Probing the Scale Invariance of the Inflationary Power Spectrum in Expanding Quasi-Two-Dimensional Dipolar Condensates

Abstract

We consider an analogue de Sitter cosmos in an expanding quasi-two-dimensional Bose-Einstein condensate with dominant dipole-dipole interactions between the atoms or molecules in the ultracold gas. It is demonstrated that a hallmark signature of inflationary cosmology, the scale invariance of the power spectrum of inflaton field correlations, experiences strong modifications when, at the initial stage of expansion, the excitation spectrum displays a roton minimum. Dipolar quantum gases thus furnish a viable laboratory tool to experimentally investigate, with well-defined and controllable initial conditions, whether primordial oscillation spectra deviating from Lorentz invariance at trans-Planckian momenta violate standard predictions of inflationary cosmology.

Roton entanglement in quenched dipolar Bose-Einstein condensates

“…Magnetic dipole-dipole interaction (DDI) dominated condensates [34] have been realized with chromium [35], dysprosium [36], and erbium [37] atoms, and the realization of BECs made up of molecules with permanent electric dipoles [38] is now at the forefront of ongoing research cf., e.g., [39,40]. For the creation of quasiparticle pairs in a time-dependent background, we will demonstrate that the existence of a deep roton minimum in the excitation spectrum [41][42][43][44][45] plays a dominant role. Various ramifications of the dipolar BEC roton, originally defined for and observed in the strongly interacting superfluid helium II [46,47], have been recently experimentally investigated in ultracold dipolar quantum gases [48][49][50][51].…”

“…To ensure stability in the DDI dominated regime [42], we impose that the system remains in the quasi-2D regime during its whole temporal evolution. In z direction, we thus assume that the condensate density is a Gaussian, ρ z (z) = (π d 2 z ) −1/2 exp − z 2 /d 2 z , where d z = b(t)d z,0 with d z,0 = 1/ √ mω z,0 and b(t) the scale factor [45]. We can then integrate out the z dependence and obtain the effective quasi-2D interaction, which is…”

“…(5) below. It encapsulates the effects of time-dependent trapping frequency and coupling in the following equation of motion for the scale factor b [45,54] b…”

Quantum simulation of dark energy candidates

“…Excerpts from this catalogue of analogue models include conformal Schwarzschild black holes [26,27], rotating black holes [28], Bañados-Teitelboim-Zanelli (BTZ) black holes [29], Friedmann-Robertson-Walker geometries [30,31], inflation [32,33] and extensions to general relativity such as aether fields [26]. Three of us have extended this catalogue to include gravitational wave space-times [34,35].…”

Simulating general relativity and non-commutative geometry by non-paraxial quantum fluids

“…The simulations are realizable in Earth-based laboratories in a human-life timescale. Researchers aim at realizing analog experimental models of black holes [9][10][11], Hawking radiation [12][13][14][15], inflation and universe expansion [16,17], dark-matter models [18], and related phenomena [19][20][21]. The analogy is a fundamental tool in physics, and experimental and theoretical analogs may deepen our understanding of quantum gravity theories [22], and of other challenging proposals as time-asymmetric quantum mechanics [23][24][25].…”