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Physical Review A

Collective spontaneous emission beyond the rotating-wave approximation

Yong Li, Jörg Evers, Hang Zheng, Shi‐Yao Zhu

Published May 22, 2012• 35 citations
Publisher

Abstract

The collective spontaneous emission of $N$ multilevel atoms is studied in optical vector theory and without applying the rotating-wave approximation. The counter-rotating terms are included using a unitary transformation method. We analyze the decay dynamics starting from two initial conditions, the standard Dicke and timed Dicke states. In addition to the dependence on ensemble volume and density, we also study the effect of the ensemble geometry on cooperative emission for spheres, cubes, and quasi-two-dimensional shapes in different orientations. Finally, time-dependent cooperative spontaneous emission rates are introduced and investigated.

DOI
10.1103/physreva.85.053830

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The collective spontaneous emission of NNN multilevel atoms is studied in optical vector theory and without applying the rotating-wave approximation. The counter-rotating terms are included using a unitary transformation method. We analyze the decay dynamics starting from two initial conditions, the standard Dicke and timed Dicke states. In addition to the dependence on ensemble volume and density, we also study the effect of the ensemble geometry on cooperative emission for spheres, cubes, and quasi-two-dimensional shapes in different orientations. Finally, time-dependent cooperative spontaneous emission rates are introduced and investigated.
The spectrum of cooperative light emission from ensembles of multilevel atoms is studied in optical vector theory and without applying the rotating-wave approximation. The effects of counter-rotating terms are included using a unitary transformation method. The spectra are analyzed and interpreted in terms of the radiative eigenmodes of the atom ensemble. We further show how the qualitative features arise from the structure of the underlying two-particle dipole-dipole interaction induced by the the vacuum field. We predict that for a suitable modification of the ensemble properties, the sign of the cooperative Lamb shift can be reversed, while still maintaining strong superradiant emission. Finally, we discuss the effects of finite detection resolution and of averaging over many realizations of the random distribution of atoms for given ensemble parameters.
We study cooperative single-photon spontaneous emission from NNN multilevel atoms for different atomic distributions in optical vector theory. Instead of the average approximation for interatomic distance or the continuum approximation (sums over atoms replaced by integrals) for atomic distribution, the positions of every atom are taken into account by numerical calculation. It is shown that the regularity of atomic distribution has considerable influence on cooperative spontaneous emission. For a small atomic sample (compared with radiation wavelength), obtaining strong superradiance requires not only the uniform excitation (the Dicke state) but also the uniform atomic distribution. For a large sample, the uniform atomic distribution is beneficial to subradiance of the Dicke state, while the influence of atomic distribution on the timed Dicke state is weak and its time evolution obeys exponential decay approximately. In addition, we also investigate the corresponding emission spectrum and verify the directed emission for the timed Dicke state for a large atomic sample.
The spontaneous decay of a multilevel atom interacting with the electromagnetic field in free space is investigated with a unitary transformation method, which is introduced in order to include all rotating and counter-rotating terms in the Hamiltonian. By using the ground state of the total Hamiltonian, the evolution of the effective decay rate and the energy shift are calculated. When the atomic transition frequency is smaller than the central frequency of the spectrum, the Zeno effect dominates, and if the atomic transition frequency is larger than the central frequency, the anti-Zeno effect will dominate. The time evolution of the energy shift is obtained. The counter-rotating terms lead to a shift toward the low frequency region for the frequency distribution of the emitted photon.
Superradiance is an extensive cooperative spontaneous emission phenomenon, exhibited by some atomic collective-spin states. However, distinct initial states differ in their decay dynamics. Dicke states ∣j,m⟩|j,m\rangle∣j,m⟩ with distinct numbers of excitations n=m+jn=m+jn=m+j, driven by vacuum fluctuations, have their peak emission intensity shifted in time. Rotating Dicke states relative to the decay axis introduces an interesting parity structure that affects the pulse profile and photon correlations. Squeezed-bath prepared states undergo a squeezing-controlled crossover to the rotated Dicke states, making the emission character dependent on the amount of squeezing transferred from light to the atomic state. For semiclassical states with a macroscopic dipole moment, like the atomic coherent state, the emission intensity depends on their polarization. We present detailed results on the superradiant dynamics of a representative selection of states expanded in Dicke states to highlight the initial state as an independent dynamical control parameter. For large-NNN, we are able to predict fairly accurately the pulse profile in each case using the mean-field approximation, an approach based on the Fokker--Planck equation. We also present comparative results on the intensity correlation function, quantify the coherent and incoherent contributions of the emission, and contrast between small and large ensembles.
We study the collective spontaneous emission of a linear atomic chain excited by a single photon. The interaction between the atoms and the common vacuum field can significantly change the eigenenergy and the spontaneous emission rate of the system. Due to the dipole-dipole interactions, the system prepared in a single-photon timed Dicke state is the superposition of superradiant and subradiant eigenstates that can have a nonexponential decay dynamics. We can tune the frequency and linewidth of the superradiant and subradiant emission from a timed Dicke state by changing the direction of the atomic dipole moment or the atomic separation. In addition, the emission direction of the superradiant and subradiant photons also depends on the polarization of the atoms.
We investigate the collective spontaneous emission from an ensemble of two-level atoms evenly distributed inside a sphere with a low density. An initial symmetric single-excitation state is considered and polarizations for all atoms are assumed to be aligned in the same direction. We find that the superradiant decay rate of the ensemble exhibits oscillatory features dependent on the radius of the sphere and the atomic radiation wavelength, indicating that the collective emission rate can be less than the single-atom decay rate for certain parameters. Moreover, the system exhibits a hidden equivalence where the collective emission from the ensemble gives the same radiation rate as the case of a two-atom model where one atom is at the center of the sphere and the other effective large atom, composed of all other atoms, is localized at the edge of the sphere along the polarization direction. Our result hence provides a potential method towards exploring complex many-body physics by simplifying the model into a two-body problem.