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

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 ${\omega }_0{\sum }_i{a}_i^{†}{a}_i$, 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 $⟨a_i^{†}{a}_j⟩$. 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.

15 pages, 7 figures, final journal version

References in corpus (19)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• QuTiP: An open-source Python framework for the dynamics of open quantum systems
• Ultrastrong coupling regimes of light-matter interaction
• A short introduction to the Lindblad Master Equation
• Coherent and Collective Quantum Optical Effects in Mesoscopic Systems
• Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa
• Entanglement tongue and quantum synchronization of disordered oscillators
• Macroscopic quantum computation using Bose-Einstein condensates
• Cooperative emission of light by an ensemble of dipoles near a metal nanostucture: The plasmonic Dicke effect
• Cavity QED of Strongly Correlated Electron Systems: A No-go Theorem for Photon Condensation
• Plasmon-mediated superradiance near metal nanostructures
• Quantum synchronization and entanglement of two qubits coupled to a driven dissipative resonator
• Quantum Synchronisation Enabled by Dynamical Symmetries and Dissipation
• Level Splitting in Association with the Multiphoton Bloch-Siegert Shift
• Multiphoton Bloch-Siegert shifts and level-splittings in spin-one systems
• Exploring Quantum Synchronization with a Composite Two-Qubit Oscillator
• Coherent Plasma in a Lattice
• Numerical Simulations Unveil Superradiant Coherence in a Lattice of Charged Quantum Oscillators
• Spectral Analysis of Proton Eigenfunctions in Crystalline Environments