Abstract
It is known that ensembles of interacting oscillators or qubits can exhibit the phenomenon of quantum synchronization. In this work, a set of (Formula presented.) identical two-state systems that we call “harmonic qubits” is considered, because the kinetic part of their Hamiltonian is of the form (Formula presented.), coupled through a multi-state “photon” mode subject to dissipation. It has been proven numerically that when the coupling between the qubits and the photon is sufficiently strong, the ensemble condenses into a ground state with negative energy, the energy gap is proportional to (Formula presented.) and there are clear cross correlations (Formula presented.). Here, the energy spectrum of the excited states of this system is the point of interest. In order to obtain information on the coherent transitions, a weak coupling of each qubit is introduced with an external oscillator of variable frequency (Formula presented.) and it is checked via Monte Carlo time evolution for which values of (Formula presented.) variations in the occupation of the external oscillator occur. After adding a second external oscillator coupled to the first only through the (Formula presented.) qubits, the energy transfer is also considered between the two external oscillators in dependence on their frequency, a transfer which is possible only through the excited states of the qubits. Above threshold (when (Formula presented.)), resonant transfer is found at frequencies that are definitely higher, and growing with (Formula presented.). This signals the presence of collective excited states, separated by large energy gaps, which are absent below threshold.