We consider a complete study of the influence of the cavity size on the spontaneous decay of an atom excited state, roughly approximated by a harmonic oscillator. We confine the oscillator-field system in a spherical cavity of radius $R$ , perfectly reflective, and work in the formalism of dressed coordinates and states, which allows to perform non-perturbative calculations for the probability of the atom to decay spontaneously from the first excited state to the ground state. In free space, $R\to\infty$ , we obtain known exact results an for sufficiently small $R$ we have developed a power expansion calculation in this parameter. Furthermore, for arbitrary cavity size radius, we developed numerical computations and showed complete agreement with the exact one for $R\to\infty$ and the power expansion results for small cavities, in this way showing the robustness of our results. We have found that in general the spontaneous decay of an excited state of the atom increases with the cavity size radius and vice versa. For sufficiently small cavities the atom practically does not suffers spontaneous decay, whereas for large cavities the spontaneous decay approaches the free-space $R\to\infty$ value. On the other hand, for some particular values of the cavity radius, in which the cavity is in resonance with the natural frequency of the atom, the spontaneous decay transition probability is increased compared to the free-space case. Finally, we showed how the probability spontaneous decay go from an oscillatory time behaviour, for finite cavity radius, to an almost exponential decay, for free space.We consider a complete study of the influence of the cavity size on the spontaneous decay of an atom excited state, roughly approximated by a harmonic oscillator. We confine the oscillator-field system in a spherical cavity of radius $R$, perfectly reflective, and work in the formalism of dressed coordinates and states, which allows to perform non-perturbative calculations for the probability of the atom to decay spontaneously from the first excited state to the ground state. In free space, $R\to\infty$, we obtain known exact results an for sufficiently small $R$ we have developed a power expansion calculation in this parameter. Furthermore, for arbitrary cavity size radius, we developed numerical computations and showed complete agreement with the exact one for $R\to\infty$ and the power expansion results for small cavities, in this way showing the robustness of our results. We have found that in general the spontaneous decay of an excited state of the atom increases with the cavity size radius and vice versa. For sufficiently small cavities the atom practically does not suffers spontaneous decay, whereas for large cavities the spontaneous decay approaches the free-space $R\to\infty$ value. On the other hand, for some particular values of the cavity radius, in which the cavity is in resonance with the natural frequency of the atom, the spontaneous decay transition probability is increased compared to the free-space case. Finally, we showed how the probability spontaneous decay go from an oscillatory time behaviour, for finite cavity radius, to an almost exponential decay, for free space.

arXiv:1711.00288Nov 1, 20170 citations

Spontaneous Emission

Galina A. Nemova

SPIE eBooksMar 23, 20220 citations

Kinetics of spontaneous decay in cold atomic systems

Oleg Prepelita

We discuss the spontaneous decay in a system of cold identical two-level atoms when, due to the strong dipole–dipole interaction, the collision-induced spontaneous decay plays a leading role in the process. We show that the time profile of the spontaneous transition is essentially non-exponential. Also, we argue that at a low initial temperature of the atomic system the spontaneous decay is accompanied by strong heating caused by the inelastic atom–atom collisions. We show that the spontaneous emission spectrum is asymmetric. In addition, the width of the emission spectrum is a function of time. When atoms decay, the emission spectrum becomes broader. The spectrum’s asymmetry and the atomic system’s heating have the same physical origin: coming from the peculiarities of the atoms’ distribution function.We discuss the spontaneous decay in a system of cold identical two-level atoms when, due to the strong dipole–dipole interaction, the collision-induced spontaneous decay plays a leading role in the process. We show that the time profile of the spontaneous transition is essentially non-exponential. Also, we argue that at a low initial temperature of the atomic system the spontaneous decay is accompanied by strong heating caused by the inelastic atom–atom collisions. We show that the spontaneous emission spectrum is asymmetric. In addition, the width of the emission spectrum is a function of time. When atoms decay, the emission spectrum becomes broader. The spectrum’s asymmetry and the atomic system’s heating have the same physical origin: coming from the peculiarities of the atoms’ distribution function.

Canadian Journal of PhysicsDec 11, 20200 citations

Spontaneous emission

Luca Salasnich

Springer eBooksJan 1, 20200 citations

Non-Markovian dynamic evolution of spontaneous emission decay of a two-level atom embedded in one-dimensional photonic crystals

Nian-Hua Liu, Jingping Xu, Shi‐Yao Zhu

The dynamic evolution of atomic spontaneous emission in one-dimensional photonic crystals (1DPC) is investigated by using mode functions for the 1DPC. Our attention is focused on the non-Markovian processes in the first several optical cycles of the spontaneous emission decay. The integral-differential dynamic equation is directly solved by numerical calculation without using the Markovian approximation. The interference of the multireflected fields plays an important role in the non-Markovian processes. Due to the interference of the fields successive arrived at the atom due to the reflection at the interfaces, the decay rate shows a series of pulselike peaks. If the interference is constructive, the spontaneous decay is enhanced, while if the interference is destructive, the spontaneous decay is suppressed. The steady decay rate is approximately equal to the vacuum decay rate, when the atomic transition frequency corresponds to an allowed normal mode of the 1DPC. The spontaneous emission decay is suppressed if the atomic transition frequency is within the forbidden gap of the 1DPC.The dynamic evolution of atomic spontaneous emission in one-dimensional photonic crystals (1DPC) is investigated by using mode functions for the 1DPC. Our attention is focused on the non-Markovian processes in the first several optical cycles of the spontaneous emission decay. The integral-differential dynamic equation is directly solved by numerical calculation without using the Markovian approximation. The interference of the multireflected fields plays an important role in the non-Markovian processes. Due to the interference of the fields successive arrived at the atom due to the reflection at the interfaces, the decay rate shows a series of pulselike peaks. If the interference is constructive, the spontaneous decay is enhanced, while if the interference is destructive, the spontaneous decay is suppressed. The steady decay rate is approximately equal to the vacuum decay rate, when the atomic transition frequency corresponds to an allowed normal mode of the 1DPC. The spontaneous emission decay is suppressed if the atomic transition frequency is within the forbidden gap of the 1DPC.

Physical Review BAug 11, 20069 citations

R

, perfectly reflective, and work in the formalism of dressed coordinates and states, which allows to perform non-perturbative calculations for the probability of the atom to decay spontaneously from the first excited state to the ground state. In free space,

R\to\infty

, we obtain known exact results an for sufficiently small

R

we have developed a power expansion calculation in this parameter. Furthermore, for arbitrary cavity size radius, we developed numerical computations and showed complete agreement with the exact one for

R\to\infty

and the power expansion results for small cavities, in this way showing the robustness of our results. We have found that in general the spontaneous decay of an excited state of the atom increases with the cavity size radius and vice versa. For sufficiently small cavities the atom practically does not suffers spontaneous decay, whereas for large cavities the spontaneous decay approaches the free-space

R\to\infty

value. On the other hand, for some particular values of the cavity radius, in which the cavity is in resonance with the natural frequency of the atom, the spontaneous decay transition probability is increased compared to the free-space case. Finally, we showed how the probability spontaneous decay go from an oscillatory time behaviour, for finite cavity radius, to an almost exponential decay, for free space.