Synthetic Unruh effect in cold atoms

Abstract

We propose to simulate a Dirac field near an event horizon using ultracold atoms in an optical lattice. Such a quantum simulator allows for the observation of the celebrated Unruh effect. Our proposal involves three stages: (1) preparation of the ground state of a massless 2D Dirac field in Minkowski spacetime; (2) quench of the optical lattice setup to simulate how an accelerated observer would view that state; (3) measurement of the local quantum fluctuation spectra by one-particle excitation spectroscopy in order to simulate a De Witt detector. According to Unruh's prediction, fluctuations measured in such a way must be thermal. Moreover, following Takagi's inversion theorem, they will obey the Bose-Einstein distribution, which will smoothly transform into the Fermi-Dirac as one of the dimensions of the lattice is reduced.Comment: v4 17 pages, 12 figures, minor changes, similar to the published versio

Experimental realization of a relativistic harmonic oscillator

“…While theories of the relativistic harmonic oscillator have been discussed for decades [1][2][3][4][5], the combination of special relativity and harmonic motion has proven resistant to physical realization. The infeasibility of realizing harmonic traps with depths on the order of a particle's rest mass energy (Boltzmann's constant times nearly six billion degrees Kelvin for an electron) has motivated work studying relativistic phenomena in disparate physical contexts, including a measurement of the Dirac oscillator spectrum in an array of microwave resonators [6] and proposals and realizations of effective relativistic effects in trapped atoms [7][8][9][10][11][12][13], trapped ions [14][15][16], photonic waveguides [17], and graphene [18].…”

Local quantum thermometry using Unruh–DeWitt detectors

“…From her point of view, this motion will translate into a change of her metric, which will become Rindler. Thus, as opposed to our case, she will observe the Minkowski vacuum through the lens of a Rindler Hamiltonian, as shown in [5].…”

“…Moreover, a detailed proposal for a quantum simulator to explore Unruh physics in cold atoms has been put forward [5]. The idea behind all the proposed quantum simulators on curved space-times [1][2][3][4][5] is the following: a static metric with an inhomogeneous time-lapse function |g 00 (x)| 1/2 for fermionic systems can be simulated by tuning the local hopping amplitudes between the cells of an optical lattice. This relation can be also understood in reverse: an inhomogeneity in the hopping amplitudes may be read as a non-trivial space-time metric.…”

Thermality from a Rindler quench

“…Recent experimental work includes the observation of a classical mode conversion that underlies the Hawking effect in the quantum theory [28], the observation of classical superradiance [29], the observation of quantum phenomena characteristic of an expanding cosmology [30], and observations interpreted as analogue Hawking radiation [31,32]. Laboratory analogues of the Unruh effect have been proposed in a Bose-Einstein condensate [33] and in ultracold fermionic atoms in an optical lattice [34,35], and related proposals are discussed in [36,37]. A laboratory analogue of the Gibbons-Hawking effect, a curved spacetime counterpart of the Unruh effect, has been proposed in [38,39].…”

“…The purpose of this paper is to provide new evidence that the optical lattice proposal of [34,35] has the requisite properties to simulate the Unruh effect, despite having energetic and causal properties that differ from those in the usual setting of the Unruh effect.…”