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Acta Physica Sinica

THE MULTI-PHOTON QUANTUM STATITISCAL THEORY OF DRIVEN OPTICAL SYSTEMS (II)——BAD CAVITY CASE

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

Published Jan 1, 1988• 3 citations
Publisher

Abstract

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).

DOI
10.7498/aps.37.1438

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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).
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).
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, 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.
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.
The photon statistics of the transmitted light from a driven cavity containing a single resonant two-level atom are studied in the bad-cavity limit. For weak driving fields, the second-order intensity correlation function shows novel nonclassical behavior due to the interference of the driving field and forward reradiation from the atom. This behavior is related to squeezing in the cavity transmission. A physical interpretation is given in terms of the reduced quantum state of the coupled atom-field system following photodetection.>
We recently reported that the transmitted light from a driven optical cavity containing a single-atom absorber shows strong nonclassical features.1 Also, Savage and Carmichael2 have shown that this single-atom system can be operated in a regime in which the transmitted light has a bimodal photon-counting distribution; as the saturation photon number is increased this bimodality develops into a single-atom version of absorptive optical bistability. We present results for the degree of second-order coherence and the spectrum of the transmitted light in the operating regime at the onset of bimodality. In this regime we can study the onset of low frequency behavior associated with transitions between the local states defined by the peaks of the bimodal distribution. Our results are calculated numerically, using a supercomputer to solve matrix element equations derived in the Fock-state basis. Our numerical approach also allows us to extend our analytical study of nonclassical effects in single-atom cavity-enhanced absorption. Our analytical results are restricted either to the bad-cavity limit1 or to weak driving fields outside this limit. We can now study how the nonclassical effects identified in these analytical calculations are changed by using finite driving fields outside the bad-cavity limit.