  Dimerized magnets forming alternating Heisenberg chains exhibit quantum
coherence and entanglement and thus can find potential applications in quantum
information and computation. However, magnetic systems typically undergo
thermal decoherence at finite temperatures. Here, we show inelastic neutron
scattering results on an alternating antiferromagnetic-ferromagnetic chain
compound Na$_2$Cu$_2$TeO$_6$ that the excited quasiparticles can counter
thermal decoherence and maintain strong correlations at elevated temperatures.
At low temperatures, we observe clear dispersive singlet-triplet excitations
arising from the dimers formed along the crystalline $b$-axis. The excitation
gap is of $\sim$18 meV and the bandwidth is about half of the gap. The band top
energy has a weak modulation along the [100] direction, indicative of a small
interchain coupling. The gap increases while the bandwidth decreases with
increasing temperature, leading to a strong reduction in the available phase
space for the triplons. As a result, the Lorentzian-type energy broadening
becomes highly asymmetric as the temperature is raised. These results are
associated with a strongly correlated state resulting from hard-core constraint
and quasiparticle interactions. We consider these results to be not only
evidence for strong correlations at finite temperatures in Na$_2$Cu$_2$TeO$_6$,
but also for the universality of the strongly correlated state in a broad range
of quantum magnetic systems.
