Many-body quantum optics in a cascaded chiral network

Technical Summary: Many-body quantum optics in a cascaded chiral network

Problem Statement
Chiral quantum emitters, which interact with light exclusively in one propagation direction, are theoretically predicted to host novel many-body regimes of light and matter. These systems enable ordered, one-way interactions mediated by photons, allowing for the stabilization of entangled states and the formation of photon bound states that are inaccessible in reciprocal (bidirectional) systems. However, experimental realization has been hindered by stringent requirements for the emitter-bath interface: emitters must couple exclusively to one direction with near-unit probability while suppressing all other decay channels. Previous implementations faced significant trade-offs: optical systems often suffered from frequency disorder and probabilistic coupling, while microwave implementations were limited to one or two emitters due to loss, frequency crowding, and the use of bulky off-chip components. Furthermore, composite interfaces often lost directionality beyond the single-photon regime, preventing access to strongly nonlinear many-body dynamics.

Methodology
The authors realized a deterministic cascaded network comprising four superconducting qubits coupled to a shared microwave waveguide. The architecture addresses previous limitations through the following design choices:

• Device Architecture: The system consists of two device chips connected by a 45 cm superconducting aluminum cable, forming a four-qubit chain. Each chip contains two "giant atom" emitters (transmon qubits) coupled to a coupled-cavity array (CCA) waveguide at two distinct points.
• Chiral Coupling Mechanism: Directionality is achieved via parametric driving of flux-tunable couplers embedded within the CCA. By modulating the coupler frequencies, a synthetic gauge field is created in the emitter-coupler loop, breaking time-reversal symmetry. This imparts specific phases ($\phi_L$ and $\phi_R$) to the coupling, resulting in unidirectional emission with high Purcell factors ($P_{1D} \sim 20$) and directionality ratios ($\eta_d \sim 100$).
• Scalability Solution: Instead of using dedicated spectral filters that cause frequency crowding, the authors embed tunable couplers directly within the CCA. The array's bandgap naturally suppresses parasitic sidebands, allowing for multiple emitters without compromising coherence or directionality.
• Experimental Protocols:
  • Elastic Scattering: Weak coherent drives were used to measure transmission and phase accumulation, verifying the cascaded nature of the system.
  • Driven-Dissipative Stabilization: The chain was driven by a continuous microwave tone to exploit collective decay into the waveguide. By tuning qubit detunings, the system was steered toward specific entangled steady states (dimers or multipartite states).
  • Photon Sorting: Weak coherent pulses were scattered off the chain to observe the temporal sorting of output photons based on photon number, a signature of strong photon-photon interactions.

Key Contributions and Results

1. Realization of a Deterministic Cascaded Network: The authors demonstrated the first experimental realization of a cascaded network with more than two emitters that maintains deterministic chiral coupling. The system spans from millimeters (on-chip) to nearly half a meter (cable), with measured transmission following the product of individual transmissions ($t = \prod t_j$) and exhibiting a $2\pi N$ phase accumulation for $N$ qubits.
2. Stabilization of Reconfigurable Entanglement: By exploiting the absence of information backflow in the chiral chain, the team stabilized two distinct types of entangled steady states:
   • Dimerized States: Achieved by setting specific detunings ($\delta_1 = -\delta_2, \delta_3 = -\delta_4$), resulting in finite concurrence between adjacent qubit pairs (1-2 and 3-4) while decoupling the pairs from each other.
   • Genuine Multipartite Entanglement: Achieved by rearranging detunings ($\delta_1 = -\delta_4, \delta_2 = -\delta_3$), resulting in finite concurrence between all qubit pairs. The authors measured a genuine multipartite negativity (GMN) of $6.3 \times 10^{-2}$, confirming the presence of genuine multipartite entanglement, a regime inaccessible to reciprocal waveguide schemes which typically only support pairwise entanglement.
   • Directionality Verification: Experiments confirmed that the upstream dimer's dynamics were unaffected by the presence of the downstream dimer, demonstrating the one-way nature of the interaction.
3. Observation of Photon Bound States: By scattering weak coherent pulses, the authors observed photons sorted in time by their photon number. Due to the photon-number dependence of the Wigner delay ($\sim 1/n^2$), multi-photon bound states arrived earlier than single-photon components. The measured output field and correlators ($G^{(1)}$ and $G^{(2)}$) revealed distinct peaks corresponding to two- and three-photon bound states, providing direct evidence of strong, distributed photon-photon interactions mediated by the emitters.

Significance
The paper claims to provide the first experimental access to many-body light-matter regimes predicted for cascaded quantum systems. By overcoming the bottlenecks of loss, frequency crowding, and nonlinearity, this work establishes a platform for exploring:

• Matter Regimes: The stabilization of pure multipartite entangled dark states and topologically ordered states that are robust against decoherence and do not require precise phase-length matching, unlike bidirectional systems.
• Light Regimes: The generation of correlated multi-photon transport and photon bound states, which serve as a resource for photonic quantum logic and metrology.

The authors position this work as a concrete entry point for future developments in modular superconducting quantum computing (via all-to-all connectivity mediated by traveling photons) and the exploration of emergent many-body phenomena in larger chiral arrays. They note that while current Purcell factors are limited by thermal waveguide occupation, the demonstrated architecture provides the necessary foundation for scaling to tens of emitters and accessing the full many-body landscape of cascaded systems.