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arXiv:1601.06766 · New Journal of Physics

On the observation of nonclassical excitations in Bose–Einstein condensates

Andreas Finke, Piyush Jain, Silke Weinfurtner

Published Nov 8, 2016• 33 citations
arXivHTMLPDF

Abstract

In the recent experimental and theoretical literature well-established nonclassicality criteria from the field of quantum optics have been directly applied to the case of excitations in matter-waves. Among these are violations of Cauchy–Schwarz inequalities, Glauber–Sudarshan P-nonclassicality, sub-Poissonian number-difference squeezing (also known as the two-mode variance) and the criterion of nonseparability. We review the strong connection of these criteria and their meaning in quantum optics, and point out differences in the interpretation between light and matter waves. We then calculate observables for a homogeneous Bose–Einstein condensate undergoing an arbitrary modulation in the interaction parameter at finite initial temperature, within both the quantum theory as well as a classical reference. We conclude that to date in experiments relevant for this scenario nonclassical effects have not conclusively been observed and conjecture that additional, noncommuting, observables have to be measured to this end. Moreover this has important implications for proposed analog gravity models where the observation of nonclassical effects is a major goal.

DOI
10.1088/1367-2630/18/11/113017

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In the recent experimental and theoretical literature well-established nonclassicality criteria from the field of quantum optics have been directly applied to the case of excitations in matter-waves. Among these are violations of Cauchy–Schwarz inequalities, Glauber–Sudarshan P-nonclassicality, sub-Poissonian number-difference squeezing (also known as the two-mode variance) and the criterion of nonseparability. We review the strong connection of these criteria and their meaning in quantum optics, and point out differences in the interpretation between light and matter waves. We then calculate observables for a homogeneous Bose–Einstein condensate undergoing an arbitrary modulation in the interaction parameter at finite initial temperature, within both the quantum theory as well as a classical reference. We conclude that to date in experiments relevant for this scenario nonclassical effects have not conclusively been observed and conjecture that additional, noncommuting, observables have to be measured to this end. Moreover this has important implications for proposed analog gravity models where the observation of nonclassical effects is a major goal.
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In this paper, we study quadrature squeezings of two Bose–Einstein condensates with collision and nonclassical properties of pair entanglement in four wave mixing in Bose–Einstein condensates. With the aid of a numerical method, we find that the two modes (pair entanglement modes) a1 and a2 may exhibit quadrature squeezing, in which they are affected by the initial phase. It is shown that the two pump modes exhibit the same super-Poissonian distribution. The analysis for the mode-mode correlation shows that there always exists a violation of the Cauchy-Schwartz inequality, which means that correlation between the two pump modes is nonclassical.
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An analytic operator solution of a generalized quantum mechanical Hamiltonian of two-mode Bose-Einstein condensates (BECs) is obtained for short-time dynamics and the same is used to investigate the nonclassical properties of the modes present in the system. Nonclassical characters are observed by means of single-mode and intermodal quadrature squeezing, single-mode and intermodal sub-Poissonian boson statistics, and intermodal entanglement. In addition to the traditionally studied lower-order nonclassical properties, signatures of higher-order nonclassical characters of two-mode BEC systems are also obtained by investigating the possibility of higher-order antibunching and higher-order entanglement. The mutual relation among the observed nonclassicalities and their evolution (variation) with time and the ratio of the single boson tunneling amplitude ($\ensuremath{\varepsilon}$) and the coupling constant for the intramodal interaction ($\ensuremath{\kappa}$) are also reported.