Entanglement and particle production from cosmological perturbations: a quantum optical simulation approach

TL;DR

The paper develops a Gaussian-state, symplectic-circuit framework to study entanglement and particle production in inflationary cosmology, modeling cosmological perturbations as two-mode squeezed states evolving under a quadratic Hamiltonian. By mapping the dynamics to continuous-variable gates, it computes entanglement measures such as von Neumann entropy and logarithmic negativity across expanding and contracting backgrounds, and validates simulation results against analytic Rényi-entropy bounds. It further extends the analysis to include thermal noise, showing how mixedness degrades entanglement while increasing mode entropy, and demonstrates the utility of the CV approach for efficient, scalable exploration of cosmological quantum information. The framework provides a versatile tool for probing quantum correlations in the early universe and sets the stage for incorporating non-Gaussianities, multi-field dynamics, and connections to the primordial power spectrum and CMB observables.

Abstract

In this work, we develop a computational framework based on the Gaussian formalism and symplectic circuit representation to explore cosmological perturbations during inflation. These tools offer an efficient means to study entanglement generation and particle production, particularly when analytical methods become insufficient and numerical simulations are essential. By evolving an initial Bunch-Davies vacuum through a two-mode squeezer, we simulate the behavior of the von Neumann entropy and logarithmic negativity across a wide range of cosmological backgrounds, each characterized by a distinct equation of state. The von Neumann entropy obtained via QuGIT simulations is compared with analytic Rényi entropy bounds, thereby validating the accuracy of our circuit implementation of the cosmological squeezing Hamiltonian in both accelerating and decelerating scenarios. We further investigate the role of thermal noise and demonstrate how the von Neumann entropy and logarithmic negativity are affected by its presence.

Figures (25)

• Figure 1: Solutions for $r_k$ versus the scale factor $a$. All curves show decaying oscillations at early times before transitioning to a period of growth. This growth phase begins earlier for less negative values of $w$. Consequently, at any given late time, a less negative $w$ (e.g., $w=-0.7$) results in a significantly larger value for $r_k$ compared to more negative values.
• Figure 2: Numerical solutions for $sin(2\phi_k)$ as a function of scale factor $a$ for expanding accelerating background. The solution oscillates rapidly initially and then dampens depending on the value of $w$. For higher values ($w=-0.7$) transition occurs earlier, but for lower values ($w=-1.3$) the oscillations occur until much later and then finally settles at zero.
• Figure 3: Numerical solutions for $r_k$ as a function of scale factor $a$ for expanding accelerating background ($w= -1$), with varying k. Modes with smaller k exit the horizon earlier, which allows them more time to grow and reach a larger final value. The inset shows the oscillations of the modes before the horizon exit.
• Figure 4: Numerical solutions for $r_k$ as a function of scale factor $a$ for expanding decelerating background. For smaller $w$, the squeezing occurs for a much longer time, and it reaches a higher final value compared to higher $w$ values. Oscillations can be seen after the squeezing stops.
• Figure 5: Numerical solutions for $sin(2\phi_k)$ as a function of scale factor $a$ for expanding decelerating background. All curves begin at $0$ and start oscillating. For higher $w$, the oscillation begins much earlier compared to lower values. For $w = -0.2$ and $0.0$, the transition to oscillation occurs much later, which isn't visible in the graph.