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Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento

Superradiant states in two-level and harmonic-oscillator systems

W. Żakowicz

Published Jul 1, 1971• 0 citations
Publisher
DOI
10.1007/bf02770094

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arXiv:2112.08134•Physical Review A•Jun 1, 2022•16 citations
The evolution of a small spherical system of many harmonic oscillators, initially in a coherent superradiant state, is considered. The dipole oscillators interact via their mutual fields, both longitudinal and transverse, including both radiation- and near-zone contributions. In principle, this interaction can dephase the vibration of oscillators and thereby decrease or eliminate the coherent superradiant contribution to the emitted radiation. It is shown, however, that if the system is sufficiently small, this dephasing makes only small corrections to the decay of the initial state. Thus the emission of a superradiant pulse and cooperative radiative decay are major processes in the system.
Quantum dissipation is studied in the superradiant phase of the Extended Dicke model. It is demonstrated analytically by quantum mechanical derivation of the Lindblad equation for the Dicke model in the superradiant state coupled to Caldeira-Leggett thermal bath, that the effective viscosity appearing in the semiclassical equations of motion of polaritonic condensate survives in the zero temperature limit T -> 0. The nonzero contribution to viscosity contains prefactor nB (ω, T ) + 1 with the Bose-Einstein function nB of harmonic oscillators in the thermal bath, indicating that virtual excitations of harmonic oscillators in the thermal bath coupled to the polaritons of Dicke model give rise to effective viscosity in the T -> 0 limit. Besides, it is demonstrated analytically, that correct expression for Lindbladian in the superradiant phase should be built using condensate-shifted creation and annihilation operators of the photons and pseudospin operators in Holstein-Primakoff representation of the coupled to photons two-level systems in order the system could relax to its minimum energy in T -> 0 limit due to thermal bath provided effective viscosity.
Multiple emitters coherently interacting with an electromagnetic mode give rise to collective effects such as correlated decay and coherent exchange interaction, depending on the separation of the emitters. By diagonalizing the effective non-Hermitian many-body Hamiltonian we reveal the complex-valued eigenvalue spectrum encoding the decay and interaction characteristics. We show that there are significant differences in the emerging collective effects for an array of interacting anharmonic oscillators compared to those of two-level systems and harmonic oscillators. The bosonic decay rate of the most superradiant state increases linearly as a function of the filling factor and exceeds that of two-level systems in magnitude. Furthermore, with bosonic systems, dark states are formed at each filling factor. These are in strong contrast with two-level systems, where the maximal superradiance is observed at half-filling and with larger filling factors superradiance diminishes and no dark states are formed. As an experimentally relevant setup of bosonic waveguide QED, we focus on arrays of transmon devices embedded inside a rectangular waveguide. Specifically, we study the setup of two transmon pairs realized experimentally in Zanner et al. [Nat. Phys. 18, 538 (2022)] and show that it is necessary to consider transmons as bosonic multilevel emitters to accurately recover correct collective effects for the higher excitation manifolds.