Quantum coherent oscillations in the early universe

Cosmic inflation is commonly assumed to be driven by quantum fields. Quantum mechanics predicts phenomena such as quantum fluctuations and tunneling of the field. Here, we show an example of a quantum interference effect which goes beyond the semiclassical treatment and which may be of relevance in the early Universe. We study the quantum coherent dynamics for a tilted, periodic potential, which results in genuine quantum oscillations of the inflaton field, analogous to Bloch oscillations in condensed matter and atomic systems. The underlying quantum superpositions are typically very fragile but may persist in the early Universe giving rise to quantum interference phenomena in cosmology.

Figure 1

The assumed potential for the homogeneous field $\mathrm{\Phi }$, which consists of a periodic part and an additional tilt [see Eq. (6)]. The minima (sites) are labeled by $n$, and the orange lines represent the local ground states. The field can tunnel from one site to another, governed by the rate density $\mathrm{\Omega }$. Due to the tilt in the potential, the quantum dynamics results in coherent, periodic oscillations over many sites.

Figure 2

Bloch oscillations of the system, for an initially localized state inside a potential well. The system spreads as a coherent superposition over many sites of the potential (labeled by $n$). The oscillations are periodic with frequency ${\omega }_B$, which depends on the tilt of the potential. On average, the system remains in the potential well in which it started.

Figure 3

Bloch oscillations for an initial Gaussian distribution over several potential wells. The system does not further delocalize, but the mean oscillates at frequency ${\omega }_B$. Damping of the system causes an additional slow drift downwards, which is not shown here.