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Acta Physica Sinica

THE MULTI-PHOTON QUANTUM STATISTICAL THEORY OF DRIVEN OPTICAL SYSTEMS (Ⅰ)——FOKKER-PLANCK EQUATION AND GOOD CAVITY CASE

LIN REN-MING, HUANG SI-XIAN, ZHANG LIN, 福建师范大学物理系

Published Jan 1, 1988• 1 citation
Publisher

Abstract

The systematic method of Fokker-Planck equation (FPE) for the generalized Wigner distribution is used to study the multi-photon transition process of a driven optical system. The general multi-photon FPE, the state equation and the spectrum of transmitted light in good cavity limit are obtained- The two-photon optical bistability spectrum of transmitted light is calculated and compared with single-photon case. It is shown that for multi-photon case, the atom -atom correlation is also negligible in the good cavity limit.

DOI
10.7498/aps.37.573

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In this paper, we discuss the multi-photon systems by employing the method of adiabatic elimination following the procedure of Lugiato. We come to the conclusion that, in both the "good cavity case" and the "bad cavity case", the result we get from the discussion contains the result drawn by the adiabatic elimination following the procedure of Gordon. More over, it can compute directly the correlation of the variable that has been adiabatically eliminated. Particularly in the "bad cavity case", the steady state value of the field variable correlation obtained by the method of Lugiato is different from that obtained by the method of Gordon. The method of Lugiato is self-consistent so it is much better.In the appendix, the formulae of the atomic squeezing and the multi-photon spectrum of transmitted light are presented.

Acta Physica Sinica•Jan 1, 1989•0 citations
The systematic method of Fokker-Planck equation (FPE) for the generalized Wigner distribution is used to study the multi-photon transition process of a driven optical system. The general multi-photon FPE, the state equation and the spectrum of transmitted light in good cavity limit are obtained- The two-photon optical bistability spectrum of transmitted light is calculated and compared with single-photon case. It is shown that for multi-photon case, the atom -atom correlation is also negligible in the good cavity limit.
In this paper, the multi-photon FPE of driven optical systems are treated for bad cavity case. The semi-classical linear stability analysis are performed. The non-classical effects are discussed, and it is shown that in two-photon case the atom-atom correlation enhances the non-clasical effects. This is in opposite to the single-photon case, and different from the good cavity case. The two-photon spectrum of transmitted light and resonance fluorescense are obtained, where the Rabi frequency Ωocy2 (y is the incident field).
In this paper, the multi-photon FPE of driven optical systems are treated for bad cavity case. The semi-classical linear stability analysis are performed. The non-classical effects are discussed, and it is shown that in two-photon case the atom-atom correlation enhances the non-clasical effects. This is in opposite to the single-photon case, and different from the good cavity case. The two-photon spectrum of transmitted light and resonance fluorescense are obtained, where the Rabi frequency Ω∝y2 (y is the incident field).
Quantum fluctuations for multiphoton transitions in driven optical systems are treated on the basis of a Fokker-Planck equation for the Wigner function. The equation is considered without adiabatic elimination of the atoms or the field. The linear stability is analyzed and time correlations are derived. A spectrum of transmitted light associated with vacuum Rabi splitting is obtained. The squeezing and antibunching effects in the atomic system and the field are discussed. This theory coincides with the adiabatic elimination theory for the case of both good- and bad-cavity limits.
A generalized Fokker-Planck equation is used to study the problem of single-atom optical bistability in the good-cavity limit. The effects of quantum fluctuations are investigated by linearizing fluctuations around the steady-state value. It is shown that in the good-cavity limit, quantum fluctuations are relatively small, and hence there exist both absorptive and dispersive single-atom bistability. By comparing our single-atom Fokker-Planck equation with the N-atom Fokker-Planck equation, we find that in the good-cavity limit, these two different Fokker-Planck equations reduce to identical equations. We therefore come to an important conclusion that the results obtained from the many-atom Fokker-Planck equation in the good-cavity limit are also valid for a single atom. \textcopyright{} 1996 The American Physical Society.
In this paper, we discuss the multi-photon systems by employing the method of adiabatic elimination following the procedure of Lugiato. We come to the conclusion that, in both the "good cavity case" and the "bad cavity case", the result we get from the discussion contains the result drawn by the adiabatic elimination following the procedure of Gordon. More over, it can compute directly the correlation of the variable that has been adiabatically eliminated. Particularly in the "bad cavity case", the steady state value of the field variable correlation obtained by the method of Lugiato is different from that obtained by the method of Gordon. The method of Lugiato is self-consistent so it is much better.In the appendix, the formulae of the atomic squeezing and the multi-photon spectrum of transmitted light are presented.