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.
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Lecture notes based on the course given by DB at the Winter School "Analogue Gravity in 2026" in Benasque, Spain. 42 pages and 19 figures
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.
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 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.
The Hawking effect is an exciting physical prediction lying at the intersection of the two most successful theories of the past century, namely, Einstein’s theory of relativity and quantum mechanics. In this dissertation, we put special emphasis on the quantum aspects of the Hawking process encoded in the entanglement shared by the emitted fluxes of created quanta. In particular, we employ sharp tools from quantum information theory to quantify the entanglement produced by the Hawking effect throughout the black hole evaporation process. Our framework allows us to extend previous calculations of entanglement to a larger set of cases, for instance, the situation where a black hole is immersed in a thermal bath, such as the cosmic microwave background (CMB), and the quantum state of infalling radiation is, therefore, mixed. Motivated by recent intense experimental efforts, we extend our framework to the case of an optical white-black hole pair analog gravity system created by a strong electromagnetic pulse propagating in a non-linear dielectric medium. One of the main results presented in this dissertation is the development of a numerical code that recreates the Hawking process in such an optical analog. Utilizing this code together with our quantum information tools, we study how different input quantum states of light alter the amount of the entanglement produced in the Hawking pairs. We find that although ambient thermal noise and detector inefficiencies, unsurprisingly, tend to reduce quantum correlations in the Hawking process, when horizons are illuminated with single-mode squeezed states of light, the entanglement generated increases in a tunable manner. As a last application in optical analogs, we investigate the laser configuration in which two strong electromagnetic pulses propagate in a non-linear dielectric medium exchanging Hawking quanta, thus, stimulating each other. In such a setup, we observe that not only the number of Hawking quanta created is exponentially increased but also the entanglement shared between the mode of the electromagnetic field inside the laser cavity with the modes of the field outside the cavity grows with time. We conclude that these novel results open a promising window for the observability of the quantum origin of the Hawking effect in the lab.
Hawking radiation, the spontaneous emission of thermal photons from an event horizon, is one of the most intriguing and elusive predictions of field theory in curved spacetimes. A formally analogue phenomenon occurs at the supersonic transition of a fluid: in this respect, ultracold gases stand out among the most promising systems but the theoretical modelling of this effect has always been carried out in semiclassical approximation, borrowing part of the analysis from the gravitational analogy. Here we discuss the exact solution of a one-dimensional Bose gas flowing against an obstacle, showing that spontaneous phonon emission (the analogue of Hawking radiation) is predicted without reference to the gravitational analogy. Long after the creation of the obstacle, the fluid settles into a stationary state displaying the emission of sound waves (phonons) in the upstream direction. A careful analysis shows that a precise correspondence between this phenomenon and the spontaneous emission of radiation from an event horizon requires additional conditions to be met in future experiments aimed at identifying the occurrence of the Hawking-like mechanism in Bose-Einstein condensates.
Hawking radiation, the spontaneous emission of thermal photons from an event horizon, is one of the most intriguing and elusive predictions of field theory in curved spacetimes. A formally analogue phenomenon occurs at the supersonic transition of a fluid: in this respect, ultracold gases stand out among the most promising systems but the theoretical modelling of this effect has always been carried out in semiclassical approximation, borrowing part of the analysis from the gravitational analogy. Here we discuss the exact solution of a one-dimensional Bose gas flowing against an obstacle, showing that spontaneous phonon emission (the analogue of Hawking radiation) is predicted without reference to the gravitational analogy. Long after the creation of the obstacle, the fluid settles into a stationary state displaying the emission of sound waves (phonons) in the upstream direction. A careful analysis shows that a precise correspondence between this phenomenon and the spontaneous emission of radiation from an event horizon requires additional conditions to be met in future experiments aimed at identifying the occurrence of the Hawking-like mechanism in Bose-Einstein condensates.
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.