Light-matter interaction in resonant environments remains at the core of quantum optics since the invention of the laser more than half a century ago. Let us imagine a large ensemble of identical two-level atoms spaced far apart with respect to their resonant wavelength. When some of the constituents are initially prepared in their excited states, we obtain some spontaneously-emitted radiation in free space. In the steady state, all the atoms will have returned to their ground state and radiation will have ceased. If we now irradiate the atoms uniformly by an external coherent field on resonance, we expect some steady-state excitation yet no trace of cooperation between the individual scatterers. The atoms remain distinguishable through their separate scattering records. The situation changes if the atoms are closely spaced together in comparison to their resonant wavelength; coherent interaction then causes the ensemble to emit light as a high intensity pulse, a phenomenon termed superradiance [1].  

Image credit: C. Lledó

Let's now go back to the former case of a large atom spacing. What will happen instead if we make all atoms weakly interact with a common cavity mode which is driven by an external coherent field? The answer is provided by the quantum statistical theory of optical bistability. Due to the nonlinearity of the interaction, the system observables switch between two metastable states with a lifetime exceeding appreciably the decoherence timescale. A linearized treatment of quantum fluctuations about these two states reveals a departure from the classical theory of radiation even at very low intensities; the fluctuations exhibit both photon antibunching and squeezing [2].

"The atoms here, while retaining their distinguishable character, communicate with each other via the channel set up by the intracavity field", Themis remarks.

The bandwidth of this channel is provided by the ratio of the two decoherence rates, i.e., the rates through which we extract information about the coupled light-matter system. Nevertheless, fluorescence maintains its distinct character when compared to forwards photon scattering, since unlike-atom correlations - which do not add up constructively to form a common channel - must be distinguished from like-atom correlations [3]. 

In the report recently published by JETP Letters, we focus on the atom-light correlations in the weak-excitation limit. In the other work which has just appeared in Physical Review A, we explore the coherence properties of atomic polarization, an internal system degree of freedom hidden from direct observation. We therefore formulate a method to extract the missing information via an auxiliary cavity mode  coupled to the atomic ensemble and supported by a lossy cavity, as depicted in the side schematic based on a proposal by H. J. Carmichael.

"The auxiliary field carries the collective atomic polarization which can now be collected as forwards photon scattering of a weak intensity", Themis observes.

To conclude, we envisage a further step along the investigation of macroscopic dissipative systems seeing beyond the scope of a quantum master equation for optical bistability. This consists in characterizing the modifications to atomic emission occurring when the ensemble develops macroscopic coherence to form a Bose-Einstein condensate (BEC) and occupies a single mode of a matter-wave field. We then speak of a superatom instead of separate distinguishable emitters. Several experiments have focused on this quantum coherence interplay against dissipation since the last fifteen years (see e.g., [4]), following inspiring proposals for realizing BEC interferometers driven by weak resonant monochromatic beams at the beginning of our century (see e.g., [5] and references therein). A new path lies ahead in probing coherent light-matter interaction.

[1] R. H. Dicke, Phys. Rev. 93, 99 (1954).
[2] H. J. Carmichael, Statistical Methods in Quantum Optics 2, Non-classical fields, Springer 2008, Ch. 15. 
[3] H. J. Carmichael, Z. Phys. B 42, 183 (1981). 
[4] F. Brennecke, T. Donner, S. Ritter, et al., Nature 450, 268 (2007). 
[5] N. N. Rosanov, V. A. Smirnov, and S. V. Fedorov, JETP Letters 129, 803 (2006). 

Links to the two articles: