On-demand analog space-time in superconducting networks: grey holes, dynamical instability and exceptional points

There has been considerable effort to mimic analog black holes and wormholes in solid state systems. Lattice realizations in particular present specific challenges. One of those is that event horizons in general have both white and black hole (grey hole) character, a feature guaranteed by the Nielsen-Ninomiya theorem. We here explore and extend the capability of superconducting circuit hardware to implement on-demand spacetime geometries on lattices, combining nonreciprocity of gyrators with the nonlinearity of Josephson junctions. We demonstrate the possibility of the metric sharply changing within a single lattice point, thus entering a regime where the modulation of system parameters is “trans-Planckian”, and the Hawking temperature ill-defined. Instead of regular Hawking radiation, we find an instability in the form of an exponential burst of charge and phase quantum fluctuations over short time scales - a robust signature even in the presence of an environment. Moreover, we present a loop-hole for the typical black/white hole ambiguity in lattice simulations: exceptional points in the dispersion relation allow for the creation of pure black (or white) hole horizons, at the expense of a radical change in the dynamics of the wormhole interior.

💡 Research Summary

The manuscript investigates how superconducting circuit networks can be engineered to create on‑demand analog space‑time geometries on a lattice, and what novel phenomena emerge when such geometries contain horizons. The authors combine two key ingredients: non‑reciprocal gyrators, which provide direction‑dependent coupling, and the strong nonlinearity of Josephson junctions, which allow the effective inductance to be tuned, even to negative values, by means of a rapid flux‑quench. By spatially varying the effective inductance and gyration strength, the dispersion relation of the collective phase mode (the analog scalar field) can be locally “over‑tilted”, i.e. the group velocity of one propagation direction exceeds the effective light‑cone speed. This creates an apparent horizon separating a normal region (bidirectional signal propagation) from a worm‑hole‑like region (unidirectional propagation).

A central result is that, because the metric can be changed within a single lattice site, the surface gravity (the spatial gradient of the group velocity) can be made extremely large. The corresponding Hawking temperature would be in the 100 mK–1 K range, well above the typical base temperature of dilution refrigerators. However, the authors demonstrate that a true, stationary Hawking radiation does not appear. Instead, the sudden “quench” that creates the horizon triggers a dynamical instability: charge and phase quantum fluctuations grow exponentially in a short burst (tens of nanoseconds). This burst is robust against environmental dissipation because the environment tends to suppress fluctuations rather than amplify them. The instability therefore provides a clear, experimentally accessible signature of the horizon formation, distinct from ordinary thermal noise or relaxation processes.

The paper also addresses a well‑known lattice artifact: the Nielsen‑Ninomiya theorem forces any periodic Brillouin zone to contain at least two zero‑energy crossings, meaning that a horizon on a lattice inevitably has both black‑hole and white‑hole character (a “grey hole”). The authors propose a loophole based on exceptional points (EPs) in the Bogoliubov‑transformed spectrum. By coupling circuit nodes not only to nearest neighbours but also to next‑nearest neighbours, the dispersion inside the wormhole region can acquire a complex eigenvalue branch that avoids a second zero crossing. The spectrum thus detours into the complex plane, and the horizon becomes purely black (signals only flow inward) or purely white (signals only flow outward). This EP‑based design, however, radically changes the interior dynamics: the whole wormhole interior evaporates simultaneously after the quench, rather than radiating only from the horizon.

Methodologically, the authors develop a full quantum‑field‑theoretic description of the circuit. Starting from the lumped‑element Lagrangian, they map the phase field onto a scalar field on a curved background with metric components u(x) and v(x). They perform a Bogoliubov transformation to diagonalize the quadratic Hamiltonian, then use Klich’s determinant formula to compute time‑dependent correlation matrices after the quench. The analytical results are complemented by numerical simulations of charge‑phase variance growth, confirming the exponential burst.

The manuscript also discusses practical implementation. Negative inductance is achieved by a rapid flux pulse that drives a Josephson junction into a regime where its effective inductance L ∝ 1/ cos φ becomes negative. Alternative routes such as 0‑π junctions or multi‑stable JJ designs are mentioned. While long chains (tens of sites) provide a clean theoretical picture, the authors argue that a few‑site prototype already exhibits the essential physics and is within reach of current superconducting‑circuit fabrication capabilities.

Finally, the authors speculate on long‑time behavior. After the initial burst, the system’s energy is redistributed throughout the lattice, leading to a global “evaporation” of the analog horizon. This differs fundamentally from Hawking radiation, which is a steady, thermal flux. The paper connects this phenomenon to the broader field of non‑Hermitian physics, where EPs give rise to unconventional dynamics, and suggests that the observed instability could serve as a tabletop platform for studying back‑reaction of quantum fields on an emergent geometry.

In summary, the work demonstrates that superconducting circuits can realize sharply varying analog metrics, generate horizons, and reveal a new instability‑driven “burst” of quantum fluctuations as a clear experimental signature. By exploiting exceptional points, the authors also show how to lift the intrinsic black/white hole ambiguity of lattice models, at the cost of a dramatically altered interior dynamics. The results open new avenues for analog gravity experiments, non‑Hermitian topological physics, and the exploration of quantum‑field back‑reaction in engineered quantum systems.