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:2001.05496 · Physical Review A

Analog spacetimes from nonrelativistic Goldstone modes in spinor condensates

Justin H. Wilson, Jonathan B. Curtis, Victor M. Galitski

Published Apr 25, 2022• 7 citations
arXivHTMLPDF

Abstract

It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an Einstein-Hilbert metric and exhibit a host of phenomena coming from quantum field theory in curved space, including Hawking radiation. We extend this analogy to any nonrelativistic Goldstone mode in a flowing spinor Bose-Einstein condensate. In addition to showing the linear dispersive result for all such modes, we show that the quadratically dispersive modes couple to a special nonrelativistic spacetime called a Newton-Cartan geometry. The kind of spacetime (Einstein-Hilbert or Newton-Cartan) is intimately linked to the mean-field phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudospin-1/2 condensate where we can tune between relativistic and nonrelativistic geometries. We uncover the fate of Hawking radiation upon such a transition: it vanishes and remains absent in the Newton-Cartan geometry despite the fact that any fluid flow creates a horizon for certain wave numbers. Finally, we use the coupling to different spacetimes to compute and relate various energy and momentum currents in these analog systems. While this result is general, present-day experiments can realize these different spacetimes including the magnon modes for spin-1 condensates such as $^{87}\mathrm{Rb}$, $^{7}\mathrm{Li}$, $^{41}\mathrm{K}$ (Newton-Cartan), and $^{23}\mathrm{Na}$ (Einstein-Hilbert).

DOI
10.1103/physreva.105.043316

Related papers

Analogue spacetimes from nonrelativistic Goldstone modes in spinor condensates

Justin H. Wilson, Jonathan B. Curtis, Victor M. Galitski

It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an Einstein-Hilbert metric and exhibit a host of phenomena coming from quantum field theory in curved space, including Hawking radiation. We extend this analogy to any nonrelativistic Goldstone mode in a flowing spinor Bose-Einstein condensate. In addition to showing the linear dispersive result for all such modes, we show that the quadratically dispersive modes couple to a special nonrelativistic spacetime called a Newton-Cartan geometry. The kind of spacetime (Einstein-Hilbert or Newton-Cartan) is intimately linked to the mean-field phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudo-spin-1/2 condensate where we can tune between relativistic and nonrelativistic geometries. We uncover the fate of Hawking radiation upon such a transition: it vanishes and remains absent in the Newton-Cartan geometry despite the fact that any fluid flow creates a horizon for certain wave numbers. Finally, we use the coupling to different spacetimes to compute and relate various energy and momentum currents in these analogue systems. While this result is general, present day experiments can realize these different spacetimes including the magnon modes for spin-1 condensates such as $^{87}$Rb, $^{7}$Li, $^{14}$K (Newton-Cartan), and $^{23}$Na (Einstein-Hilbert).

•Jan 15, 2020•0 citations

Emergent quantum field theories on curved spacetimes in spinor Bose-Einstein condensates: From scalar to Proca fields

Christian F. Schmidt, S. Brunner, Stefan Floerchinger

We consider excitations of a spin-1 Bose-Einstein-condensate in the vicinity of different mean-field configurations and derive mappings to emergent relativistic quantum field theories minimally coupled to curved acoustic spacetimes. The quantum fields are typically identified with Nambu-Goldstone bosons, such that the structure of the analog quantum field theories on curved spacetimes depends on the (spontaneous) symmetry breaking pattern of the respective ground state. The emergent spacetime geometries are independent of each other and exhibit bimetricity in the polar and antiferromagnetic phase, whereas one has trimetricity in the ferromagnetic phase. Compared to scalar BECs, the spinor degrees of freedom allow us to investigate massive vector and scalar fields where the former is a spin-nematic rotation mode in the polar phase, which can be cast into a Proca field that is minimally coupled to a curved spacetime that emerges on length scales larger than the spin-healing length. Finally, we specify the Zeeman couplings and the condensate trap to be spacetime-dependent such that a cosmological Friedmann-Lemaître-Robertson-Walker metric can be achieved. This work enables a pathway towards quantum-simulating cosmological particle production of Proca quanta via quenching the quadratic Zeeman coefficient or via magnetic field ramps, which both result in the creation of spin-nematic squeezed states.

arXiv:2506.13297•Physical Review A•Nov 18, 2025•0 citations

Analogue Hawking radiation, superradiance and sonic horizons in Bose-Einstein condensates

Tracy R. Slatyer

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.

•Jan 1, 2005•0 citations

Analogue Hawking radiation in an exactly solvable model of BEC

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.

arXiv:1703.05041•Europhysics Letters (EPL)•Sep 1, 2017•19 citations

QUASIPARTICLES IN SUPERFLUIDS AND SUPERCONDUCTORS

Jonathan B. Curtis

Quasiparticle descriptions are a powerful tool in condensed matter physics as they provide an analytical treatment of interacting systems. In this thesis we will apply this tool to theoretically describe two systems: a superconductor interacting with cavity photons and a flowing Bose-Einstein condensate forming a sonic black hole. First we will consider a two-dimensional s-wave BCS superconductor coupled to microwave cavity photons. We show how a nonequilibrium occupation of the photons can induce a nonequilibrium distribution of superconductor Bogoliubov quasiparticles, yielding an enhancement of the superconducting gap. The analytic dependence of this enhancement is provided in terms of the photon spectral and occupation functions, offering a large parameter space over which enhancement exists. Next, we analyze the equilibrium properties of a similar superconductor-cavity structure which has strong sub-dominant d-wave pairing interaction. In this case there is a collective mode known as the Bardasis-Schrieffer mode, which is essentially an uncondensed d-wave Cooper pair. We show that by driving an external supercurrent through the sample the Bardasis-Schrieffer mode can be hybridized with cavity photons, forming exotic Bardasis-Schrieffer-polaritons. We then turn to consider a flowing Bose-Einstein condensate. In the presence of inhomogeneous flow, the long-wavelength motion of quasiparticles can be mapped onto the kinematics of matter fields in a curved spacetime. This mapping allows for the simulation of a black hole and its interactions with quantum fields via analogy. We show that in the case of a step-like jump in the condensate flow the emission of analogue Hawking radiation is accompanied by evanescent modes which are pinned to the event horizon. Finally, we generalize this setup to include pseudo-spin half spinor Bose condensates. In this case, we show that the analogue spacetime the quasiparticles experience can be of the exotic Newton-Cartan type. Newton-Cartan gravity -- the geometric formulation of Newtonian gravity -- is realized when the Goldstone mode disperses quadratically as opposed to linearly. The nature of the analogue spacetime is controlled by the presence or absence of an easy-axis anisotropy in the boson spin-exchange interaction. We conclude by arguing that this Newton-Cartan spacetime can be experimentally realized in current platforms.

•Jan 1, 2020•0 citations

Quantum geometry of gravitons

M. Mehraeen

We uncover the quantum geometric structure of graviton Wigner functions and stress-energy tensors via quantum field theory in curved spacetime, revealing the phase-space geometry of spacetime and relativistic quantum-state manifolds. We show that the polarization mode expansion of the underlying graviton field operator is fully captured by quantum geometry, as encoded in the spinor-helicity formalism, thereby establishing the geometric framework from the outset. Applying this to a weak gravitational background, we demonstrate the roles of the quantum metric and connection in describing graviton transport beyond the chiral vortical effect. We also clarify the role of the quantum metric in normalizing the perfect-fluid graviton stress tensor within this approach. This work paves the path for explorations of multistate Hilbert-space geometry in high-energy and gravitational physics. In addition, this framework naturally encompasses lower-spin excitations, allowing for a unified quantum geometric treatment of bosonic and fermionic many-body systems in condensed matter and particle physics.

hep-thCross-listedarXiv:2609.15237•Sep 15, 2026
It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an Einstein-Hilbert metric and exhibit a host of phenomena coming from quantum field theory in curved space, including Hawking radiation. We extend this analogy to any nonrelativistic Goldstone mode in a flowing spinor Bose-Einstein condensate. In addition to showing the linear dispersive result for all such modes, we show that the quadratically dispersive modes couple to a special nonrelativistic spacetime called a Newton-Cartan geometry. The kind of spacetime (Einstein-Hilbert or Newton-Cartan) is intimately linked to the mean-field phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudospin-1/2 condensate where we can tune between relativistic and nonrelativistic geometries. We uncover the fate of Hawking radiation upon such a transition: it vanishes and remains absent in the Newton-Cartan geometry despite the fact that any fluid flow creates a horizon for certain wave numbers. Finally, we use the coupling to different spacetimes to compute and relate various energy and momentum currents in these analog systems. While this result is general, present-day experiments can realize these different spacetimes including the magnon modes for spin-1 condensates such as 87Rb^{87}\mathrm{Rb}87Rb, 7Li^{7}\mathrm{Li}7Li, 41K^{41}\mathrm{K}41K (Newton-Cartan), and 23Na^{23}\mathrm{Na}23Na (Einstein-Hilbert).
It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an Einstein-Hilbert metric and exhibit a host of phenomena coming from quantum field theory in curved space, including Hawking radiation. We extend this analogy to any nonrelativistic Goldstone mode in a flowing spinor Bose-Einstein condensate. In addition to showing the linear dispersive result for all such modes, we show that the quadratically dispersive modes couple to a special nonrelativistic spacetime called a Newton-Cartan geometry. The kind of spacetime (Einstein-Hilbert or Newton-Cartan) is intimately linked to the mean-field phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudo-spin-1/2 condensate where we can tune between relativistic and nonrelativistic geometries. We uncover the fate of Hawking radiation upon such a transition: it vanishes and remains absent in the Newton-Cartan geometry despite the fact that any fluid flow creates a horizon for certain wave numbers. Finally, we use the coupling to different spacetimes to compute and relate various energy and momentum currents in these analogue systems. While this result is general, present day experiments can realize these different spacetimes including the magnon modes for spin-1 condensates such as 87^{87}87Rb, 7^{7}7Li, 14^{14}14K (Newton-Cartan), and 23^{23}23Na (Einstein-Hilbert).
We consider excitations of a spin-1 Bose-Einstein-condensate in the vicinity of different mean-field configurations and derive mappings to emergent relativistic quantum field theories minimally coupled to curved acoustic spacetimes. The quantum fields are typically identified with Nambu-Goldstone bosons, such that the structure of the analog quantum field theories on curved spacetimes depends on the (spontaneous) symmetry breaking pattern of the respective ground state. The emergent spacetime geometries are independent of each other and exhibit bimetricity in the polar and antiferromagnetic phase, whereas one has trimetricity in the ferromagnetic phase. Compared to scalar BECs, the spinor degrees of freedom allow us to investigate massive vector and scalar fields where the former is a spin-nematic rotation mode in the polar phase, which can be cast into a Proca field that is minimally coupled to a curved spacetime that emerges on length scales larger than the spin-healing length. Finally, we specify the Zeeman couplings and the condensate trap to be spacetime-dependent such that a cosmological Friedmann-Lemaître-Robertson-Walker metric can be achieved. This work enables a pathway towards quantum-simulating cosmological particle production of Proca quanta via quenching the quadratic Zeeman coefficient or via magnetic field ramps, which both result in the creation of spin-nematic squeezed states.
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.
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.
Quasiparticle descriptions are a powerful tool in condensed matter physics as they provide an analytical treatment of interacting systems. In this thesis we will apply this tool to theoretically describe two systems: a superconductor interacting with cavity photons and a flowing Bose-Einstein condensate forming a sonic black hole. First we will consider a two-dimensional s-wave BCS superconductor coupled to microwave cavity photons. We show how a nonequilibrium occupation of the photons can induce a nonequilibrium distribution of superconductor Bogoliubov quasiparticles, yielding an enhancement of the superconducting gap. The analytic dependence of this enhancement is provided in terms of the photon spectral and occupation functions, offering a large parameter space over which enhancement exists. Next, we analyze the equilibrium properties of a similar superconductor-cavity structure which has strong sub-dominant d-wave pairing interaction. In this case there is a collective mode known as the Bardasis-Schrieffer mode, which is essentially an uncondensed d-wave Cooper pair. We show that by driving an external supercurrent through the sample the Bardasis-Schrieffer mode can be hybridized with cavity photons, forming exotic Bardasis-Schrieffer-polaritons. We then turn to consider a flowing Bose-Einstein condensate. In the presence of inhomogeneous flow, the long-wavelength motion of quasiparticles can be mapped onto the kinematics of matter fields in a curved spacetime. This mapping allows for the simulation of a black hole and its interactions with quantum fields via analogy. We show that in the case of a step-like jump in the condensate flow the emission of analogue Hawking radiation is accompanied by evanescent modes which are pinned to the event horizon. Finally, we generalize this setup to include pseudo-spin half spinor Bose condensates. In this case, we show that the analogue spacetime the quasiparticles experience can be of the exotic Newton-Cartan type. Newton-Cartan gravity -- the geometric formulation of Newtonian gravity -- is realized when the Goldstone mode disperses quadratically as opposed to linearly. The nature of the analogue spacetime is controlled by the presence or absence of an easy-axis anisotropy in the boson spin-exchange interaction. We conclude by arguing that this Newton-Cartan spacetime can be experimentally realized in current platforms.
We uncover the quantum geometric structure of graviton Wigner functions and stress-energy tensors via quantum field theory in curved spacetime, revealing the phase-space geometry of spacetime and relativistic quantum-state manifolds. We show that the polarization mode expansion of the underlying graviton field operator is fully captured by quantum geometry, as encoded in the spinor-helicity formalism, thereby establishing the geometric framework from the outset. Applying this to a weak gravitational background, we demonstrate the roles of the quantum metric and connection in describing graviton transport beyond the chiral vortical effect. We also clarify the role of the quantum metric in normalizing the perfect-fluid graviton stress tensor within this approach. This work paves the path for explorations of multistate Hilbert-space geometry in high-energy and gravitational physics. In addition, this framework naturally encompasses lower-spin excitations, allowing for a unified quantum geometric treatment of bosonic and fermionic many-body systems in condensed matter and particle physics.