Planck-scale traces from the interference pattern of two Bose-Einstein condensates

Abstract

We analyze the possible effects arising from Planck scale regime upon the interference pattern of two non-interacting Bose-Einstein condensates. We start with the analysis of the free expansion of a condensate, taken into account the effects produced by a deformed dispersion relation, suggested in several quantum-gravity models. The analysis of the condensate free expansion, in particular, the modified free velocity expansion, suggests in a natural way, a modified uncertainty principle that could leads to new phenomenological implications related to the quantum structure of space time. Finally, we analyze the corresponding separation between the interference fringes after the two condensates overlap, in order to explore the sensitivity of the system to possible signals caused by the Planck scale regime.

Modified uncertainty principle from the free expansion of a Bose–Einstein condensate

“…With this aim, we will analyze the behaviour of the solutions to this modified condensate scenario under free expansion using numerical tools, where we taken into account the effects produced by the leading order deformation, and the next-to leading order deformation in Eq. ( 2) together with the interactions among the particles within the system extending the results reported in [13].…”

“…Notice that we have included in the total energy of the cloud, the leading order modification in the deformed dispersion relation Eq. ( 2), through the linear operator | |∇| 2 | [6,13], where α = ξ 1 mc/2M p . Also, we have inserted the next-to leading order deformation in Eq.…”

“…Over the last few years, the use of many-body systems as theoretical tools in the search for possible Planck scale effects has become a very interesting line of research [1][2][3][4][5][6]. In particular, systems related to Bose-Einstein condensates are promising pathways in the search for low-energy traces of Planck scale physics [4][5][6][7][8][9][10][11][12][13]. These studies suggest that remarkable properties associated with Bose-Einstein condensates could be used to obtain representative bounds on the deformation parameters associated with quantum gravity models [4,[8][9][10] or in specific cases where it is possible to explore the sensitivity of these systems to Planck scale effects [5][6][7][12][13][14].…”

“…Along these lines, in [13] we presented a study where the free velocity expansion of a Bose-Einstein condensate leads in a natural way to modifications of Heisenberg's uncertainty principle. If we assume as a fundamental fact that the energy per particle is modified due to the quantum structure of space time, then the predicted modified free velocity expansion suggests a linear deformation in Heisenberg's uncertainty principle,…”

“…The parameters ξ 1 , ξ 2 , and ξ 3 , are model dependent [23,24], and should take positive or negative values close to 1 (see Ref. [13] for more details). In fact, the form of the energy dispersion relation (2), was recently constrained a Electronic address: ecastellanos@mctp.mx b Electronic address: cescamilla@mctp.mx by using high precision atom-recoil frequency measurements [23,25].…”