Quantum simulation of the bosonic Kitaev chain

Analog quantum simulation (AQS) offers a promising approach to studying classically intractable quantum systems, particularly lattice models with topological properties. These systems often suffer from the sign problem, making traditional methods like quantum Monte Carlo unsuitable. Recent research has focused on non-Hermitian systems, which exhibit unique phenomena like chiral transport and the non-Hermitian skin effect (NHSE). The bosonic Kitaev chain (BKC), a 1D bosonic tight-binding model with hopping and pairing terms, is a prime example. Despite being Hermitian, it displays effective non-Hermitian dynamics and topological properties. This paper details the experimental implementation of the BKC using a multimode superconducting parametric cavity, offering a platform to explore genuinely quantum non-Hermitian effects without the challenges of dissipative systems.

The study builds upon previous work demonstrating the feasibility of AQS using multimode superconducting parametric cavities, specifically simulating a plaquette of the bosonic Creutz ladder. Similar work has been conducted in classical non-Hermitian optics and chiral photon transport. The BKC, analogous to the fermionic Kitaev chain, has been theoretically explored, predicting phase-dependent chiral transport and NHSE. This work aims to experimentally verify these predictions and further explore the potential of the AQS platform for studying topological non-Hermitian systems.

The researchers implemented a 3-site BKC in synthetic dimensions using a multimode superconducting parametric cavity. Cavity modes represent lattice sites. Parametric pumping at mode-difference and mode-sum frequencies creates complex hopping and pairing terms. The magnitudes and phases of these pumps control the Hamiltonian parameters. Open and periodic boundary conditions were implemented by controlling the pump tones. Measurements were performed using a vector network analyzer (VNA) to determine eigenmode frequencies from reflection coefficients and phase-sensitive transport measurements to probe chiral transport. A twisted-tubes picture was used to intuitively explain the role of individual hopping and pairing phases. Input-output theory was used to quantitatively analyze the transport, considering signal and idler frequencies and the effects of both hopping and pairing terms. The equations of motion for the position and momentum quadratures were derived, including damping terms to account for photon loss. The spectrum of the dynamical matrix was analyzed for open and periodic boundary conditions. The experimental setup involved injecting a signal into the central site and measuring reflected and transported signals at all sites.

The experiment successfully demonstrated key features of the BKC: 1. **Phase-dependent chiral transport:** The researchers observed that the transport magnitude was strongly dependent on the input phase, with maximal transport at the favored phase and strong suppression at the orthogonal phase. This phase sensitivity, more pronounced in the chiral chain, demonstrated the chiral nature of transport. 2. **Quadrature wavefunction localization:** In the chiral chain, the x and p quadrature wavefunctions exhibited strong localization at opposite ends of the chain, a clear signature of the NHSE. In the trivial chain, the wavefunctions were delocalized. This contrasts with the delocalized quadratures observed in the trivial chain. 3. **Sensitivity to boundary conditions:** Measurements on a separate device with periodic boundary conditions revealed discontinuities in the spectrum under certain phase conditions. These discontinuities indicated the system's approach to dynamical instability, a direct consequence of the non-trivial topology in the chiral regime. This instability was linked to the alignment of the tubes (twisted-tubes picture), creating circulating gain that leads to amplification and instability under periodic boundary conditions. The experimental results were consistent with the theoretical predictions based on the input-output theory and the twisted-tubes model. The gauge-invariant phase was calibrated by injecting a signal into the central site and observing the phase-dependent transport to the ends.

The experimental results successfully demonstrate the creation and control of non-Hermitian topological effects in a quantum simulator. The observation of chiral transport, quadrature wavefunction localization, and boundary condition sensitivity provides strong evidence for the nontrivial topology of the BKC. The agreement between experiment and theory validates the modeling approach and the accuracy of the simulation. These results expand the set of topologically nontrivial models that can be simulated under genuinely quantum conditions. The twisted-tubes picture proved to be a powerful tool for understanding the observed transport phenomena.

This work successfully demonstrated the quantum simulation of the bosonic Kitaev chain, showcasing phase-dependent chiral transport, quadrature wavefunction localization, and sensitivity to boundary conditions. These findings provide experimental evidence for the non-Hermitian skin effect and nontrivial topology. Future research could explore longer chains, investigate many-body non-Hermitian dynamics, and explore the use of this system as a phase-dependent amplifier or for generating entangled multimode states.

The study focused on a 3-site chain, limiting the exploration of the NHSE's scaling behavior with system size. The absolute calibration of the pump phases at the sample was challenging, relying on a twisted-tubes picture for interpretation. The experimental observation of dynamical instability was limited to the region near the instability threshold, and exploring this in more detail could provide further insights. Also, the current design and setup can only handle three lattice sites, limiting scalability.