These lecture notes develop polariton fluids of light as programmable simulators of quantum fields on tailored curved spacetimes, with emphasis on acoustic horizons and the Hawking effect. After introducing exciton-polariton physics in semiconductor microcavities, we detail the theoretical tools to study the mean field and the quantum hydrodynamics of this driven-dissipative quantum system. We derive the mapping to relativistic field theories and cast horizon physics as a pseudounitary stationary scattering problem. We present the Gaussian optics circuit that describes observables and fixes detection weights for the horizon modes in near- and far-field measurements. We provide a practical experimental toolkit (phase-imprinted flows, coherent pump-probe spectroscopy, balanced and homodyne detection) and a step-by-step workflow to extract amplification, quadrature squeezing, and entanglement among correlations. Finally, we discuss the potential of this platform to investigate open questions in quantum field theory in curved spacetime, such as near horizon effects and quasinormal modes, as well as other phenomena universal to rotating geometries, from rotational superradiance to dynamical instabilities. We further outline the interplay between rotational superradiance and the Hawking effect, proposing to spatially resolve measurements as a roadmap for `dumb hole spectroscopy' and the study of entanglement dynamics in curved spacetimes.
These lecture notes develop polariton fluids of light as programmable simulators of quantum fields on tailored curved spacetimes, with emphasis on acoustic horizons and the Hawking effect. After introducing exciton-polariton physics in semiconductor microcavities, we detail the theoretical tools to study the mean field and the quantum hydrodynamics of this driven-dissipative quantum system. We derive the mapping to relativistic field theories and cast horizon physics as a pseudounitary stationary scattering problem. We present the Gaussian optics circuit that describes observables and fixes detection weights for the horizon modes in near- and far-field measurements. We provide a practical experimental toolkit (phase-imprinted flows, coherent pump-probe spectroscopy, balanced and homodyne detection) and a step-by-step workflow to extract amplification, quadrature squeezing, and entanglement among correlations. Finally, we discuss the potential of this platform to investigate open questions in quantum field theory in curved spacetime, such as near horizon effects and quasinormal modes, as well as other phenomena universal to rotating geometries, from rotational superradiance to dynamical instabilities. We further outline the interplay between rotational superradiance and the Hawking effect, proposing to spatially resolve measurements as a roadmap for `dumb hole spectroscopy' and the study of entanglement dynamics in curved spacetimes.
The Hawking effect amplifies fluctuations in the vicinity of horizons, both in black holes and in analogue platforms.
Here, we consider a polariton simulator and numerically examine the \emph{stimulated} Hawking effect using a coherent probe incident on the horizon from the exterior.
We implement an experimentally realistic effective spacetime that supports a quasinormal mode (QNM) in the vicinity of the horizon.
We find that the stimulated Hawking effect manifests as transmission into a negative-energy Bogoliubov channel inside the horizon, consistent with pseudo-unitary Bogoliubov scattering.
Moreover, transmission across the horizon peaks at the QNM frequency.
The computed spectral signatures provide a practical guide for future experimental investigations of the Hawking effect and its interplay with QNMs, an open question in quantum field theory in curved spacetime.
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.
Excitons-polaritons of semiconductor microcavities are quasiparticles originating from the dressing of optical cavity photons by the interactions between quantum well electron-hole pairs. In planar geometry, their belonging to the family of quantum fluids has been many times demonstrated through the observation of macroscopic coherence phenomena, such as superfluidity and Bose-Einstein condensation. Like ultracold atoms, polaritons support on their surface a set of collective excitations, the Bogoliubov modes, whose spectrum encompasses the key information to describe the dynamics of quantum fluids. In this thesis, we present a wide variety of results concerning the detection and control of such modes in different configurations. Thanks to the development of a new high-resolution coherent spectroscopy method, we carried out a detailed study of the spectrum of polariton collective excitations. In particular, we highlighted the effects of the driven-dissipative nature of the system on the fundamental dynamics of the fluid, by investigating the interplay between the Bogoliubov modes and the polariton bistability under coherent pumping. This was the opportunity to reveal, in addition to the well-known phonon-type excitations, precursors of dynamical instability and the so-called ghost branch. Moreover, we studied the behavior of out-of-equilibrium phase transitions: first, via the effect of the system dimension on the bistability and, second, with the onset of a Goldstone mode, as a result of a spontaneous symmetry breaking in a parametric oscillation regime. Finally, we designed a pumping geometry that directly controls the instability modes between dark solitons of a pair guided by an intensity channel, leading to the formation of vortex-antivortex streets in the density.
Analogue gravity explores how collective excitations in condensed matter systems can reproduce the behavior of fields in curved spacetimes. An important example is the acoustic black holes that can occur for sound in a moving fluid. In these lecture notes, we focus on atomic Bose-Einstein condensates (BECs), quantum fluids that provide an interesting platform for analogue gravity studies thanks to their accurate theoretical description, remarkable experimental control, and ultralow temperatures that allow the quantum nature of sound to emerge. We give a pedagogical introduction to analogue black holes and the theoretical description of BECs and their elementary excitations, which behave as quantum fields in curved spacetimes. We then apply these tools to survey the current understanding of black-hole superradiance and analogue Hawking radiation, including explicit examples and numerical methods.
The Hawking effect -- the amplification of fluctuations at the horizon -- has been detected in quantum fluids through real-space density correlations. However, real-space observables integrate over frequency, mixing distinct scattering channels into a single interference pattern and obscuring the spectral and entanglement structure of the emission. Here, we numerically compute momentum-space two-point correlations in a transcritical quantum fluid, using the truncated Wigner approximation applied to a realistic, driven-dissipative polariton system. We spectrally resolve the Hawking--partner as well as greybody factor channels and find that both carry comparable correlation strength, demonstrating that the well-known real-space ``moustache'' is an interference between these spectrally distinct contributions. The Hawking--partner channel is dominated by negative correlations, a direct signature of quantum-vacuum pair creation. All features reach amplitudes detectable in state-of-the-art experiments. Our results establish that the full three-mode output state must be considered for entanglement characterization, and provide a general framework applicable to any quantum fluid.
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.