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.
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.
The Hawking effect can be understood as a broad kinematic phenomenon associated with mode behavior near a horizon. While astrophysical black holes produce one specific realization of this radiation, this perspective inspires extensive theoretical and experimental efforts to create event horizons in diverse physical systems to observe the resulting analogue Hawking emission. One of the most successful realizations is the fiber-optical analogue, based on nonlinear quantum optics. In these notes, we introduce and motivate this system while outlining the theoretical concepts underlying the gravitational analogy. Finally, we review key experiments and discuss their impact on the field.
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 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.
We introduce a convenient set of analytical tools (the Gaussian formalism) and diagrams (symplectic circuits) to analyze multimode scattering events in analogue gravity, such as pair creation \`a la Hawking by black hole and white hole analogue event horizons. The diagrams prove to be valuable Ans\"atze for the scattering dynamics, especially in settings where direct analytic results are not straightforward and one must instead rely on numerical simulations. We use these tools to investigate entanglement generation in single- and multihorizon scenarios, in particular when the Hawking process is stimulated with classical (e.g., thermal noise) and nonclassical (e.g., single-mode squeezed vacuum) input states---demonstrating, for instance, that initial squeezing can enhance the production of entanglement and overcome the deleterious effects that initial thermal fluctuations have on the output entanglement. To make further contact with practical matters, we examine how attenuation degrades quantum correlations between Hawking pairs. The techniques that we employ are generally applicable to analogue gravity setups of (Gaussian) bosonic quantum systems, such as analogue horizons produced in optical analogues and in Bose-Einstein condensates, and should be of great utility in these domains. We show the applicability of these techniques by putting them in action for an optical system containing a pair white-black hole analogue, extending our previous analysis of [Phys. Rev. Lett. 128, 091301 (2022)].
The aim of this thesis is to highlight applications of quantum optics in two very distinct fields: space-based quantum communication and the Hawking effect in analogue gravity. Regarding the former: We simulate and analyze a constellation of satellites, equipped with entangled photon-pair sources, which provide on-demand entanglement distribution ser- vices to terrestrial receiver stations. Satellite services are especially relevant for long-distance quantum-communication scenarios, as the loss in satellite-based schemes scales more favor- ably with distance than in optical fibers or in atmospheric links, though establishing quantum resources in the space-domain is expensive. We thus develop an optimization technique which balances both the number of satellites in the constellation and the entanglement-distribution rates that they provide. Comparisons to ground-based quantum-repeater rates are also made. Overall, our results suggest that satellite-based quantum networks are a viable option for establishing the backbone of future quantum internet. Regarding the latter: The Hawking effect was discussed in the astrophysical context of the spontaneous decay of black holes into blackbody radiation, i.e. Hawking radiation. However, this effect seems to be universal, appearing anywhere that an event horizon (a region which restricts the flow of information to one direction) forms. Here, we analyze the Hawking effect in an optical-analogue gravity system, building on prior theoretical results regarding this effect in dielectric media. We provide a simplification of the process via the Bloch- Messiah decomposition, which allows us to decompose the Hawking effect into a discrete set of elementary processes. With this simplification and utilizing a popular entanglement measure (the logarithmic negativity), we examine the quantum correlations of the stimulated Hawking effect, explicitly showing that an environmental background temperature, along with backscattering, can lead to entanglement “sudden-death", even when the number of entangled Hawking-pairs is comparatively large. We also discuss the prospect of enhancing and “reviving" entanglement using single-mode, non-classical resources at the input. Though much of the discussion is phrased in terms of an optical-analogue model, the methods used and results obtained apply just as well to a variety of other systems supporting this effect. Finally, we provide decompositions of more exotic scenarios consisting of e.g. a white-hole– black-hole pair which share an interior region.
The optical fiber is a revolutionary technology of the past century. It enables us to manipulate single modes in nonlinear interactions with precision at the quantum level without involved setups. This setting is useful in the field of analogue gravity (AG), where gravitational phenomena are investigated in accessible analogue lab setups. These lecture notes provide an account of this AG framework and applications. Although light in nonlinear dielectrics is discussed in textbooks, the involved modelling often includes many assumptions that are directed at optical communications, some of which are rarely detailed. Here, we provide a self-contained and sufficiently detailed description of the propagation of light in fibers, with a minimal set of assumptions, which is relevant in the context of AG. Starting with the structure of a step-index fiber, we derive linear-optics propagating modes and show that the transverse electric field of the fundamental mode is well approximated as linearly polarized and of a Gaussian profile. We then incorporate a cubic nonlinearity and derive a general wave envelope propagation equation. With further simplifying assumptions, we arrive at the famous nonlinear Schrödinger equation, which governs fundamental effects in nonlinear fibers, such as solitons. As a first application in AG, we show how intense light in the medium creates an effective background spacetime for probe light akin to the propagation of a scalar field in a black hole spacetime. We introduce optical horizons and particle production in this effective spacetime, giving rise to the optical Hawking effect. Furthermore, we discuss two related light emission mechanisms. Finally, we present a second optical analogue model for the oscillations of black holes, the quasinormal modes, which are important in the program of black hole spectroscopy.