An atomic velocity sensor based on the light-dragging effect

Abstract

A velocity sensor (or velocimeter) is a device used to measure the rate of change of a moving object’s position. Such devices (which have important applications in, e.g., navigation and manufacturing) are typically based on measuring the first-order Doppler shift of electromagnetic waves that are reflecting or scattering off of a moving object. In the quantum regime, the velocity measurements of particles are important for studying fundamental physics. As an example, when a photon is absorbed by an atom, the atom will gain a recoil energy, or recoil velocity. By measuring this recoil velocity from the spectral shift of the atomic resonance, the fine-structure constant can be determined and the theory of quantum electrodynamics tested.1 Another example of its usefulness is in the measurement of the local gravitational acceleration of two different species of free-falling atoms (to test Einstein’s equivalence principle).1 All atom-based sensors rely on measuring the first-order Doppler shift of the atomic transition. By using Dopplersensitive methods to detect the population of atomic states, the velocity can be measured precisely. However, due to the thermal distribution of an atomic ensemble, the uncertainty of the measurement is limited by the Doppler width of the ensemble. Thus, to determine its center-of-mass motion, one usually needs to map or truncate the velocity distribution of the ensemble. This approach complicates the process and lowers the data rate.1 In our experiment, we demonstrate the light-dragging effect (i.e., the deviation of the phase velocity of an electromagnetic wave from the speed of light in a moving medium) and use it to directly sense the center-of-mass motion of an atomic ensemble. The light-dragging effect was first observed by Fizeau in a flowing-water experiment for the study of ether, before the era of Einstein’s special theory of relativity. It was later explained by the Lorentz addition to the first order of velocity in the equation related to Einstein’s theory.2 The effect (illustrated in Figure 1) Figure 1. Illustration of the light-dragging effect in a moving medium. The phase velocity (Vp) of light is modified by an additional term, Fd V (where Fd is the dragging coefficient and V is the velocity of the moving medium). The dragged light has a phase shift of ̊ compared to a reference light. c: The speed of light in a vacuum.