-iθ} S⁻_a S⁺b), and the drive couplings. Within the Born‑Markov approximation the dynamics are captured by a Lindblad master equation that features two directional jump operators c{→}=S⁻_a+e^{-iϕ}S⁻b and c{←}=S⁻_a+e^{iϕ}S⁻_b. Input‑output relations connect the intracavity dipoles to the transmitted and reflected fields, allowing the authors to compute coherent (elastic) and incoherent (inelastic) components of the transmission.

A key insight is that the DMI introduces an imbalance A_{b→a}−A_{a→b}=2J sinθ between the effective hopping amplitudes from qubit a to b and vice versa. When θ≠0,π, this imbalance directly biases the scattering pathways, breaking reciprocity even for symmetric detunings. The authors identify special parameter sets (e.g., J=Γ, θ=ϕ+π/2) that cancel one direction of coupling entirely, yielding a one‑way interaction. Numerical solutions of the master equation reveal that, at low drive power, the coherent transmission dominates and the system behaves linearly; as the drive strength increases, the forward and backward transmissions diverge dramatically. In the forward direction the coherent component can be strongly suppressed while the incoherent component is enhanced, whereas the opposite occurs for backward driving. This tunable balance between elastic and inelastic scattering is governed by the pair (ϕ,θ).

Beyond transmission, the paper explores steady‑state purity. By analyzing the condition ⟨c_μ†c_μ⟩=|⟨c_μ⟩|² for each direction μ, the authors find that pure steady states exist only when the propagation phase satisfies ϕ=nπ (n integer). Under this condition the jump operators become dark, and the system settles into a pure state |P⟩ that is a superposition of the ground state |gg⟩ and an antisymmetric single‑excitation Bell‑like state |D_n⟩=(|eg⟩−(−1)ⁿ|ge⟩)/√2. These pure states yield perfect transparency (unit transmission, zero reflection) for both forward and backward driving, independent of the drive strength. The existence of such states requires a finite DMI for symmetric detunings, while for antisymmetric detunings they persist even with a purely real exchange.

Entanglement is quantified using concurrence. At the pure‑state points the concurrence is reciprocal and admits a closed‑form expression. Away from these points, the concurrence becomes highly nonreciprocal: the magnitude and even the qualitative behavior of entanglement differ between forward and backward driving, and can be tuned continuously by adjusting θ and ϕ. This demonstrates that DMI provides a versatile knob for engineering direction‑dependent quantum correlations.

Photon statistics are examined through the second‑order correlation function g^{(2)}(0). In the absence of DMI, superbunching (g^{(2)}>2) appears primarily in the transmitted field, reflecting strong two‑photon correlations generated by the nonlinear qubit response. Introducing DMI redistributes these correlations: superbunching shifts to the reflected field while the transmitted field becomes more Poissonian. This redistribution is a direct consequence of the asymmetric scattering pathways and highlights DMI as a tool for shaping nonclassical light.

The authors conclude that a Dzyaloshinskii‑Moriya interaction, even when implemented in a non‑chiral waveguide, can simultaneously produce quantum nonreciprocal transmission, direction‑dependent entanglement, and controllable photon‑statistics reshaping. They discuss possible experimental platforms, including superconducting circuits with parametrically engineered complex couplings, magnetic bilayers with spacer‑mediated antisymmetric exchange, and synthetic gauge‑field schemes. The work opens avenues for designing isolators, routers, and superbunching light sources that do not rely on magnetic bias or intrinsic waveguide chirality, and suggests extensions to larger qubit arrays, multimode waveguides, and hybrid optomechanical systems.