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

Abstract

The link of two concepts, indistinguishability and entanglement, with the energy-time uncertainty principle is demonstrated in a system composed of two strongly coupled bosonic modes. Working in the limit of a short interaction time, we find that the inclusion of the antiresonant terms to the coupling Hamiltonian leads the system to relax to a state which is not the ground state of the system. This effect occurs passively by just presence of the antiresonant terms and is explained in terms of the time-energy uncertainty principle for the simple reason that at a very short interaction time, the uncertainty 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 and doubly excited states. The population distribution, correlations and entanglement are shown to be substantially depend on whether the modes decay independently or collectively to an exterior reservoir. In particular, when the modes decay independently with equal rates, entanglement with the complete distinguishability of the modes is observed. The modes can be made mutually coherent if they decay with unequal rates. However, the visibility in the single-photon interference cannot exceed 50%. When the modes experience collective damping, they are indistinguishable even if decay with equal rates and the visibility can, in principle, be as large as unity. We find that this feature derives from the decay of the system to a pure entangled state rather than the expected mixed state. When the modes decay with equal rates, the steady-state values of the density matrix elements are found dependent on their initial values.

Bipartite Entanglement in Optomechanical Cavities Driven by Squeezed Light

“…So, the entanglement can be transferred between the two independent cavity modes. The entanglement transfer depends on the kind of environment [18,19,26,63,64].…”

“…Recently, there has been substantial attention in examining entanglement in mesoscopic systems [22][23][24][25][26][27] and nanomechanical oscillators have become the key resources for the exploration of quantum mechanical characters at mesoscopic scales [28][29][30][31][32].…”

Delayed transfer of entanglement to initially populated qubits

“…Assuming that λ and µ are much larger than the damping rates of the cavities, we can make the Markov approximation in which we replace ρ(t ) by ρ(t), so that we can extract ρ(t) from the integral. The integral then can be evaluated and we arrive to the following master equation [34][35][36]…”

Exploring quantum correlations in a hybrid optomechanical system

“…Quantum entanglement has been considerably investigated in mesoscopic systems [23][24][25][26][27][28][29][30][31][32][33]. Indeed, hybrid optomechanical systems have been proposed as great candidates for the entanglement transfer from entangled light to mechanical resonators [34][35][36][37].…”