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Phonons and other quantum fields in the lab (Orale)

Christoph Ira Westbrook

Published Jun 8, 2017• 0 citations
OpenAlex

Abstract

In a quantum fluid such as a condensed Bose gas, elementary excitations such as phonons behave as quantized fields with dispersion relations and non-linearities that bear some resemblance to those of the electromagnetic field. The very low temperatures of these gases means that in some cases quantum fluctuations are important. Several remarkable phenomena in quantum electrodynamics have found acoustic analogs, and I will discuss two of them. The first is the dynamical Casimir effect, a prediction that the vacuum can generate real particles when boundary conditions are suddenly changed. That is, photon pairs can be spontaneously generated in an empty cavity with nonuniformly accelerating boundaries. A second is Hawking radiation. Here again photon pairs are generated at the horizon of a black hole. I will discuss how certain aspects of both these effects can be mimicked in a Bose Einstein condensate, and outline the state of the experimental art in this domain.

Related papers

Analogs to the dynamical Casimir effect in Bose-Einstein condensates (Orale)

Christoph Ira Westbrook

It is a remarkable prediction of quantum field theory that the vacuum can generate real particles when boundary conditions are suddenly changed. Thus the 'dynamical Casimir effect' results in the spontaneous generation of photon pairs in an empty cavity with nonuniformly accelerating boundaries. Recent advances have permitted the realization of this effect, or analogs to it in a variety of systems, some of which will be discussed at this workshop. Bose Einstein condensates are attractive candidates in which to study acoustic analogs to such phenomena because their low temperatures promise to reveal quantum effects. I will discuss a recent experiment in our group to realize an acoustic analog to the dynamical Casimir effect by modulating the confinement of a Bose-Einstein condensate. We observe correlated pairs of Bogoliubov quanta, both phonon-like and particle-like, are excited by this modulation in a process that formally resembles parametric down conversion. I will discuss our current ideas on how to observe and quantify the degree of entanglement in the excitations we observe.

•Jun 24, 2013•0 citations

Analogue gravity with Bose-Einstein condensates

Adrià Delhom, Luca Giacomelli

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.

gr-qcCross-listedarXiv:2512.14209•Dec 17, 2025•0 citations

Quantum Acoustics: A Unified Quantum Theory of Phonons Analogous to Quantum Optics

shifa liu

We develop quantum acoustics as an independent quantum discipline. The elementary bosonic quantum is the phonon, obtained by canonical quantization of the elastic displacement field of a medium. The central replacement is c → cs, ε0 → ρ0, μ0 → 1/K, ℏ → ℏ, while the Planck constant is not replaced. Phonons obey canonical commutation relations, Bose–Einstein statistics with vanishing chemical potential, and energy quantization E = ℏω. The optical–acoustic dictionary is exact at the level of canonical quantization, mode algebra, Fock, coherent, squeezed, thermal and entangled states, and at the level of linear interference in the long-wavelength, single-branch, dissipationless limit. Multi-branch, dispersive, dissipative and finite-lifetime effects are handled by the generalized dictionary stated in Chapter 56. Quantum acoustics contains a macroscopic quantum branch, but it is not identical to macro- scopic quantum mechanics. The manuscript covers classical elasticity, variational principles, canonical quantization, phonon field algebra, propagators, Green functions, wave–particle duality, Bose–Einstein statistics, blackbody radiation, Debye heat capacity, acoustic quantum constants, acoustic Bekenstein–Hawking entropy, phonon thermodynamics, phonon BEC, phonon lasers, superfluidity, Fock, coherent, squeezed, thermal, entangled and non-classical states, beam splitters, Mach–Zehnder interferometers, Fabry–Perot cavities, Hong–Ou–Mandel interference, second-order coherence, phonon qubits, single- and two-qubit gates, quantum algorithms, quantum error correction and surface-code thresholds, quantum computing architecture, quantum networks and repeaters, quantum simulation, quantum sensing, topological phononic crystals, the SSH phonon model, two-dimensional topological phononic insulators, three-dimensional phonon Weyl semimetals, non-Hermitian acoustics and the phonon skin effect, non-Bloch band theory, topological defect classification, acoustic metrics, acoustic horizons, acoustic Hawking radiation, acoustic black- hole entropy and the information paradox, acoustic cosmology, phonon–graviton mixing, gravitational-wave coupling, the phonon analogy of dark matter and dark energy, surface acoustic wave resonators, optomechanical systems, superconducting qubit–phonon hybrid systems, Bose–Einstein condensates, phononic crystals, acoustic metamaterials, gravitational-wave detectors, the complete optical–acoustic dictionary, the generalized dictionary for multi-branch, dispersive, dissipative and finite-lifetime phonons, and strong-field QED vacuum and media as an analogue of multi-refringent, dispersive and dissipative media. Acoustic Hawking radiation has been observed in Bose–Einstein condensates by Steinhauer (2016). All definitions, derivations, mathematical details, experimental proposals and comparison factors are presented with explicit assumptions and complete proofs.

•Dec 31, 2025•0 citations

Observing Hawking radiation in Bose-Einstein condensates via correlation measurements

Alessandro Fabbri

Observing quantum particle creation by black holes (Hawking radiation) in the astrophysical context is, in ordinary situations, hopeless. Nevertheless the Hawking effect, which depends only on kinematical properties of wave propagation in the presence of horizons, is present also in nongravitational contexts, for instance in stationary fluids undergoing supersonic flow. We present results on how to observe the analog Hawking radiation in Bose-Einstein condensates by a direct measurement of the density correlations due to the phonon pairs (Hawking quanta-partner) created by the acoustic horizon.

arXiv:1212.5392•Dec 21, 2012•0 citations

Phonon Scharnhorst effect: Acoustic analogue of the vacuum-fluctuation-boosted speed of light

C. W. J. Beenakker

The Scharnhorst effect in quantum electrodynamics predicts a superluminal velocity shift $δc>0$ at low photon frequencies due to vacuum fluctuations between two mirrors. Although theoretically robust (no causality violation), the effect is extraordinarily small ($δc/c\approx 10^{-32}$ for mirrors $1\,μ{\rm m}$ apart) and outside current experimental reach. Here we propose a condensed matter analogue, replacing the photons in the electromagnetic vacuum by phonon excitations of a Bose-Einstein condensate. In an idealized geometry, the two-dimensional surface of a cylinder (circumference $L$) at zero temperature, the axial speed of sound is increased due to zero-point fluctuations of the condensate by $δc/c\simeq 5\times 10^{-3}\,\tilde{g}$ at $L\simeq 2\,ξ$, to first order in the dimensionless interaction constant $\tilde{g}\simeq 10^{-1}$ of the Bose gas of healing length $ξ\simeq 1\,μ{\rm m}$. This is 28 orders of magnitude larger than the photonic effect, basically because phonons have a self-interaction while photons only interact via massive electrons. We discuss the prospects for observation of the acoustic Scharnhorst effect, the main restriction being the low-temperature requirement.

cond-mat.quant-gasCross-listedarXiv:2609.14155•Sep 15, 2026•0 citations

Quantum quenches, sonic horizons and the Hawking radiation

Alberto Parola, Manuele Tettamanti, Sergio L. Cacciatori

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.

•Mar 15, 2017•0 citations
In a quantum fluid such as a condensed Bose gas, elementary excitations such as phonons behave as quantized fields with dispersion relations and non-linearities that bear some resemblance to those of the electromagnetic field. The very low temperatures of these gases means that in some cases quantum fluctuations are important. Several remarkable phenomena in quantum electrodynamics have found acoustic analogs, and I will discuss two of them. The first is the dynamical Casimir effect, a prediction that the vacuum can generate real particles when boundary conditions are suddenly changed. That is, photon pairs can be spontaneously generated in an empty cavity with nonuniformly accelerating boundaries. A second is Hawking radiation. Here again photon pairs are generated at the horizon of a black hole. I will discuss how certain aspects of both these effects can be mimicked in a Bose Einstein condensate, and outline the state of the experimental art in this domain.
It is a remarkable prediction of quantum field theory that the vacuum can generate real particles when boundary conditions are suddenly changed. Thus the 'dynamical Casimir effect' results in the spontaneous generation of photon pairs in an empty cavity with nonuniformly accelerating boundaries. Recent advances have permitted the realization of this effect, or analogs to it in a variety of systems, some of which will be discussed at this workshop. Bose Einstein condensates are attractive candidates in which to study acoustic analogs to such phenomena because their low temperatures promise to reveal quantum effects. I will discuss a recent experiment in our group to realize an acoustic analog to the dynamical Casimir effect by modulating the confinement of a Bose-Einstein condensate. We observe correlated pairs of Bogoliubov quanta, both phonon-like and particle-like, are excited by this modulation in a process that formally resembles parametric down conversion. I will discuss our current ideas on how to observe and quantify the degree of entanglement in the excitations we observe.
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.
We develop quantum acoustics as an independent quantum discipline. The elementary bosonic quantum is the phonon, obtained by canonical quantization of the elastic displacement field of a medium. The central replacement is c → cs, ε0 → ρ0, μ0 → 1/K, ℏ → ℏ, while the Planck constant is not replaced. Phonons obey canonical commutation relations, Bose–Einstein statistics with vanishing chemical potential, and energy quantization E = ℏω. The optical–acoustic dictionary is exact at the level of canonical quantization, mode algebra, Fock, coherent, squeezed, thermal and entangled states, and at the level of linear interference in the long-wavelength, single-branch, dissipationless limit. Multi-branch, dispersive, dissipative and finite-lifetime effects are handled by the generalized dictionary stated in Chapter 56. Quantum acoustics contains a macroscopic quantum branch, but it is not identical to macro- scopic quantum mechanics. The manuscript covers classical elasticity, variational principles, canonical quantization, phonon field algebra, propagators, Green functions, wave–particle duality, Bose–Einstein statistics, blackbody radiation, Debye heat capacity, acoustic quantum constants, acoustic Bekenstein–Hawking entropy, phonon thermodynamics, phonon BEC, phonon lasers, superfluidity, Fock, coherent, squeezed, thermal, entangled and non-classical states, beam splitters, Mach–Zehnder interferometers, Fabry–Perot cavities, Hong–Ou–Mandel interference, second-order coherence, phonon qubits, single- and two-qubit gates, quantum algorithms, quantum error correction and surface-code thresholds, quantum computing architecture, quantum networks and repeaters, quantum simulation, quantum sensing, topological phononic crystals, the SSH phonon model, two-dimensional topological phononic insulators, three-dimensional phonon Weyl semimetals, non-Hermitian acoustics and the phonon skin effect, non-Bloch band theory, topological defect classification, acoustic metrics, acoustic horizons, acoustic Hawking radiation, acoustic black- hole entropy and the information paradox, acoustic cosmology, phonon–graviton mixing, gravitational-wave coupling, the phonon analogy of dark matter and dark energy, surface acoustic wave resonators, optomechanical systems, superconducting qubit–phonon hybrid systems, Bose–Einstein condensates, phononic crystals, acoustic metamaterials, gravitational-wave detectors, the complete optical–acoustic dictionary, the generalized dictionary for multi-branch, dispersive, dissipative and finite-lifetime phonons, and strong-field QED vacuum and media as an analogue of multi-refringent, dispersive and dissipative media. Acoustic Hawking radiation has been observed in Bose–Einstein condensates by Steinhauer (2016). All definitions, derivations, mathematical details, experimental proposals and comparison factors are presented with explicit assumptions and complete proofs.
Observing quantum particle creation by black holes (Hawking radiation) in the astrophysical context is, in ordinary situations, hopeless. Nevertheless the Hawking effect, which depends only on kinematical properties of wave propagation in the presence of horizons, is present also in nongravitational contexts, for instance in stationary fluids undergoing supersonic flow. We present results on how to observe the analog Hawking radiation in Bose-Einstein condensates by a direct measurement of the density correlations due to the phonon pairs (Hawking quanta-partner) created by the acoustic horizon.
The Scharnhorst effect in quantum electrodynamics predicts a superluminal velocity shift δc>0δc>0δc>0 at low photon frequencies due to vacuum fluctuations between two mirrors. Although theoretically robust (no causality violation), the effect is extraordinarily small (δc/c≈10−32δc/c\approx 10^{-32}δc/c≈10−32 for mirrors 1 μm1\,μ{\rm m}1μm apart) and outside current experimental reach. Here we propose a condensed matter analogue, replacing the photons in the electromagnetic vacuum by phonon excitations of a Bose-Einstein condensate. In an idealized geometry, the two-dimensional surface of a cylinder (circumference LLL) at zero temperature, the axial speed of sound is increased due to zero-point fluctuations of the condensate by δc/c≃5×10−3 g~δc/c\simeq 5\times 10^{-3}\,\tilde{g}δc/c≃5×10−3g~​ at L≃2 ξL\simeq 2\,ξL≃2ξ, to first order in the dimensionless interaction constant g~≃10−1\tilde{g}\simeq 10^{-1}g~​≃10−1 of the Bose gas of healing length ξ≃1 μmξ\simeq 1\,μ{\rm m}ξ≃1μm. This is 28 orders of magnitude larger than the photonic effect, basically because phonons have a self-interaction while photons only interact via massive electrons. We discuss the prospects for observation of the acoustic Scharnhorst effect, the main restriction being the low-temperature requirement.
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.