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arXiv:0907.5447 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Ramsey’s method of separated oscillating fields and its application to gravitationally induced quantum phase shifts

H. Abele, Tobias Jenke, Helmut Leeb, Jörg Schmiedmayer

Published Mar 18, 2010• 91 citations
arXivHTMLPDF

Abstract

We propose to apply Ramsey's method of separated oscillating fields to the spectroscopy of the quantum states in the gravity potential above a horizontal mirror. This method allows a precise measurement of quantum mechanical phaseshifts of a Schr\"odinger wave packet bouncing off a hard surface in the gravitational field of the Earth. Measurements with ultracold neutrons will offer a sensitivity to Newton's law or hypothetical short-ranged interactions, which is about 21 orders of magnitude below the energy scale of electromagnetism.

DOI
10.1103/physrevd.81.065019

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We propose to apply Ramsey's method of separated oscillating fields to the spectroscopy of the quantum states in the gravity potential above a horizontal mirror. This method allows a precise measurement of quantum mechanical phaseshifts of a Schr"odinger wave packet bouncing off a hard surface in the gravitational field of the Earth. Measurements with ultracold neutrons will offer a sensitivity to Newton's law or hypothetical short-ranged interactions, which is about 21 orders of magnitude below the energy scale of electromagnetism.
Neutrons not only fall classically in the gravitational field of the Earth as potatoes and other normal objects do; at certain conditions, they reveal quantum behavior, or even form well­ defined gravitational quantum states. Due to the relative simplicity of quantum mechanical rules for solving this problem, we could predict analytically the motion of a neutron in a grav­ itational field in the vicinity of a reflecting surface. Such a bouncing neutron can have only certain, discrete values of energy. These extremely small energy values turn out to be very sensitive probes to the presence of even tiny extra interactions, in particular those between the neutron and the mirror. Moreover, several emerging fields of research profit from experi­ ence and knowledge gained in the recent experimental observation of gravitational quantum states of ultracold neutrons, and extend the developed methods to atoms and anti-atoms, to whispering-gallery effect and other domains, thus providing more and more application for the method. Quantum bouncing particles could play their role in quantum tests of the equivalence principle, in explorations of gravitational properties of antimatter, in searching for new funda­ mental short-range and other interactions beyond the Standard Model of particle physics, in surface and thin-layer physics, in chemistry, and so on. In this short note we mention results of a few previous years and project nearest developments ..
We studied the neutron quantum states in the potential well formed by the Earth's gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in two lowest quantum states correspond to their expectations with an accuracy of ~25%. A spatial density distribution in a standing neutron wave above a mirror was measured for a set of a few lowest quantum states. A position-sensitive neutron detector with an extra high spatial resolution of 1-2 mu m was developed and tested for this particular task. Although this experiment was not designed or optimized to search for an additional short-range force, nevertheless it allowed us to slightly improve the published boundary in the nanometer range of characteristic distances. We studied systematical uncertainties in the chosen "flow-through" method as well as the feasibility to improve further the accuracy in this experiment
We studied the neutron quantum states in the potential well formed by the Earth's gravitational field and a horizontal mirror. The estimated characteristic sizes of the neutron wave functions in two lowest quantum states correspond to their expectations with an accuracy of ≈25 %. The spatial density distribution in a standing neutron wave above a mirror was measured for a set of a few lowest quantum states. A position-sensitive neutron detector with an extra high spatial resolution of 1 μm to 2 μm was developed and tested for this particular task. Although this experiment was not designed or optimized to search for an additional short-range force, nevertheless it allowed us to slightly improve the published boundary in the nanometer range of characteristic distances. We studied systematical uncertainties in the chosen "flow-through" method as well as the feasibility to improve further the accuracy in this experiment.
Ultracold neutrons confined in the Earth's gravitational field display quantized energy levels that have been observed for over a decade. In recent resonance spectroscopy experiments [T. Jenke et al., Nat. Phys. 7, 468 (2011)], the transition between two such gravitational quantum states was driven by the mechanical oscillation of the plates that confine the neutrons. Here we show that by applying a sinusoidal modulation with slowly varying frequency (chirp), the neutrons can be brought to higher excited states by climbing the energy levels one by one. The proposed experiment should make it possible to observe the quantum-classical transition that occurs at high neutron energies. Furthermore, it provides a technique to realize superpositions of gravitational quantum states, to be used for precision tests of gravity at short distances.
Abstract The time evolution of a quantum wave packet in the linear gravity potential is known as Quantum Bouncing Ball. The qBounce collaboration recently observed such a system by dropping wave packets of ultracold neutrons by a height of roughly 30 microns. In this article, space and momentum spectra as well as Wigner functions of the neutron wave functions in the gravitational field of the Earth are analyzed. We investigate the quantum states in the “preparation region”, into which they transition after exiting a narrow double-mirror system and where we would expect to observe free fall and bounces in classical physics. For this, we start from the stationary solutions and eigenvalues of the Schrödinger equation in terms of Airy functions and their zeros. Subsequently, we examine space and momentum distributions as well as Wigner functions in phase space for pure and mixed quantum states. The possible influence of Yukawa-like forces for small distances of several micrometers from the mirror is included through first order perturbation calculations. Those allow us to study the resulting modifications of space and momentum distributions, and phase space functions.
We propose a set of experiments in which Ramsey-fringe techniques are tailored to probe transitions originating and terminating on the same ground state level. When pulses of resonant radiation, separated by a time delay $% T, $ interact with atoms, it is possible to produce Ramsey fringes having widths of order 1/T. If each pulse contains two counterpropagating travelling wave modes, the atomic wave function is split into two or more components having different center-of-mass momenta. Matter-wave interference of these components leads to atomic gratings, which have been observed in both spatially separated fields and time separated fields. Time-dependent signals can be transformed into frequency dependent signals, leading to ground state Ramsey fringes (GSRF). The signals can be used to probe many problems of fundamental importance: a precise measurement of the earth gravitational acceleration ggg and residual gravity in a microgravity environment with an accuracy 610−9g;6 10^{-9}g;610−9g; the rotation rate measurement with an accuracy of 6 10^{-3} deg/h; the recoil frequency measurement. Since only transitions originating and terminating on the same ground state are involved, frequency measurements can be carried out using lasers phase-locked by quartz oscillators having relatively low frequency. Our technique may allow one to increase the precision by a factor of 100 (the rf- to quartz oscillator frequencies ratio) over previous experiments based on Raman-Ramsey fringes or reduce on the same factor requirements for frequency stabilization.