Historical research guide · 0422 · 2001

Analogue gravity from Bose-Einstein condensates

Carlos Barceló · S Liberati · Matt Visser

In one minute

Carlos Barceló, Stefano Liberati and Matt Visser derive an effective geometry for long-wavelength ripples in a Bose–Einstein condensate, a cloud of ultracold atoms acting as one quantum fluid. Starting from a generalized nonlinear Schrödinger equation, they show that small phase disturbances obey the same mathematical form of wave equation used for fields in curved spacetime. The effective metric depends on the cloud’s background density, flow and speed of sound. In a suitable inward-flow geometry, sound moving against the current can become trapped at an acoustic horizon. This is a model of wave propagation, not proof that the cloud bends actual spacetime or creates gravitational attraction. At high momentum, the analogy breaks down: the waves follow nonrelativistic particle behavior, and the horizon is not absolute for every frequency.

Connection

Chapter 5’s premise is that the vacuum behaves like a quantum fluid, and this is the paper showing how completely a real laboratory fluid can carry a spacetime metric on its back — groundwork for the same authors’ Analogue Gravity reviews on this site at /library/stm-9d9474c4b5 and /library/stm-a50c456d62, and a working bench for the horizon physics chapter 4 needs.

From the source

Linearized excitations of the phase of the condensate wavefunction obey a (3+1)-dimensional d’Alembertian equation coupled to a Lorentzian-signature effective metric, and this is a generic feature, independent of the explicit form of the nonlinear terms in the Schrödinger equation.Abstract; Section 9, summary and discussion, first result
The effective acoustic interval is fixed algebraically by the background density, the speed of sound and the background flow velocity, so the metric can be read straight off the condensate rather than solved for.Section 6, Equation 47
A negative scattering length — attractive forces between the atoms — is formally equivalent to an imaginary speed of sound and turns the effective metric Euclidean, so manipulating the sign of the scattering length amounts to building an analogue of a signature-changing spacetime.Section 6, first bullet following Equation 47; Section 9, summary
At high momenta the eikonal approximation recovers exactly the dispersion relation Bogoliubov derived in 1947, which interpolates between ordinary phonons at wavelengths long compared with the acoustic Compton wavelength and free-particle Schrödinger behaviour at wavelengths short compared with it — so observing a Lorentz-invariant spectrum does not guarantee that the underlying physics is Lorentz invariant.Section 8, Equation 77 and observations 1, 2 and 4, Equations 79 to 81
Because the group velocity grows without bound at large momentum, the acoustic horizon in these models is frequency-dependent rather than absolute, and high-momentum modes escape from behind it — the same escape Corley and Jacobson linked to self-amplified instabilities in configurations carrying both an inner and an outer horizon.Section 8, observation 3, Equation 78
Mimicking a fully generic gravitational field is not implausible a priori, but it would be technically very challenging, since it requires anisotropy introduced directly into the generalized nonlinear Schrödinger equation through a position-dependent 3-tensor effective mass; the crude Hawking temperature for a ten-micron acoustic hole is about a billionth of a kelvin, only three orders of magnitude below the temperature of the condensate itself.Section 9, summary and discussion, second result and Equation 82

The way in

https://doi.org/10.1088/0264-9381/18/6/312

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

Licence checked directly. The published article is free to read at the publisher but carries no Creative Commons statement, and the preprint on arXiv as gr-qc/0011026, filed 7 November 2000, sits under arXiv’s assumed licence for submissions of 1991 to 2003, which does not grant redistribution. So this page carries the summary, the claims and the authors’ own abstract, and sends the reader to the source. Published as Classical and Quantum Gravity 18, 1137–1156 (2001); the preprint’s own first page carries the title ‘Analog gravity from Bose–Einstein condensates’, written at the Physics Department, Washington University in Saint Louis, SISSA Trieste and the University of Maryland. The summary, the claims and the locators below were written from the full author text; the abstract below is the authors’ own, as filed with the preprint.

How to cite it

Carlos Barceló, S Liberati, Matt Visser (2001) Analogue gravity from Bose-Einstein condensates doi:10.1088/0264-9381/18/6/312

Where it sits in the curriculum

The vacuum as a quantum fluid