Testing Lorentz and CPT invariance with ultracold neutrons

Abstract

In this paper we investigate, within the standard model extension framework, the influence of Lorentzand CPT-violating terms on gravitational quantum states of ultracold neutrons. Using a semiclassical wave packet, we derive the effective nonrelativistic Hamiltonian which describes the neutrons vertical motion by averaging the contributions from the perpendicular coordinates to the free falling axis. We compute the physical implications of the Lorentz-and CPT-violating terms on the spectra. The comparison of our results with those obtained in the GRANIT experiment leads to an upper bound for the symmetriesviolation c n μν coefficients. We find that ultracold neutrons are sensitive to the a n i and e n i coefficients, which thus far are unbounded by experiments in the neutron sector. We propose two additional problems involving ultracold neutrons which could be relevant for improving our current bounds; namely, gravityresonance spectroscopy and neutron whispering gallery wave.

The CPT-violating effects on neutrons’ gravitational bound state

“…To obtain the quantum Hamiltonian for vertical motion, we adopt the ansatz in Ref. [12]: assuming the horizontal motion is governed by the Gaussian wave-packet…”

“…By focusing on the spin-dependent terms in [11], we obtain an effective vertical Hamiltonian in Sec. II using the reduction ansatz from [12]. As a slight glimpse on the LV spin-gravity effects, tiny LV correction to the Larmor frequency from the spin evolution equation is obtained.…”

Probing of violation of Lorentz invariance by ultracold neutrons in the Standard Model Extension

“…Recently Martín-Ruiz and Escobar [38,39] have used UCNs, quantized in the gravitational field of the Earth, as a tool to probe effects of violation of Lorentz invariance using the experimental data on the energy levels of the ground E 1 and first excited E 2 quantum gravitational states of UCNs [20]. An influence of CPT-violating effects on the quantum gravitational states of UCNs has been also investigated by Zhi Xiao [40].…”

“…An influence of CPT-violating effects on the quantum gravitational states of UCNs has been also investigated by Zhi Xiao [40]. The analysis, carried out by Martín-Ruiz and Escobar [38,39], has allowed to impose the following upper bounds on the parameters of violation of Lorentz invariance…”

CPT-violating Effects on Neutron Gravitational Bound States

“…Lorentz-violating matter-gravity couplings 2 open a broad and interesting avenue for testing Lorentz symmetry. Recently, spin-independent Lorentzviolating neutron-gravity couplings have been thoroughly studied 3 in an attempt to analyze the GRANIT experiment. 4 However, to our best knowledge, an extensive study of spin-dependent fermion-gravity couplings is still under development.…”