Excited states of coherent harmonic qubits with long-range photon coupling and dissipation

TL;DR

This paper investigates the excited states of coherent harmonic qubits coupled via a dissipative photon mode, revealing collective excited states with large energy gaps and frequency-dependent energy transfer phenomena.

Contribution

It introduces a novel analysis of the energy spectrum of harmonic qubits with long-range photon coupling, highlighting the existence of collective excited states above a certain threshold.

Findings

Resonant energy transfer occurs at higher frequencies above threshold.

Collective excited states are separated by large energy gaps.

Energy transfer depends on the number of qubits and external oscillator frequencies.

Abstract

It is known that ensembles of interacting oscillators or qubits can exhibit the phenomenon of quantum synchronization. In this work we consider a set of $N$ identical two-state systems that we call ``harmonic qubits'', because the kinetic part of their Hamiltonian is of the form $\omega_0 \sum_i a^\dagger_i a_i$, 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 $N$ and there are clear cross correlations $\langle a^\dagger_i a_j \rangle$. Here we are interested into the energy spectrum of the excited states of this system. In order to obtain information on the coherent transitions we introduce a weak coupling of each qubit with an external oscillator of variable frequency $\omega$ and we check via Monte Carlo time evolution for which values of $\omega$ variations in the occupation of the external oscillator occur. After adding a second external oscillator coupled to the first only through the $N$ qubits, we also look at the energy transfer 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 $E_0<0$) we find resonant transfer at frequencies which are definitely higher, and growing with $N$. This signals the presence of collective excited states, separated by large energy gaps, which are absent below threshold.