The entanglement of quantum systems is commonly restricted by their coupling Hamiltonian and initial state properties. Here, we prove by exact analysis of tunnel-coupled bosonic field modes that factorized multiboson two-mode states can become fully entangled via stroboscopic sign flips of the two-mode coupling. Their entanglement can exponentially grow with the number of flips. With the exception of specific prohibitive states that are invariant under such sign-flip control, this effect universally applies to two-mode state preparation. Remarkably, this linear control may provide entanglement resources for diverse quantum technological applications by readily available means.

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• Quantum control
• Quantum correlations in quantum information
• Quantum entanglement
• Tunneling & traversal time