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Register a new userDynamics of entanglement in expanding quantum fields
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We develop a novel real-time approach to computing the entanglement between spatial regions for Gaussian states in quantum field theory. The entanglement entropy is characterized in terms of local correlation functions on space-like Cauchy hypersurfaces. The framework is applied to explore an expanding light cone geometry in the particular case of the Schwinger model for quantum electrodynamics in 1+1 space-time dimensions. We observe that the entanglement entropy becomes extensive in rapidity at early times and that the corresponding local reduced density matrix is a thermal density matrix for excitations around a coherent field with a time dependent temperature. Since the Schwinger model successfully describes many features of multiparticle production in $e^+ e^-$ collisions, our results provide an attractive explanation in this framework for the apparent thermal nature of multiparticle production even in the absence of significant final state scattering.
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A surprising result in $e^+ e^-$ collisions is that the particle spectra from the string formed between the expanding quark-antiquark pair have thermal properties even though scatterings appear not to be frequent enough to explain this. We address this problem by considering the finite observable interval of a relativistic quantum string in terms of its reduced density operator by tracing over the complement region. We show how quantum entanglement in the presence of a horizon in spacetime for the causal transfer of information leads locally to a reduced mixed-state density operator. For very early proper time $tau$, we show that the entanglement entropy becomes extensive and scales with the rapidity. At these early times, the reduced density operator is of thermal form, with an entanglement temperature $T_tau=hbar/(2pi k_B tau)$, even in the absence of any scatterings.
We evaluate self-interaction effects on the quantum correlations of field modes of opposite momenta for scalar $lambda phi^4$ theory in a two-dimensional asymptotically flat Robertson-Walker spacetime. Such correlations are encoded both in the von-Neumann entropy defined through the reduced density matrix in one of the modes and in the covariance expressed in terms of the expectation value of the number operators for each mode in the evolved state. The entanglement between field modes carries information about the underlying spacetime evolution.
We study the evolution of the two scalar fields entangled via a mutual interaction in an expanding spacetime. We compute the logarithmic negativity to leading order in perturbation theory and show that for lowest order in the coupling constants, the mutual interaction will give rise to the survival of the quantum correlations in the limit of the smooth expansion. The results suggest that interacting fields can codify more information about the underlying expansion spacetime and lead to interesting observable effects.
We consider entanglement entropy between two halves of space separated by a plane, in the theory of free photon in 3+1 dimensions. We show how to separate local gauge invariant quantities that belong to the two spatial regions. We calculate the entanglement entropy by integrating over the degrees of freedom in one half space using an approximation that assumes slow variation of the magnetic fields in longitudinal direction. We find that the entropy is proportional to the transverse area as expected. Interestingly the entanglement properties of the 2D transverse and longitudinal modes of magnetic field are quite different. While the transverse fields are entangled mostly in the neighborhood of the separation surface as expected, the longitudinal fields are entangled through an infrared mode which extends to large distances from the entanglement surface. This long range entanglement arises due to necessity to solve the no-monopole constraint condition for magnetic field.
We investigate the quantum radiation produced by an Unruh-De Witt detector in a uniformly accelerating motion coupled to the vacuum fluctuations. Quantum radiation is nonvanishing, which is consistent with the previous calculation by Lin and Hu [Phys. Rev. D 73, 124018 (2006)]. We infer that this quantum radiation from the Unruh-De Witt detector is generated by the nonlocal correlation of the Minkowski vacuum state, which has its origin in the entanglement of the state between the left and the right Rindler wedges.
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