Chiral quantum state circulation from photon lattice topology

TL;DR

The paper addresses the challenge of rapid, high-fidelity reset and readout of cavity qubit states in superconducting processors. It introduces a three-cavity, one-qubit cavity-QED setup whose Fock-space Hamiltonian forms a photon lattice with topologically protected chiral boundary modes that enable unidirectional, robust circulation of any photonic state among the cavities. The authors show the circulation period $T$ is independent of $N$ (up to $O(1/N)$ corrections) and that the circulation lifetime scales as $T N^{1/2}$ for parity-preserving perturbations, with a Floquet-engineered path to realize the required three-body interactions. The work demonstrates a practical, topologically protected mechanism for fast cavity reset and readout compatible with current circuit-QED platforms, and notes that the effect persists in the classical limit and remains robust to perturbations via bulk-edge topology.

Abstract

Chiral quantum state circulation is the unidirectional transfer of a quantum state from one subsystem to the next. It is essential to the working of a quantum computer; for instance, for state preparation and isolation. We propose a cavity-QED architecture consisting of three cavities coupled to a qubit, in which \emph{any} photonic state of cavity 1 with sufficiently many photons circulates to cavity 2 after a fixed time interval, and then to cavity 3 and back to 1. Cavity-state circulation arises from topologically protected chiral boundary states in the associated photon lattice and is thus robust to perturbation. We compute the circulation period in the semi-classical limit, demonstrate that circulation persists for time-scales diverging with the total photon number, and provide a Floquet protocol to engineer the desired Hamiltonian. Superconducting qubits offer an ideal platform to build and test these devices in the near term.

Figures (4)

• Figure 1: Topological photon circulation: (a) Three cavities $b_j^\dagger$ interact with a qubit via three-body couplings $G_j$ (b) The Hamiltonian induces hopping on a triangular photon lattice on the Fock space plane $\sum_j n_j = N$ (gray). This model has topological boundary modes which carry photon current (black arrows). (c) The boundary modes result in circulation \ref{['eq:circulator']} of photons between the cavities, as seen in the dynamics of cavity populations $\langle \hat{n}_j \rangle$, shown here for an initial Fock state \ref{['eq:initial_states']}.
• Figure 2: Spectral properties: (a) Rescaled distance $\langle d \rangle$ from the edge of the photon lattice vs energy $E$ for $N=20,30,40$ photons. The band of states crossing $E = 0$ with $\langle d \rangle/N$ close to the LDA boundary value (modes) are boundary modes. (b) Rescaled circulation $\langle \mathcal{C} \rangle$ versus energy for the same $N$ values. The band of boundary modes is chiral as $\langle \mathcal{C} \rangle/gN^2 \neq 0$; indeed the value is close to that predicted by the LDA (dashed).
• Figure 3: Coherent state dynamics: Dynamics of (a) the qubit and (b) the cavities for an initial coherent state $\ket{\psi_0} = \ket{\psi_{\mathrm{coh.}}}$ with mean photon number $\bar{N} =50$. The solid lines in both panels show the semi-classical predictions \ref{['eq:semiclassical_dyn']}.
• Figure 4: Topological robustness: The sample averaged cavity population revivals $\overline{\braket{\hat{n}_3}}$ at stroboscopic times $\overline{t_q}$ for initial state $\ket{\psi_{\mathrm{Fock}}}$ at different values of $N$. The data collapse confirms that the revivals decay on a timescale $\tau \sim \sqrt{N} T$. (Inset) The dispersed wavepacket is visualized on the photon lattice at an intermediate stroboscopic time when $\braket{\hat{n}_3}/N\approx 0.9$. The area of each blue dot is proportional to the probability of the wavepacket on the associated photon lattice site.