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arXiv:0802.2315 · Journal of Physics B Atomic Molecular and Optical Physics

A scheme for amplification and discrimination of photons

A. R. Usha Devi, R. Prabhu, A. K. Rajagopal

Published Nov 19, 2008• 0 citations
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Abstract

A scheme for exploring photon number amplification and discrimination is presented based on the interaction of a large number of two-level atoms with a single mode radiation field. The fact that the total number of photons and atoms in the excited states is a constant under time evolution in Dicke model is exploited to rearrange the atom-photon numbers. Three significant predictions emerge from our study: Threshold time for initial exposure to photons, time of perception (time of maximum detection probability), and discrimination of first few photon states.

DOI
10.1088/0953-4075/41/23/235501

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A scheme for exploring photon number amplification and discrimination is presented based on the interaction of a large number of two-level atoms with a single mode radiation field. The fact that the total number of photons and atoms in the excited states is a constant under time evolution in Dicke model is exploited to rearrange the atom-photon numbers. Three significant predictions emerge from our study: Threshold time for initial exposure to photons, time of perception (time of maximum detection probability), and discrimination of first few photon states.
Photon statistics are obtained from exact closed-form solutions for both spontaneous and stimulated coherent emissions by a large number of two-level atoms in a Dicke state. Depending on the initial excitation level of the atoms, three types of photon statistics are obtained for the emitted radiation field. Moments of the photon number of the emitted field are calculated in the case of initial atomic coherent states as well as Dicke states, and in the case of n-photon stimulating pulses as well as coherent stimulating pulses. In the particular case of an initial "superradiant" Dicke state stimulated by a coherent-radiation field, the emitted radiation pulse is also fully coherent. In other cases the photon distributions undergo large fluctuations.
The quantum entanglement of the two mode coherent field interacting with a cascade three-level atom was calculated accurately with non-rotating wave approximation by using the complete quantum theory.The influences of the superposition between different atomic energy level at the initial time and the mean photon number on quantum entanglement evolution were considered.The results obtained by the numerical method show that the period of the quantum entanglement evolution becomes longer with the increase of the mean photon number when the atom initially at the single energy level,the quantum entanglement at the first few periods is reduced notably due to the fact of the atom is initially in the superposition state,it takes longer time for the entanglement to reach the maximum value with the increase of the mean photon number,moreover,because of the atom is initially in the superposition state,the periodic disappears.No matter which atom state,the quick oscillation due to the virtual photon process increases with the increasing of the mean photon number.
We introduce a complete Bell measurement on atomic qubits based on two-photon interactions with optical cavities and discrimination of coherent states of light. The dynamical system is described by the Dicke model for two three-level atoms interacting in two-photon resonance with a single mode of the radiation field, which is known to effectively generate a nonlinear two-photon interaction between the field and two states of each atom. For initial coherent states with a large mean photon number, the field state is well represented by two coherent states at half-revival time. For certain product states of the atoms, we prove the coherent generation of Greenberger-Horne-Zeilinger states with two atomic qubits and two orthogonal Schr\"odinger cat states as a third qubit. For arbitrary atomic states, we show that discriminating the two states of the field corresponds to different operations in the Bell basis of the atoms. By repeating this process with a second cavity prepared in a phase-shifted coherent state, we demonstrate the implementation of a complete Bell measurement. The experimental feasibility of our protocols is discussed for cavity-QED, circuit-QED, and trapped-ion setups.
The information entropy properties of the coupled V-type three-level atoms interacting with the coherent field are studied by means of quantum theory.Numerical calculation results show that the average photon number in the initial state plays an important role in the time evolutions of the atomic information entropy.When the average photon number in the initial state is large,the time evolution of the atomic information entropy exhibits apparent collapse and revival phenomenon.The amplitude of the excited state in the initial state,the coupling constant between two atoms,the detuning and Kerr coefficient make significant influence on the time evolution of the atomic information entropy,respectively.