A quasi-particle picture for entanglement cones and horizons in analogue cosmology

Abstract

Although particle production in curved quantum field theories (cQFTs) is key to our understanding of the early universe and black hole physics, its direct observation requires extreme conditions or unrealistic sensitivities. Recent progress in quantum simulators indicates that analogues of cosmological particle production can be observed in table-top experiments of cold atomic gases described by effective cQFTs. This promises a high degree of tunability in the synthesised curved spacetimes and, moreover, sets a clear roadmap to explore the interplay of particle production with other non-perturbative effects genuine to interacting QFTs. We hereby focus on the appearance of scalar and pseudo-scalar condensates for self-interacting Dirac fermions, and study how dynamical mass generation and spontaneous symmetry breaking affects real-time dynamics through the lens of entanglement. We use the entanglement contour (EC) to analyse the spatio-temporal structure of particle production, showing that a quasi-particle picture for the EC captures the cosmological horizon in accelerating spacetimes, while also being sensitive to the effect of different symmetry-breaking processes. In particular, we show that the combined breakdown of time-reversal symmetry due to the expanding spacetime, and parity due to a pseudo-scalar condensate, manifests through the structure of the light-cone-like propagation of entanglement.

Figures (6)

• Figure 1: Time evolution of entanglement entropy $S_A(\eta)$ for a partition of (a)$\ell_A=32$ sites from a $N_S=128$ sites system, and (b)$\ell_A=128$ sites from a $N_S=512$ sites system. The blue line represents the numerical result while the red dashed line represents the quasi-particle prediction. The parameters are set as $ma=1$, $g_0^2=0$, $\mathsf{ a}_0=0.01$ and $\mathsf{ a}_{\rm f}=10$.
• Figure 2: Spatio-temporal propagation of EC in the asymptotic flat region $\mathsf{a}_{\rm f}$, both in the free $g_0^2=0$ and in the interacting $g_0^2=1$ regimes, and setting $ma=-1$, $\mathsf{ a}_0=0.7$, $\mathsf{ a}_{\rm f}=1.3$, ${\sf H}a=100$ (sudden expansion). The dashed white lines indicate the light-cone-like predictions based on the group velocity after the sudden expansion.
• Figure 3: (a) Evolution of entanglement entropy of a $\ell_A=64$ partition of a $N_S=512$ sites system after an expansion with a vanishing pseudo-scalar condensate $\Pi=0$. The blue line represents the numerical result while the red dashed line represents the quasi-particle prediction. The parameters are set as $ma=1$, $\mathsf{ a}_0=0.01$, $\mathsf{ a}_{\rm f}=10$, $g_0^2=3$ and ${\sf H}a=100$. (b) Evolution of the scalar and pseudo-scalar condensates for a system of $N_S=512$ sites, showing their persistent oscillating behaviour. The parameters are set as $ma=-1$, $\mathsf{ a}_0=0.7$, $\mathsf{ a}_{\rm f}=1.3$, $g_0^2=3$ and ${\sf H}a=100$. (c) Evolution of entanglement entropy of a $\ell_A=64$ partition of a $N_S=512$ sites system after an expansion with both a non-vanishing scalar and pseudo-scalar condensates, $\Sigma,\Pi\neq0$. The blue line represents the numerical result while the red dashed line represents the quasi-particle prediction. The parameters are the same as in (b). (d) Evolution of entanglement contour of a $\ell_A=64$ partition of a $N_S=512$ sites system after an expansion with both a non-vanishing scalar and pseudo-scalar condensates, $\Sigma,\Pi\neq0$. We show the contribution from the upper component of the spinor field to the EC, $S_i^u$. The white lines correspond to the curves $x(\eta)=\int^\eta v_g(\eta')d\eta'$. The parameters are the same as in (b).
• Figure 4: Spatio-temporal propagation of EC during a de Sitter expansion, using conformal and cosmological time respectively, and setting $ma=1$, ${\sf H}a=0.1$, $g_0^2=2$, $\mathsf{ a}_0=1/3$, with $\eta$ and $t$ expressed in lattice units. The expansion in (a) starts at $\eta_0a=-30$ and extends to the distant future $\eta\to0^{-}$, approximated by $\eta a=-0.001362$. The shaded regions denote the asymptotic spatial boundary that particles cannot cross. In (b), the corresponding expansion covers $t_0=0$ to $ta\to\infty$, here approximated by $t=100/a$.
• Figure 5: Time evolution of EC for different phases for a partition $A$ of $N_A=32$ sites, from a system of $N_S=128$ sites. (a) Numerical time evolution of EC for each leg of the ladder, for an expansion with $\Pi\neq0$, with $ma=-1$, $g^2=0$, $\mathsf{ a}_0=0.7$, $\mathsf{ a}_{\rm f}=1.3$, $\mathsf{H}=100$ (quench limit). (b) Numerical time evolution of EC, with all the sites shown in the horizontal axis, alternating up and down spinors, for an expansion with $\Pi\neq0$, with $ma=-1$, $g^2=0$, $\mathsf{ a}_0=0.7$, $\mathsf{ a}_{\rm f}=1.3$, $\mathsf{H}=100$ (quench limit).