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arXiv:2204.04271 · Armenian Journal of Physics

Collapse and Revival of n-Photon Coherent States and n-Photon Squeezed Coherent States

Moorad Alexanian

Published Apr 7, 2022• 2 citations

Abstract

We introduce the set of n-photon coherent states and the set of n-photon squeezed coherent states and study their collapse and revival and compare their behavior with the collapse and revival of the corresponding zero-photon coherent states and zero-photon squeezed coherent states, respectively. The set of n-photon squeezed coherent states (n = 0, 1, 2, ···) forms a basis of the Hilbert state of photons and may be of some interest. We notice that the presence of a few extra photons in the n-photon states as compared to the corresponding zero-photon states makes a large difference in the behavior of their collapse and revival. This indicates the large effect that a few extra photons make in the n-photon states as compared to the corresponding zero-photon states in their collapse and revival.

DOI: 10.54503/18291171-2022.15.1-25

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We introduce the set of n-photon coherent states and the set of n-photon squeezed coherent states and study their collapse and revival and compare their behavior with the collapse and revival of the corresponding zero-photon coherent states and zero-photon squeezed coherent states, respectively. The set of n-photon squeezed coherent states (n = 0, 1, 2, ···) forms a basis of the Hilbert state of photons and may be of some interest. We notice that the presence of a few extra photons in the n-photon states as compared to the corresponding zero-photon states makes a large difference in the behavior of their collapse and revival. This indicates the large effect that a few extra photons make in the n-photon states as compared to the corresponding zero-photon states in their collapse and revival.

We investigate some of the fundamental features of the interaction of squeezed light with two-level atoms in the framework of the Jaynes-Cummings model. We start our analysis by calculating the collapses and revivals of the atomic inversion. We discuss the degree of purity of the field (given by the entropy) and its disentanglement from the atomic source. The connection with the evolution of the Q-function is also made. We notice that contrary to the coherent state case, the field turns into a nearly pure (squeezed) state at the revival time as if the field was prepared in a coherent state. The field also becomes a superposition of squeezed states at half of the revival time, and this is confirmed by investigating the photon number distribution. The phase properties of the field are discussed using the Pegg-Barnett formalism.

We determine the Rabi oscillations for coherent and squeezed coherent states via one- and two-photon atomic transitions in two- and three-level atoms, respectively. The effect of squeezing coherent states is to reduce the large number of photons of mesoscopic scale to fewer photons and so be able to use numerical solutions with the aid of the Jaynes-Cummings model. We maximize the squeezing of the coherent state by minimizing the ratio of the photon number variance to photon number, thus narrowing the region where revival occurs.

It is well-known that the interaction among atoms/molecules and quantized electromagnetic fields with a small number of photons provides a peculiar quantum nature, i.e., collapses and revivals in the Rabi oscillations. In this study, we investigate the intermolecular interaction (dipole–dipole interaction) effect on the collapse-revival behavior using several dimer models (composed of two kinds of two-state monomers with slightly different excitation energies) with different intermolecular distances in the presence of a two-mode squeezed coherent field, in which each mode is initially correlated. It is found that although the collapse-revival behavior is fairly overlapped and indistinct in the case of a noninteracting dimer under the present two-mode squeezed coherent field, the decrease in the intermolecular distance (the increase in the intermolecular interaction) resurrects relatively distinct collapse-revival behavior with longer collapse and revival times. By analyzing the quantum behavior from the viewpoint of the dynamics of two-mode Pegg–Barnett photon-phase distributions and off-diagonal dimer density matrices, this feature is found to closely relate to a significant change in the degree of contribution between one- and two-photon processes caused by the variation in the intermolecular interaction.

With the help of a two-photon Jaynes-Cummings model, which is an exactly solvable model, we have dealt analytically with the dynamical behavior of the atom and the field for a two-photon process in squeezed and coherent fields under the appropriate approximation. The features of collapses and revivals of Rabi oscillations for the atom and the field in a two-photon process represent strict periodicity. The phase jump and the large and negative frequency for the combination Rabi oscillation are exhibited in the case of a squeezed field. The results show that squeezing in a field strikingly affects the evolution behavior of the atom and the field.