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Canadian Journal of Physics

Kinetics of spontaneous decay in cold atomic systems

Oleg Prepelita

Published Dec 11, 2020• 0 citations
Publisher

Abstract

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.

DOI
10.1139/cjp-2020-0353

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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.
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The interaction between electromagnetic radiation and two three-level atoms is investigated. The atom-atom separation is assumed to be smaller than the corresponding mean resonance wavelength. The total radiance rate of the atomic system is calculated as a function of time. Explicit results are given for several different initial states of the atomic system. Some of them exhibit superradiance, and some act as photon-trapping states. Instead of exponential decay, the oscillations appear in the time evolution of the radiation rate due to the correlation between atoms. The decay constants and coupling decay constants show strong effects on the emission rates. Completely differing from two identical double-level atoms, the cooperative effects always exist in the three-level atomic system except for the case in which the coupling decay constants ${\ensuremath{\gamma}}_{12}$ and ${\ensuremath{\gamma}}_{21}$ are zero.
The role of the collective antisymmetric state in entanglement creation by spontaneous emission in a system of two non-overlapping two-level atoms has been investigated. Populations of the collective atomic states and the Wootters entanglement measure (concurrence) for two sets of initial atomic conditions are calculated and illustrated graphically. Calculations include the dipole-dipole interaction and a spatial separation between the atoms that the antisymmetric state of the system is included throughout even for small interatomic separations. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. It is found that the ability of spontaneous emission to create transient entanglement relies on the absence of population in the collective symmetric state of the system. For the initial state of only one atom excited, entanglement builds up rapidly in time and reaches a maximum for parameter values corresponding roughly to zero population in the symmetric state. On the other hand, for the initial condition of both atoms excited, the atoms remain unentangled until the symmetric state is depopulated. A simple physical interpretation of these results is given in terms of the diagonal states of the density matrix of the system. We also study entanglement creation in a system of two non-identical atoms of different transition frequencies. It is found that the entanglement between the atoms can be enhanced compared to that for identical atoms, and can decay with two different time scales resulting from the coherent transfer of the population from the symmetric to the antisymmetric state. In addition, it was found that a decaying initial entanglement between the atoms can display a revival behaviour.
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Abstract. We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulas for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r12 and interact with each other via the dipole-dipole interaction, and the antisymmetric state of the system is included throughout, even for small inter-atomic separations, in contrast to the small sample model. It is shown that for sufficiently large values of the dipole-dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.
We discuss the creation of entanglement between two two-level atoms in the dissipative process of spontaneous emission. It is shown that spontaneous emission can lead to a transient entanglement between the atoms even if the atoms were prepared initially in an unentangled state. The amount of entanglement created in the system is quantified by using two different measures: concurrence and negativity. We find analytical formulae for the evolution of concurrence and negativity in the system. We also find the analytical relation between the two measures of entanglement. The system consists of two two-level atoms which are separated by an arbitrary distance r 12 and interact with each other via the dipole–dipole interaction, and the antisymmetric state of the system is included throughout, even for small interatomic separations, in contrast to the small-sample model. It is shown that for sufficiently large values of the dipole–dipole interaction initially the entanglement exhibits oscillatory behaviour with considerable entanglement in the peaks. For longer times the amount of entanglement is directly related to the population of the slowly decaying antisymmetric state.