Volume 1llA, number 1,2 PHYSICS LETTERS 26 August 1985 OPTICAL BISTABILITY WITH INTERACTING ATOMS Deb Shankar RAY Department of Chemistry, Physical Section, Jadavpur University, Calcutta 700 032, India Received 9 May 1985; accepted for publication 19 June 1985 The effect of interatomic interaction (dipole-dipole) on optical bistabiUty has been analysed. It has been shown that for certain ranges of interaction the van der Waals loop diminishes or completely disappears. The cooperative behaviour in the,interaction be- tween a single mode radiation field and a collection of N identical two-level atoms confined in a volume of dimension less than the radiation wavelength has been considered by a number of workers in the recent past. One of the most important phenomena which exhibit such cooperative behaviour is optical bistability [1,2] where a light transmitting system such as a non- linear Fabry-P~rot interferometer is made to operate in two stable states displaying hysteresis when the system jumps from one state to another. The theoret- ical treatments [3,4] leading to analytical results for the input-output characteristics of light display, the van der Waals scenario, which is reminiscent of the gas-liquid phase transition. All these models, however, are based on the common assumption that the atoms are non-interacting. The object of the present paper is to show that if we include the dipole-dipole interac- tion between the atoms the usual van der Waals scenario gets changed by a shortening of the hysteresis loop. When the interaction is strong enough we ob- serve a complete disappearance of the hysteresis loop. This suggests that the interatomic interaction can in. fluence considerably the nature of the phase transition. Secondly, the inclusion of such an interaction lowers the critical cooperation number above which the onset of bistability occurs. It is interesting to note that a consideration of this interaction by Agarwal et al. [5] leads to effects like the splitting of Rabi side bands into doublets in the resonance fluorescence spectrum. The physical processes required for the analysis of 0.375-9601/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) the cooperative behaviour in optical bistability within the Dicke model [6] are: (i) An interaction of the atoms with an external classical driving field near resonance with an atomic transitiorL (ii) A dipole-dipole interaction between the atoms. (iii) A cooperative interaction with a single quasi- mode of the interferometer containing the atoms. (iv) Irreversible atomic decay into the vacuum. The evolution of the atom is described by the re- duced density operator p of the atom in terms of the master equation, dp/dt = -i~21 IS + + S-, p] + if [Sz, p] -i[eS z + VS+S-,p] + AsP + AAP. (1) The equation is derived under the rotating wave, Born, Marker approximation upon the adiabatic elimination of cavity field operators. The irreversible contributions are Asp = (2g2/K)(S- - pS+S - -½S+S-p), (2) and AAp = + (3) l which describe the collective (or supperradiant) and single atomic decay, respectively. The summation in the expression for AAP runs over allN atoms of the system. S + and S- are the collective polarisation operators, ~21 is the Rabi frequency of the external field;g measures the atom-quantum field coupling 25