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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Identical particle model on biophoton emission

T. C. Liu, Songhao Liu, F. A. Popp, Aoqing Tang

Published Sep 23, 1996• 0 citations
Publisher

Abstract

Biophoton emission (PE) method is a non-invasive way revealing biophysical interactions in living tissues. Since its mechanism is not very clear, its acceptance is limited. Gu has presented the quantum theory on biophoton emission according to the Dicke model. However, the Dicke model does not apply to biological system. In this paper, we studied PE by using the identical particle model, the interaction of identical particles by quantum chemistry, as well as the transition of the system interacting with radiation by the time quantum theory on radiation-matter interaction put forward by the first author and his cooperators. It was shown that the identical particles form coherent states, the photon emission probability of the superradiant state is a liner function of N and N2, and the one of the subradiant state is zero. In other words, the photon emission intensity represents the coherent states of the identical particle system. The linear relationship of N and N2 agrees with the PE experiment results on early drosophila embryos. The research on the cell division cycle showed that the superradiant states correspond to the late S phase. This is why PE can be used to differentiate human tumor tissues from normal ones. We also studied induced PE.

DOI
10.1117/12.251949

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•Jan 1, 2007•0 citations
Biophoton emission (PE) method is a non-invasive way revealing biophysical interactions in living tissues. Since its mechanism is not very clear, its acceptance is limited. Gu has presented the quantum theory on biophoton emission according to the Dicke model. However, the Dicke model does not apply to biological system. In this paper, we studied PE by using the identical particle model, the interaction of identical particles by quantum chemistry, as well as the transition of the system interacting with radiation by the time quantum theory on radiation-matter interaction put forward by the first author and his cooperators. It was shown that the identical particles form coherent states, the photon emission probability of the superradiant state is a liner function of N and N2, and the one of the subradiant state is zero. In other words, the photon emission intensity represents the coherent states of the identical particle system. The linear relationship of N and N2 agrees with the PE experiment results on early drosophila embryos. The research on the cell division cycle showed that the superradiant states correspond to the late S phase. This is why PE can be used to differentiate human tumor tissues from normal ones. We also studied induced PE.
Dicke model describes a collective interaction between the two-level atoms and the light cavity and has been predicted to show a peculiar quantum phase transition, which is a second-order phase transition from a normal phase (in a weak-coupling strength) to a superradiant phase (in a strong-coupling strength). The model plays an important role in illustrating the quantum ground-state properties of many-body macroscopic quantum states. In the experiment, Dicke quantum phase transition in an open system could be formed by a Bose-Einstein condensate coupled to a high-finesse optical cavity. This experiment on the Bose-Einstein condensate trapped in the optical cavity have opened new frontiers, which could combine the cold atoms with quantum optics and makes it possible to enter into the strongly coupled regime of cavity quantum electrodynamics. In strong coupled regime, the atoms exchange the photons many times before spontaneous emission and cavity losses set in. It has become a hot research topic in recent years and plays an important role in many fields of modern physics, such as condensed matter physics, nuclear physics, etc. It can be applied to the manipulation of the geometric phase and entanglement in quantum information and computing. Quantum phase transition has been widely studied for the Dicke model as a typical example. Many different research methods about the mean-field approximation have been used to analyze the ground state properties of the Dicke model. In this paper, we study the ground state properties of two-component Bose-Einstein condensate in a single-mode cavity. Meanwhile, the associated quantum phase transition is described by the spin-coherent-state variational method, whose advantage is that the ground state energy and wave function can be obtained without the thermodynamic limit. By taking the average in the boson coherent state, we obtain an equivalent effective pesudospin Hamiltonian, which will be diagonalized by using the spin coherent state. Finally, we can obtain the energy functional, which is the basics of the variation to obtain the numerical solution of photon number and the expression of the atomic number and the ground state energy. This paper presents a rich phase diagram, which can be manipulated by changing the atom-field coupling imbalance between two components and the atom-field frequency detuning. While in the single-mode Dicke model there exist only the normal phase and the superradiation phase. When the frequency of one component atom is zero or the frequency of the two component atoms are equal in optical cavity, the system returns to the standard Dicke model, in which there occurs the second-order phase transition from the normal phase to the superradiant phase by adjusting the atom-field coupling. In conclusion, we discover that the stimulated radiation comes from the collective state of atomic population inversion, which does not exist in the single-mode Dicke model. Meanwhile, the new stimulated-radiation state S and S, which can only be produced by one component of the atom, are observed in the two-component Bose-Einstein condensates in the single-mode optical cavity. By adjusting the atom-field coupling imbalance and the atom-field frequency detuning (the blue or red detuning), the order of the superradiation state and the stimulated-radiation states can be exchanged between the two components of the atom.
Abstract It is shown that when nonresonant interactions between atoms and a vacuum electromagnetic field are included in analysis of emission of a localized ensemble of identical atoms, a delay must appear in the cooperative radiation pulse emitted by the atomic ensemble that is initially in a half-excited state. At the same time, the emission of cooperative radiation from a completely excited ensemble for certain parameters must begin without any delay. This contradicts the familiar facts of the conventional Dicke superradiance, in the theory of which nonresonant interactions are disregarded. The model taking into account nonresonant interactions along with other factors of the Dicke model is called the generalized Dicke model.
A normalized variance of a radiation field is introduced to study the coherence properties of spontaneous and induced emissions in the Dicke model Hamiltonian. It is shown that a superradiant emission from an atomic Dicke state cannot be in a coherent state, though the Dicke state emits photons in a Poisson distribution for the photon number. In the case of the induced omission for an initially intense coherent radiation field, the time evolution of the normalized variance is calculated to see to what extent the initially coherent state remains coherent. We obtain the time evolution of the expectation values of the atomic operators and the photon number operator. These solutions are then compared with semi-classical solutions obtained by taking the diagonal coherent state representation.
Dicke superradiance, i.e., the enhanced spontaneous emission of coherent radiation, is often attributed to radiation emitted by synchronized dipoles coherently oscillating in phase. At the same time, Dicke derived superradiance assuming atoms in entangled Dicke states which do not display any dipole moment. To shed light on this apparent paradox, we study the intensity distribution arising from two identical two-level atoms prepared either in an entangled Dicke state or in a separable atomic state with a nonvanishing dipole moment. We find that the two configurations produce similar far-field intensity patterns, although they stem from fundamentally distinct types of coherence: while in the second case the atoms display coherence among the individual particles, leading to Young-type interference like that known from classical dipoles, atoms in Dicke states possess collective quantum coherence stemming from entanglement and quantum correlations of the state, leading to an interference pattern resulting from enhanced spontaneous emission. This demonstrates that the radiation generated by synchronized dipoles and Dicke superradiance---even if they do produce the same interference pattern---are fundamentally distinct phenomena and have to be interpreted in different ways.
A system of many #we-level atoms or molecules in a collective Dieke state (1) interacting with a single resonant mode of the quantized radiation field has often been adopted as a quantum-mechanical model for a point laser (2). In a previous paper (3) we reported exact dosed-form solutions and photon statistics of coherent spontaneous emission for the model atom-field state in the l imit of infinitely large co-operation number. The purpose of this paper is to report more general results based on this modeI. We give the exact closed-form solutions and photon statistics of coherent emission in the presence of an applied field for the model atom-field state in the same limit. For an initial atomic Dicke state interacting with an applied field in a coherent (Glauber) state (a), the emitted pulse can be desoribed in terms of Glauber states only when the levels of excitation of the initial Dicke states are (~ superradiant ~ (~). For an initially highly inverted system or low excited system, the photon distributions undergo large fluctuations. The model interaction Hamil tonian is given by