Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2609.14155

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

C. W. J. Beenakker

cond-mat.quant-gasquant-phSubmitted Sep 12, 2026• Announced Sep 15, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

Comments
7 pages, 2 figures

Related papers

Phonons and other quantum fields in the lab (Orale)

Christoph Ira Westbrook

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.

•Jun 8, 2017•0 citations

Slow sound in matter-wave dark soliton gases

Muzzamal Iqbal Shaukat, Eduardo V. Castro, Hugo Terças

We demonstrate the possibility of drastically reducing the velocity of phonons in quasi-one-dimensional Bose-Einstein condensates. Our scheme consists of a dilute dark soliton ``gas'' that provide the trapping for the impurities that surround the condensate. We tune the interaction between the impurities and the condensate particles in such a way that the dark solitons result in an array of qutrits (three-level structures). We compute the phonon-soliton coupling and investigate the decay rates of these three-level qutrits inside the condensate. As such, we are able to reproduce the phenomenon of acoustic transparency based purely on matter-wave phononics, in analogy with the electromagnetically induced transparency effect in quantum optics. Thanks to the unique properties of transmission and dispersion of dark solitons, we show that the speed of an acoustic pulse can be brought down to \ensuremath{\sim}5 $\ensuremath{\mu}\mathrm{m}$/s, \ensuremath{\sim}${10}^{3}$ times lower than the condensate sound speed. This is a value that greatly underdoes most of the reported studies for phononic platforms. We believe the present work could pave the stage for a new generation of ``stopped-sound''-based quantum information protocols.

arXiv:1810.10923•Physical review. B./Physical review. B•May 9, 2019•6 citations

Analogue stochastic gravity phenomena in two-component Bose-Einstein condensates: Sound cone fluctuations

Wei-Can Syu, Da-Shin Lee, Chi-Yong Lin

We investigate the properties of the condensates of cold atoms at zero temperature in the tunable binary Bose-Einstein condensate system with a Rabi transition between atomic hyperfine states. We use this system to examine the effect of quantum fluctuations in a tunable quantum gas on phonon propagation. We show that the system can be represented by a coupled two-field model of a gapless phonon and a gapped mode, which are analogous to the Goldstone and Higgs particles in particle physics. We then further trace out the gapped modes to give an effective purely phononic theory using closed-time-path formalism. In particular, we are interested in the sound cone fluctuations due to the variation of the speed-of-sound acoustic metric, induced by quantum fluctuations of the gapped modes. These fluctuations can be interpreted as inducing a stochastic space-time, and thus are regarded as analogue phenomena of light cone fluctuations presumably arising from quantum gravity effects. The effects of fluctuations can be displayed in the variation in the travel time of sound waves. We suggest the relevant experiments to discuss the possibility of experimental observations.

arXiv:1901.11187•Physical review. D/Physical review. D.•May 7, 2019•7 citations

An acoustic probe for quantum vorticity in Bose-Einstein condensates

Antonin Coutant, Silke Weinfurtner

We investigate the deformation of wavefronts of sound waves in rotating Bose-Einstein condensates. In irrational fluid flows Berry et al. identified this kind of deformation as the hydrodynamic analogue of the Aharonov-Bohm effect. We study this effect in Bose-Einstein condensates and obtain the Aharonov-Bohm phase shift at all wavelengths. We show that this deformation of wave fronts is seen in both phase and density fluctuations. For wavelengths larger than the healing length, the phase fluctuations experience a phase shift of the order of $2π$ times the winding number. We also consider lattices of vortices. If the angular momentum of the vortices are aligned, the total phase shift is $2π$ times the number of vortices in the condensate. Because of this behaviour the hydrodynamic Aharonov-Bohm can be utilized as a probe for quantum vorticity, whose experimental realization could offers an alternative route to investigate quantum turbulence in the laboratory.

arXiv:1504.00691•Apr 2, 2015•1 citation

Slow sound in matter-wave dark soliton arrays

Muzzamal Iqbal Shaukat, Eduardo V. Castro, Hugo Terças

We demonstrate the possibility of drastically reducing the velocity of phonons in quasi one-dimensional Bose-Einstein condensates. Our scheme consists of a dilute dark-soliton gas that provide the trapping for the impurities that surround the condensate. We tune the interaction between the impurities and the condensate particles in such a way that the dark solitons result in an array of {\it qutrits} (three-level structures). We compute the phonon-soliton coupling and investigate the decay rates of these three-level qutrits inside the condensate. As such, we are able to reproduce the phenomenon of acoustic transparency based purely on matter wave phononics, in analogy with the electric induced transparency (EIT) effect in quantum optics. Thanks to the unique properties of transmission and dispersion of dark solitons, we show that the speed of an acoustic pulse can be brought down to $\sim 5$ $\mu$m/s, $\sim 10^3$ times lower than the condensate sound speed. This is a record value that greatly underdoes most of the reported studies for phononic platforms. We believe the present work could pave the stage for a new generation of stopped-sound based quantum information protocols.

•Oct 25, 2018•0 citations

Interferometric Unruh Detectors for Bose-Einstein Condensates

Cisco Gooding, Steffen Biermann, Sebastian Erne +4 more

The Unruh effect predicts a thermal response for an accelerated detector moving through the vacuum. Here we propose an interferometric scheme to observe an analogue of the circular Unruh effect using a localized laser coupled to a Bose-Einstein condensate (BEC). Quantum fluctuations in the condensate are governed by an effective relativistic field theory, and as demonstrated, the coupled laser field acts as an effective Unruh-DeWitt detector thereof. The effective speed of light is lowered by 12 orders of magnitude to the sound velocity in the BEC. For detectors traveling close to the sound speed, observation of the Unruh effect in the analogue system becomes experimentally feasible.

arXiv:2007.07160•Physical Review Letters•Nov 20, 2020•92 citations
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.
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.
We demonstrate the possibility of drastically reducing the velocity of phonons in quasi-one-dimensional Bose-Einstein condensates. Our scheme consists of a dilute dark soliton ``gas'' that provide the trapping for the impurities that surround the condensate. We tune the interaction between the impurities and the condensate particles in such a way that the dark solitons result in an array of qutrits (three-level structures). We compute the phonon-soliton coupling and investigate the decay rates of these three-level qutrits inside the condensate. As such, we are able to reproduce the phenomenon of acoustic transparency based purely on matter-wave phononics, in analogy with the electromagnetically induced transparency effect in quantum optics. Thanks to the unique properties of transmission and dispersion of dark solitons, we show that the speed of an acoustic pulse can be brought down to \ensuremath{\sim}5 $\ensuremath{\mu}\mathrm{m}$/s, \ensuremath{\sim}103{10}^{3}103 times lower than the condensate sound speed. This is a value that greatly underdoes most of the reported studies for phononic platforms. We believe the present work could pave the stage for a new generation of ``stopped-sound''-based quantum information protocols.
We investigate the properties of the condensates of cold atoms at zero temperature in the tunable binary Bose-Einstein condensate system with a Rabi transition between atomic hyperfine states. We use this system to examine the effect of quantum fluctuations in a tunable quantum gas on phonon propagation. We show that the system can be represented by a coupled two-field model of a gapless phonon and a gapped mode, which are analogous to the Goldstone and Higgs particles in particle physics. We then further trace out the gapped modes to give an effective purely phononic theory using closed-time-path formalism. In particular, we are interested in the sound cone fluctuations due to the variation of the speed-of-sound acoustic metric, induced by quantum fluctuations of the gapped modes. These fluctuations can be interpreted as inducing a stochastic space-time, and thus are regarded as analogue phenomena of light cone fluctuations presumably arising from quantum gravity effects. The effects of fluctuations can be displayed in the variation in the travel time of sound waves. We suggest the relevant experiments to discuss the possibility of experimental observations.
We investigate the deformation of wavefronts of sound waves in rotating Bose-Einstein condensates. In irrational fluid flows Berry et al. identified this kind of deformation as the hydrodynamic analogue of the Aharonov-Bohm effect. We study this effect in Bose-Einstein condensates and obtain the Aharonov-Bohm phase shift at all wavelengths. We show that this deformation of wave fronts is seen in both phase and density fluctuations. For wavelengths larger than the healing length, the phase fluctuations experience a phase shift of the order of 2π2π2π times the winding number. We also consider lattices of vortices. If the angular momentum of the vortices are aligned, the total phase shift is 2π2π2π times the number of vortices in the condensate. Because of this behaviour the hydrodynamic Aharonov-Bohm can be utilized as a probe for quantum vorticity, whose experimental realization could offers an alternative route to investigate quantum turbulence in the laboratory.
We demonstrate the possibility of drastically reducing the velocity of phonons in quasi one-dimensional Bose-Einstein condensates. Our scheme consists of a dilute dark-soliton gas that provide the trapping for the impurities that surround the condensate. We tune the interaction between the impurities and the condensate particles in such a way that the dark solitons result in an array of {\it qutrits} (three-level structures). We compute the phonon-soliton coupling and investigate the decay rates of these three-level qutrits inside the condensate. As such, we are able to reproduce the phenomenon of acoustic transparency based purely on matter wave phononics, in analogy with the electric induced transparency (EIT) effect in quantum optics. Thanks to the unique properties of transmission and dispersion of dark solitons, we show that the speed of an acoustic pulse can be brought down to ∼5\sim 5∼5 μ\muμm/s, ∼103\sim 10^3∼103 times lower than the condensate sound speed. This is a record value that greatly underdoes most of the reported studies for phononic platforms. We believe the present work could pave the stage for a new generation of stopped-sound based quantum information protocols.
The Unruh effect predicts a thermal response for an accelerated detector moving through the vacuum. Here we propose an interferometric scheme to observe an analogue of the circular Unruh effect using a localized laser coupled to a Bose-Einstein condensate (BEC). Quantum fluctuations in the condensate are governed by an effective relativistic field theory, and as demonstrated, the coupled laser field acts as an effective Unruh-DeWitt detector thereof. The effective speed of light is lowered by 12 orders of magnitude to the sound velocity in the BEC. For detectors traveling close to the sound speed, observation of the Unruh effect in the analogue system becomes experimentally feasible.