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arXiv:2302.13409 · Physics Letters A

A charged Coulomb Bose gas with dipole-dipole interactions

Abdelâali Boudjemâa

Published Feb 22, 2023• 6 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2023.128712

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We study the equilibrium correlation function of the polaron-dressed tunnelling operator in the dissipative two-state system and compare the asymptoptic dynamics with that of the position correlations. For an Ohmic spectral density with damping strength K = ½, the correlation functions are obtained in analytic form for all times at any T and any bias. For K < 1, the asymptotic dynamics is found by using a diagrammatic approach within a Coulomb gas representation. At T = 0, the tunnelling or coherence correlations drop as t −2 K , whereas the position correlations show universal decay ∝ t −2 . The former decay law is a signature of unscreened attractive charge-charge interactions, while the latter is due to unscreened dipole-dipole interactions.
Matter-wave interferometers with microparticles will enable the next generation of quantum sensors to probe minute quantum phase information. Therefore, estimating the loss of coherence and the degree of entanglement degradation for such interferometers is essential. In this paper, we provide a noise analysis in frequency-space focusing on electromagnetic sources of dephasing. We assume that our matter-wave interferometer has a residual charge or dipole which can interact with a neighboring particle in the ambience. We investigate the dephasing due to the Coulomb, charge-induced dipole, charge-permanent dipole, and dipole-dipole interactions. All these interactions constitute electromagnetically driven dephasing channels that can affect single or multiple interferometers. As an example, we apply the obtained formulas to situations with two adjacent microparticles, which can provide insight for the noise analysis in the quantum gravity-induced entanglement of masses (QGEM) protocol and the c-not gate: we compute the dephasing due to a gas of environmental particles interacting via dipole-dipole and charge-charge couplings, respectively. To obtain simple analytical dephasing formulas, we employ uniform probability distributions for the impact parameter and for the angles characterizing the relative orientation with respect to the interferometer and a Gaussian distribution for the velocities of the environmental particles. In both cases, we show that the dephasing rate grows with the number density of particles present in the vacuum chamber, as expected.