Temporal and Spatial Dependence of Quantum Entanglement from a Field Theory Perspective

Abstract

We consider the entanglement dynamics between two Unruh-DeWitt detectors at rest separated at a distance $d$. This simple model when analyzed properly in quantum field theory shows many interesting facets and helps to dispel some misunderstandings of entanglement dynamics. We find that there is spatial dependence of quantum entanglement in the stable regime due to the phase difference of vacuum fluctuations the two detectors experience, together with the interference of the mutual influences from the backreaction of one detector on the other. When two initially entangled detectors are still outside each other's light cone, the entanglement oscillates in time with an amplitude dependent on spatial separation $d$. When the two detectors begin to have causal contact, an interference pattern of the relative degree of entanglement (compared to those at spatial infinity) develops a parametric dependence on $d$. The detectors separated at those $d$ with a stronger relative degree of entanglement enjoy longer disentanglement times. In the cases with weak coupling and large separation, the detectors always disentangle at late times. For sufficiently small $d$, the two detectors can have residual entanglement even if they initially were in a separable state, while for $d$ a little larger, there could be transient entanglement created by mutual influences. However, we see no evidence of entanglement creation outside the light cone for initially separable states.

21 pages, 8 figures. Minor changes. Some plots are re-expressed in logarithmic negativity. No change in the overall results

References in corpus (9)

• Finite-Time Disentanglement via Spontaneous Emission
• Dark periods and revivals of entanglement in a two qubit system
• Dynamics of the entanglement between two oscillators in the same environment
• Exact Master Equation and Quantum Decoherence of Two Coupled Harmonic Oscillators in a General Environment
• Backreaction and Unruh effect: New insights from exact solutions of uniformly accelerated detectors
• Disentanglement of two harmonic oscillators in relativistic motion
• Induced decoherence and entanglement by interacting quantum spin baths
• Non-Markovian Dynamics and Entanglement in Quantum Brownian Motion
• Generation of Entanglement Outside of the Light Cone

Cited by in corpus (49)

• Observer dependent entanglement
• Relativistic Quantum Information in Detectors-Field Interactions
• The Rotating-Wave Approximation: Consistency and Applicability from an Open Quantum System Analysis
• The relativistic quantum channel of communication through field quanta
• Entanglement creation between two causally-disconnected objects
• Radiative processes of uniformly accelerated entangled atoms
• Quantum thermodynamics from the nonequilibrium dynamics of open systems: energy, heat capacity and the third law
• Vacuum entanglement enhancement by a weak gravitational field
• Quantum teleportation in vacuum using only Unruh-DeWitt detectors
• Entanglement dynamics for uniformly accelerated two-level atoms coupled with electromagnetic vacuum fluctuations
• Nonequilibrium Steady State in Open Quantum Systems: Influence Action, Stochastic Equation and Power Balance
• Radiative processes of two entangled atoms outside a Schwarzschild black hole
• Relativistic quantum information and time machines
• Quantum teleportation between moving detectors
• Quantum teleportation between moving detectors in a quantum field
• Quantum entanglement and entropy in particle creation
• Non-Markovian Dynamics and Entanglement of Two-level Atoms in a Common Field
• Entanglement dynamics for uniformly accelerated two-level atoms in the presence of a reflecting boundary
• Distance and Coupling Dependence of Entanglement in the Presence of a Quantum Field
• Entanglement dynamics in a Kerr spacetime
• Entanglement Dynamics of Detectors in an Einstein Cylinder
• Fluctuation-Dissipation and Correlation-Propagation Relations from the Nonequilibrium Dynamics of Detector-Quantum Field Systems
• Boundary Effects on Quantum Entanglement and its Dynamics in a Detector-Field System
• Dissipation suppression for an Unruh-DeWitt battery with a reflecting boundary
• Modulated Entanglement Evolution Via Correlated Noises
• Nonequilibrium Nonlinear Open Quantum Systems I. Functional Perturbative Analysis of a Weakly Anharmonic Oscillator
• Information carrying capacity of a cosmological constant
• Fluctuation-Dissipation and Correlation-Propagation Relations in $(1+3)$D Moving Detector-Quantum Field Systems
• "Hot Entanglement"? -- A Nonequilibrium Quantum Field Theory Scrutiny
• Vacuum entanglement probes for ultra-cold atom systems
• Generalized uncertainty relations and entanglement dynamics in quantum Brownian motion models
• Unruh deWitt probe of late time revival of quantum correlations in Friedmann spacetimes
• Quantum Brownian motion of multipartite systems and their entanglement dynamics
• Unruh-DeWitt detectors as mirrors: Dynamical reflectivity and Casimir effect
• Extraction of entanglement from quantum fields with entangled particle detectors
• Fulling-Davies-Unruh effect for accelerated two-level single and entangled atomic systems
• Dynamical Response of an Unruh-DeWitt Detector in a Quantum Field over the History of the Universe
• Probing Planckian physics in de Sitter space with quantum correlations
• Hot entanglement? -- Parametrically coupled quantum oscillators in two heat baths: instability, squeezing and driving
• Effect of Interatomic Separation on Entanglement Dynamics in a Two-Atom Two-Mode Model
• Two-mode Gaussian quantum states measured by collinearly and noncollinearly accelerating observers
• Pathways toward understanding Macroscopic Quantum Phenomena
• Detectors interacting through quantum fields: Non-Markovian effects, non-perturbative generation of correlations and apparent non-causality
• Time dependent field correlators from holographic EPR pairs
• Local entanglement generation in the adiabatic regime
• Zeroth Law in Quantum Thermodynamics at Strong Coupling: `in Equilibrium', not `Equal Temperature'
• Single and entangled atomic systems in thermal bath and the Fulling-Davies-Unruh effect
• Autangle: A case of Quantum Narcissism?
• Detection of quantum entanglement across the event horizon