Abstract
In this work, a chain of N identical two-level atoms coupled with a quantized electromagnetic field, initially prepared via a single-photon Fock state, is investigated. The N-particle state amplitude of the system is calculated for several space configurations of the atoms in the Weisskopf-Wigner approximation. It was shown that the space configuration of an atomic chain, the total number of atoms, and even the available volume for the field modes define the behavior of the system state amplitude with time. Applying the condition of ‘cyclic bonds’, presented in this work, to the elaborated theory allows to describe the system time evolution, practically, for any space configuration.
Highlights
The collective absorption of photons by an ensemble of identical atoms ‘provides valuable insights into the many-body physics of photons and atoms’
Conclusions in this work, we investigated a chain of N identical two-level long distanced atoms prepared ‘via a singlephoton Fock state’
The functional dependence of the atomic state amplitudes on a space configuration and time is derived in the Weiskopf-Wiegner approximation
Summary
The collective absorption (emission) of photons by an ensemble of identical atoms ‘provides valuable insights into the many-body physics of photons and atoms’ (quoted from [1]). When the average distances between atoms are much less than the ‘resonant transition’ wavelength of emitted (absorbed) light, the cooperative coupling leads to a substantial radiative shift of the transition energy and significant change in decay rate of the ensemble state. The latter was revealed through the various theoretical (for example, some relatively modern researches in [2,3,4,5]) and experimental investigations (see starting, for example, from [6,7] to the modern applications like described in [8] and impressively effective experimental realizations as in [1]). The calculations of the state amplitudes of the atomic system are made for several approximations in resonator (cavity) characteristics and for several types of space configurations of the atoms in the chain
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