Abstract
Ultracold fermionic atoms in an optical lattice, with a sudden position-dependent change (a quench) in the effective dispersion relation, have been proposed by Rodríguez-Laguna et al as an analogue spacetime test of the Unruh effect. We provide new support for this analogue by analysing a massless scalar field on a (1+1)-dimensional continuum spacetime with a similar quench: an early time Minkowski region is joined at a constant time surface, representing the quench, to a late time static region in which left and right asymptotically Rindler domains are connected by a smooth negative curvature bridge. We show that the quench is energetically mild, and late time static observers, modelled as a derivative-coupling Unruh–DeWitt detector, see thermality, in a temperature that equals the Unruh temperature for observers in the asymptotic Rindler domains. The Unruh effect hence prevails, despite the energy injected into the field by the quench and despite the absence of a late time Killing horizon. These results strengthen the motivation to realise the experimental proposal.
Highlights
In relativistic quantum field theory, an observer’s measurements of a quantum field depend on the observer’s motion
A related effect exists for nonlinear uniform accelerations [8], including circular motion [9, 10, 11, 12], and the circular motion version is related to the spin depolarisation of particle beams in accelerator storage rings [13, 14, 15, 16], originally predicted by different methods [17, 18] and observed [19], and here establishing a direct connection between the observation and the circular motion Unruh effect has remained elusive [16]
An experimental confirmation of the Unruh effect would be significant since the mathematics underpinning the effect is closely related to the mathematics in Hawking’s prediction of black hole radiation [24] and to the mathematics of the early universe quantum effects that may be responsible for the origin of structure in the present-day Universe [25, 26]
Summary
In relativistic quantum field theory, an observer’s measurements of a quantum field depend on the observer’s motion. (We set on c = = kB = 1.) It is shown in [34, 35] by a combination of analytic and numerical methods that the field’s behaviour at constant χ, sufficiently far from χ = 0 in terms of the lattice scale, has thermal characteristics, in a position-dependent temperature that approximates 1/(2π|χ|) This thermality is interpreted as an analogue of the Unruh effect, on the grounds that the regions χ > 0 and χ < 0 of (1.1) each cover one Rindler wedge of Minkowski spacetime, the worldlines of constant χ = 0 have proper acceleration 1/|χ|, and the usual Unruh effect states that an observer in a Rindler wedge at constant χ experiences the Minkowski vacuum as thermal at the Unruh temperature 1/(2π|χ|) [1, 2, 3, 4, 5, 6].
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