Hawking radiation is a fundamental result of quantum field theory in curved spacetime, yet its direct observation remains beyond current experimental capabilities. Circuit quantum electrodynamics provides a practical platform for realizing analogue systems where Hawking-like radiation may be studied under controlled laboratory conditions. In this work, we analyze two superconducting-circuit analogues of Schwarzschild black holes: a tunable dc-SQUID transmission line and a SNAIL-based transmission line supporting solitonic solutions of the KdV equation. We investigate the conditions under which these architectures can generate an observable Hawking temperature and study the impact of dissipation and thermal noise using an open quantum systems approach. To assess the observability of the Hawking signal, we propose complementing particle number measurements with estimates of the Hilbert-Schmidt distance to the thermal bath. Our analysis establishes practical detectability thresholds and shows that Hawking temperatures above approximately 73 mK remain distinguishable under realistic experimental conditions. While the tunable transmission line architecture can reach temperatures of about 113 mK and therefore appears more viable, the solitonic model requires further optimization and more demanding experimental conditions.
Hawking radiation is a fundamental result of quantum field theory in curved spacetime, yet its direct observation remains beyond current experimental capabilities. Circuit quantum electrodynamics provides a practical platform for realizing analogue systems where Hawking-like radiation may be studied under controlled laboratory conditions. In this work, we analyze two superconducting-circuit analogues of Schwarzschild black holes: a tunable dc-SQUID transmission line and a SNAIL-based transmission line supporting solitonic solutions of the KdV equation. We investigate the conditions under which these architectures can generate an observable Hawking temperature and study the impact of dissipation and thermal noise using an open quantum systems approach. To assess the observability of the Hawking signal, we propose complementing particle number measurements with estimates of the Hilbert-Schmidt distance to the thermal bath. Our analysis establishes practical detectability thresholds and shows that Hawking temperatures above approximately 73 mK remain distinguishable under realistic experimental conditions. While the tunable transmission line architecture can reach temperatures of about 113 mK and therefore appears more viable, the solitonic model requires further optimization and more demanding experimental conditions.
Abstract Hawking radiation is one of the quantum features of a black hole that can be understood as a quantum tunneling across the event horizon of the black hole, but it is quite difficult to directly observe the Hawking radiation of an astrophysical black hole. Remarkable experiments of analogue black holes on various platforms have been performed. However, due to the experimental difficulty of accurately constructing curved spacetime and precisely measuring the thermal spectrum, Hawking radiation and its quantum nature, such as entanglement, have not been adequately investigated. Based on the recent architecture breakthrough of tunable couplers for superconducting processors, we experimentally realize an analogue black hole using our newly developed chip with a chain of 10 superconducting transmon qubits with interactions mediated by 9 transmon-type tunable couplers. By developing efficient techniques to engineer the couplings between qubits via tuning couplers, we achieve both flat and curved spacetime backgrounds. The quantum walks of quasi-particle in the curved spacetime reflect the gravitational effect near the black hole, resulting in the behavior of Hawking radiation. By virtue of the state tomography measurement of all 7 qubits outside the analogue event horizon, we show that Hawking radiation can be verified. In addition, an entangled pair is prepared inside the horizon and the dynamics of entanglement in the curved spacetime is directly measured. Our results would stimulate more interests to explore the related features of black holes using the programmable superconducting processor with tunable couplers.
A black hole laser in analogues of gravity amplifies Hawking radiation, which is unlikely to be measured in real black holes, and makes it observable. There have been proposals to realize such black hole lasers in various systems. However, no progress has been made in electric circuits for a long time, despite their many advantages such as high-precision electromagnetic wave detection. Here we propose a black hole laser in Josephson transmission lines incorporating metamaterial elements capable of producing Hawking-pair propagation modes and a Kerr nonlinearity due to the Josephson nonlinear inductance. A single dark soliton obeying the nonlinear Schrödinger equation produces a black hole-white hole horizon pair that acts as a laser cavity through a change in the refractive index due to the Kerr effect. We show that the resulting laser is a squeezed-state laser characterized by squeezing parameters. We also evaluate the degree of quantum correlation between Hawking and its partner radiations using entanglement entropy which does not require simultaneous measurements between them. As a result, the obtained entanglement entropy depending on the soliton velocity provides strong evidence that the resulting laser is derived from Hawking radiation with quantum correlation generated by pair production from the vacuum.
Abstract The black hole information paradox arises from the tension between the thermal spectral properties of Hawking radiation and the unitarity principle in quantum mechanics. To explore the dynamical evolution characteristics of quantum fields in this context, we employ the standard quantization formalism for Dirac fields in Schwarzschild spacetime and investigate the coupling structure of particle and antiparticle modes within a framework that transcends the single-mode approximation. By calculating the states of externally observable subsystems, we systematically derive the evolution of concurrence and first-order coherence as functions of the Hawking temperature. Additionally, we assess the impact of varying initial parameters on these quantities. We further contrast the quantum entanglement differences between the observable exterior region and the black hole interior across diverse temperature regimes. These results provide valuable insights into the evolution of entanglement and coherence in curved spacetime.
The circuit dynamics constructed by traveling-wave parametric amplifiers (TWPA), using superconducting nonlinear asymmetric elements (SNAILs), are known to be approximately described by the Korteweg-de Vries (KdV) or modified KdV equations in the continuum limit and admit soliton solutions. The soliton spatially modulates the effective propagation velocity of the weak probe field, which leads to the effective realization of the causal structure of the analogue event horizons in the SNAIL-TWPA circuit system. In this paper, we derive the master equation for the weak probe field where the background soliton acts as an effective potential. We show the absence of normalizable negative modes in the SNAIL-TWPA circuit system by using the language of supersymmetric quantum mechanics. We also present the first study of quasi-normal modes (QNM) of the SNAIL-TWPA analogue black-white hole system by semi-analytic and numerical methods. Based on the resultant QNM frequency, we clarify the timescale at which nonlinear dispersion becomes effective in the SNAIL-TWPA circuit system and demonstrate how ringdown is excited.
The propagation of fluctuations in the velocity potential of an inviscid, irrotational fluid is governed by a wave equation very similar to that governing the propagation of massless scalar fields in curved spacetime. This similarity allows certain fluid systems to be used as experimentally realisable models for objects that cannot be studied under controlled conditions, such as black holes and ultrarelativitsic rotating stars. The analogy applies only to the propagation of fields in a fixed background, not to the behaviour of the background itself. However, even this limited similarity has excited a great deal of interest from researchers, since it suggests that phenomena such as superradiance and Hawking radiation may have analogues in superfluids. In recent years, experimental advances in the creation and manipulation of Bose-Einstein condensates have provided researchers with very low temperature systems possessing a uniquely simple microscopic theory. Furthermore, under certain long-length-scale approximations, Bose-Einstein condensates can be described as classical irrotational inviscid fluids, and therefore can be treated as analogues of appropriate gravitational systems. We present a comprehensive and detailed critical review of the mean-field theory of Bose-Einstein condensates, the conditions under which Bose-Einstein condensates can be treated as an analogue gravity system, the construction of analogue black holes, and several derivations of Hawking radiation and analogue Hawking radiation. The interdisciplinary nature of analogue gravity means that the relevant results are widely scattered in the literature, and we consider this critical review and discussion of the relevant literature to be a central and noteworthy element of the project. We then analyse in detail a recent derivation of analogue Hawking radiation in Bose-Einstein condensates as a consequence of quantum depletion. We elucidate the methodology and the physical meaning of the results by comparison with the derivations of Hawking radiation considered previously, and discuss possible extensions and improvements. We also present an original investigation of analogue superradiance in simple vortices, with the vortex density profile chosen to mimic a realistic vortex in a Bose-Einstein condensate. We find that superradiant amplification occurs and is likely to be significant, but our long-length-scale approximation is of dubious validity near the scattering point.
Hawking radiation is a fundamental spontaneous phenomenon in which the event horizon of a black hole transforms the vacuum state into a pair of correlated particles: the Hawking radiation and its partner. This emission can also be stimulated by a state other than the vacuum. A similar phenomenon, known as analogue Hawking radiation, has been observed across various physical systems, but experimental realizations have largely remained in the classical regime. This work presents an experimental verification of analogue Hawking radiation stimulated by a single-particle state, producing a verifiably single-photon Hawking output. Using heralded single photons generated via spontaneous four-wave mixing, we stimulate the analogue Hawking effect in an optical fiber. We characterize the resulting Hawking signal by measuring its spectral dependence, intensity scaling, and heralded second-order correlation. Our results establish a platform for exploring quantum correlations and entanglement in analogue gravity. Researchers experimentally demonstrate analogue Hawking radiation stimulated by a single photon in an optical fiber. This work enables new studies of quantum effects in nonlinear optics and analogue gravity.