Probing neutron's electric neutrality with Ramsey Spectroscopy of gravitational quantum states of ultra-cold neutrons

We propose to test the electric neutrality of neutrons by a new technique using the spectroscopy of quantum states of ultra-cold neutrons in the gravity potential above a vertical mirror. The new technique is an application of Ramsey's method of separated oscillating fields to neutron's quantum states in the gravity potential of the earth. In the presence of an electric field E parallel or antiparallel to the direction of the acceleration of the earth g, the energy of the quantum states changes due to an additional electrostatic potential if a neutron carries a non-vanishing charge. In the long run our new method has the potential to improve the current limit for the electric charge of the neutron by 2 orders of magnitude.