It has been widely accepted that the conventional lasing threshold, occurring around unity intracavity photon number, can be eliminated by making the so-called
β parameter approach unity. Recently, it has been shown that the photon statistics become incoherent when the intracavity mean photon number is decreased below unity even for
β≈1. Here, we report systematic measurement of the photon statistics in a superradiant laser as a function of the intracavity photon number. Our superradiant laser was based on the single-atom superradiance driven by twolevel atoms in a quantum superposition state traversing a high-Q cavity one by one. The lasing did not exhibit the conventional threshold and the photon statistics remained near coherent even well below unity photon number. Moreover, the coherence got better as the excited-state population in the initial superposition state was made smaller.
Lasing threshold in the conventional lasers is the minimum input power required to initiate laser oscillation. It has been widely accepted that the conventional laser threshold occurring around a unity intracavity photon number can be eliminated in the input-output curve by making the so-called β parameter approach unity. The recent experiments, however, have revealed that even in this case the photon statistics still undergo a transition from coherent to thermal statistics when the intracavity mean photon number is decreased below unity. Since the coherent output is only available above the diminished threshold, the long-sought promise of thresholdless lasers to produce always coherent light has become questionable. Here, we present an always-coherent thresholdless laser based on superradiance by two-level atoms in a quantum superposition state with the same phase traversing a high-Q cavity. Superradiant lasing was observed without the conventional lasing threshold around the unity photon number and the photon statistics remained near coherent even below it. The coherence was improved by reducing the coupling constant as well as the excited-state amplitude in the superposition state. Our results pave a way toward always-coherent thresholdless lasers with more practical media such as quantum dots, nitrogen-vacancy centers and doped ions in crystals.
We discuss the cooperative decay of initial atomic excitation for a pencil-shaped active volume filled with two-level atoms. As long as the length of the sample is much smaller than a certain maximal cooperation length, the atom-field interaction producing the superradiant pulse can be treated in terms of the simplest possible laser model (single mode). The basic laser master equation turns out to be exactly solvable if specified for the superradiance limit which is characterized by two conditions: (i) The photons escape from the low-
Q cavity so fast that they cannot feed themselves back into atomic excitation to any appreciable amount (this no-feedback condition is equivalent to the above-mentioned requirement for the length of the sample). (ii) The incoherent atomic decay due to natural relaxation is so slow that the individual atomic dipoles do not dephase before engaging themselves cooperatively in the interaction with the electromagnetic field. The present paper presents the derivation and general discussion of the equations describing the statistical properties of atoms and field in a superradiant pulse. Analytical and numerical solutions will be presented in a subsequent paper.