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The link of two concepts, indistinguishability and entanglement, with theenergy-time uncertainty principle is demonstrated in a system composed of twostrongly coupled bosonic modes. Working in the limit of a short interactiontime, we find that the inclusion of the antiresonant terms to the couplingHamiltonian leads the system to relax to a state which is not the ground stateof the system. This effect occurs passively by just presence of theantiresonant terms and is explained in terms of the time-energy uncertaintyprinciple for the simple reason that at a very short interaction time, theuncertainty in the energy is of order of the energy of a single excitation,thereby leading to a distribution of the population among the zero, singly anddoubly excited states. The population distribution, correlations andentanglement are shown to be substantially depend on whether the modes decayindependently or collectively to an exterior reservoir. In particular, when themodes decay independently with equal rates, entanglement with the completedistinguishability of the modes is observed. The modes can be made mutuallycoherent if they decay with unequal rates. However, the visibility in thesingle-photon interference cannot exceed $50\%$. When the modes experiencecollective damping, they are indistinguishable even if decay with equal ratesand the visibility can, in principle, be as large as unity. We find that thisfeature derives from the decay of the system to a pure entangled state ratherthan the expected mixed state. When the modes decay with equal rates, thesteady-state values of the density matrix elements are found dependent on theirinitial values.

physical review. a/physical review, a

Evidence of indistinguishability and entanglement determined by the  energy-time uncertainty principle in a system of two strongly coupled bosonic  modes