Perfect quantum state transfer in a dispersion-engineered waveguide

TL;DR

The paper tackles the fundamental limitation of time-reversal symmetry in quantum state transfer within a chiral waveguide by proposing a passive, dispersion-engineered waveguide design that passively time-reverses the emitted photon pulse. It derives analytic dispersion relations for both well-separated and closely spaced qubits, and uses multiparameter optimization to enhance transfer fidelity in intermediate regimes, achieving near-unity transfer (≥98%). An inhomogeneous, spatially tailored dispersion segment is introduced to render the scheme robust to variations in qubit separation, complemented by adjoint-based optimization to push performance toward unity. The approach is fully passive and compatible with on-chip photonics, with potential extensions to quantum memories and multi-excitation state transfers, highlighting engineered dispersion as a powerful resource for waveguide QED networks.

Abstract

High-fidelity state transfer is fundamentally limited by time-reversal symmetry: one qubit emits a photon with a certain temporal pulse shape, whereas a second qubit requires the time-reversed pulse shape to efficiently absorb this photon. This limit is often overcome by introducing active elements. Here, we propose an alternative solution: by tailoring the dispersion relation of a waveguide, the photon pulse emitted by one qubit is passively reshaped into its time-reversed counterpart, thus enabling perfect absorption. We analytically derive the optimal dispersion relations in the limit of small and large qubit-qubit separations, and numerically extend our results to arbitrary separations via multiparameter optimization. We further propose a spatially inhomogeneous waveguide that renders the state transfer robust to variations in qubit separations. In all cases, we obtain near-unity transfer fidelity (>= 98%). Our dispersion-engineered waveguide provides a compact and passive route toward on-chip quantum networks, highlighting engineered dispersion as a powerful resource in waveguide quantum electrodynamics.

Figures (3)

• Figure 1: State transfer between two qubits coupled to a chiral waveguide with (a) linear and (b) engineered dispersions. Snapshots of the emitted photon pulse are shown at different times. (c) Dispersion relations required for perfect state transfer (see text for details) for different qubit-qubit distances $d$ (normalized by the pulse width $v_\mathrm{g} / \gamma$). (d) Qubit population dynamics in the dispersion-engineered waveguide (solid lines) and the linear-dispersion waveguide (dashed red line for the second qubit).
• Figure 2: (a) Maximum absorption probability of the second qubit using the analytical [orange, see Eq.\ref{['eq:dispersion']}], small-distance [green, see Eq. \ref{['eq:dispersion_d0']}] and numerically optimized [purple] dispersion relations. As before, we assume $\gamma=\pi\times10^{-4}\omega_\mathrm{q}$. In the small-distance limit, the first qubit decays biexponentially under the analytical dispersion of Eq. (\ref{['eq:dispersion']}). The decay rates and weights [defined in Eq. \ref{['eq:biexponential']}] are plotted against the qubit distance $d$ in (b). (c) Dispersion relation at $d=2v_\mathrm{g}/\gamma$ where the linear contribution $\omega_l \equiv \omega\Delta t/d$ has been subtracted for better visualization. (d) Populations as a function of time for the dispersion relations of panel (c). The dashed lines are for the analytical dispersion; the solid lines are for the numerically optimized dispersion.
• Figure 3: (a) Maximal excitation probability of the second qubit (dashed gray line) versus deviation $\Delta d$ from the assumed separation $d$ [see (b) for an illustration]. The state transfer fidelity decreases with $|\Delta d|$. We propose to solve this by a spatially inhomogeneous waveguide, whose dispersion (minus the linear part, for visibility) is shown by the 3D mesh grid in (b). This dispersion varies adiabatically in space within a length $2L$, minimizing reflection and effectively suppressing it for $L\gtrsim \lambda_q\equiv2\pi v_g/\omega_\mathrm{q}$ (panel c). The dispersion of this segment is chosen to time-reverse the pulse. As a result, the maximum occupation of qubit $2$ is near unity regardless of the distance variation [(a), red line].