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Quantum Optics Journal of the European Optical Society Part B

A non-classical state of laser radiation above the threshold and the origin of coherence

Vladimir P Bykov

Published Oct 1, 1991• 1 citation
Publisher

Abstract

The quantum-mechanical state of laser radiation near the generation threshold is studied. It is shown that there is a second threshold in laser generation which lies above the first one. At the second threshold coherence appears in laser radiation. In a small region between the two thresholds the laser radiation is in an essentially quantum state, in which the average field strength is close to zero, but the average energy keeps a macroscopic value. Active atoms in superposition states are the sources of coherence in lasers. The laser active medium sufficiently enlarges the characteristic time of coherence.

DOI
10.1088/0954-8998/3/5/004

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The quantum-mechanical state of laser radiation near the generation threshold is studied. It is shown that there is a second threshold in laser generation which lies above the first one. At the second threshold coherence appears in laser radiation. In a small region between the two thresholds the laser radiation is in an essentially quantum state, in which the average field strength is close to zero, but the average energy keeps a macroscopic value. Active atoms in superposition states are the sources of coherence in lasers. The laser active medium sufficiently enlarges the characteristic time of coherence.
In this Letter, we give a new, to the best of our knowledge, perspective on the origin of light coherence in lasers. We demonstrate that a coherence appears below the lasing threshold and manifests itself as long-range correlations between polarizations of active medium atoms. These correlations contribute to the formation of a collective state of atomic polarizations and electromagnetic field modes, which interacts more effectively with the active medium and lases when pumping exceeds the lasing threshold. We demonstrate that inhibiting these atomic correlations leads to the destruction of the collective state and suppression of lasing. The obtained results open up new ways to control coherence.
The basic phenomena of interaction between atoms and e.m. fields can be discussed in some detail without the need of a detailed model of the atom. Absorption and stimulated emission of radiation can be explained satisfactorily by the theory, where a classical electromagnetic wave provides a time-dependent perturbation to the energy of the atomic electrons. Laser radiation appears to a very good approximation to be a classical travelling wave of well-defined amplitude and phase. The radiation produced by a continuous laser is a good approximation to a coherent state. For conventional sources of radiation, the interaction energy is small compared with the energy an electron possesses by virtue of the attraction to the atomic nucleus, so perturbation theory produces quite acceptable results. The quantum mechanical analogy to the distortion of the classical charge cloud is given by the writing down of a general state function for the system, Ψ.
We present a quantum theory of a spaser-based nanolaser, under the bad-cavity approximation. We find first- and second-order correlation functions g(1)(τ) and g(2)(τ) below and above the generation threshold, and obtain the average number of plasmons in the cavity. The latter is shown to be of the order of unity near the generation threshold, where the spectral line narrows considerably. In this case the coherence is preserved in a state of active atoms in contradiction to the good-cavity lasers, where the coherence is preserved in a state of photons. The damped oscillations in g(2)(τ) above the generation threshold indicate the unusual character of amplitude fluctuations of polarization and population, which become interconnected in this case. Obtained results allow to understand the fundamental principles of operation of nanolasers.
Spontaneous and stimulated emission from atoms in a free one-dimensional space is considered from the quantum-mechanical point of view. The resolvent method is used to calculate the field density matrix, average electric field, and electromagnetic field energy density for a spontaneously emitting atom. For an atom emitting in the field of another atom, calculations are made of the electric field of the spontaneous and stimulated radiation. It is shown how the coherence length and coherence time of the spontaneous radiation increase. The application of these results in laser theory to explain the formation of a radiation mode structure and consequent appearance of coherent radiation is discussed.
A quantum theory for noise in the steady state of the laser oscillator above threshold is presented. The concept of operator noise source is introduced. A simple laser model operating in a single mode with resonant frequency tuned to the center of the material line is considered. The resonance linewidth of the inverted material is collision-broadened, and assumed to be much broader than the cold-cavity width. We restrict ourselves to one type of collision. The quantum description of this laser model leads to nonlinear operator equations. These are linearized, but this linearization is justified only for operation "sufficiently" above threshold. The first- and second-order Glauber functions and the expectation value of the field commutator are derived for the field inside the laser cavity. These results are compared with the predictions of a "semiclassical" theory in which the classical equations contain noise sources such that properties of the field below threshold are correctly predicted. Our results differ by certain terms from the results of this semiclassical theory. These terms are too small to have been detected experimentally.