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Physical Review A

Theory of quenching quantum fluctuations of a laser system with a ladder-type configuration

Deshui Yu, Jingbiao Chen

Published Feb 19, 2010• 7 citations
Publisher

Abstract

The theory of a laser system with a ladder-type configuration is studied in detail based on the quantum Langevin approach. By using an external field to link the lower lasing level with another atomic level, whose decay rate is much larger, laser intensity significantly increases and the quantum-limited linewidth can be quenched. We also discuss the spectrum of fluctuations of the output field, and the result shows that the fluctuations at low frequencies can be much suppressed too. On the other hand, this quenching approach can realize a laser output between two atomic levels, whose decay rates do not satisfy the usual lasing condition that the decay rate of the lower lasing level should be larger than that of the upper lasing level. It will be very useful to realize a laser output with the wavelength we want. This quenching approach has been widely used in the absorption spectrum of the ytterbium optical lattice clock and in the laser cooling approach for calcium atoms. Here we apply it in the stimulated emission of lasers.

DOI
10.1103/physreva.81.023818

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The theory of a laser system with a ladder-type configuration is studied in detail based on the quantum Langevin approach. By using an external field to link the lower lasing level with another atomic level, whose decay rate is much larger, laser intensity significantly increases and the quantum-limited linewidth can be quenched. We also discuss the spectrum of fluctuations of the output field, and the result shows that the fluctuations at low frequencies can be much suppressed too. On the other hand, this quenching approach can realize a laser output between two atomic levels, whose decay rates do not satisfy the usual lasing condition that the decay rate of the lower lasing level should be larger than that of the upper lasing level. It will be very useful to realize a laser output with the wavelength we want. This quenching approach has been widely used in the absorption spectrum of the ytterbium optical lattice clock and in the laser cooling approach for calcium atoms. Here we apply it in the stimulated emission of lasers.
The theory of a quantum-limited phase-matching effect in a $\ensuremath{\Lambda}$-type lasing system is studied in detail based on the quantum Langevin approach. Two quasimonochromatic fields are directly generated based on two lasing transitions. We find that the coherence between two lasers can well exceed the linewidth of either laser field. This result denotes that two field phases match each other although either laser field has a high phase fluctuation. Unlike the phase-matching effect based on atomic absorption, the final coherence between two laser fields here is not limited by saturation broadening, and the higher laser intensities lead to a higher coherence. Additionally, based on a linear stability analysis, we find that the instability of the field steady state can substantially restrict the occurrence of this phase-matching effect in the bad-cavity limit for a high pump rate. We also discuss the spectrum of amplitude fluctuations of output fields, and the result shows that the squeezing of amplitude fluctuations at low frequencies for a single field oscillating inside the cavity is damaged in the case of two fields oscillating.
We develop a quantum theory of a correlated-emission laser (CEL) with injected atomic coherence for arbitrary initial atomic conditions and arbitrary atomic decay rates. The effect of initial atomic coherence on the CEL is studied. It is shown that, with a proper form of the initial atomic coherence and equal atomic decay rates between the two upper levels of V-type three-level lasing atoms, the diffusion coefficients for the relative phase and the relative amplitude of two laser modes can vanish under certain conditions. These conditions, plus equal cavity-loss rates, lead to the vanishing of the normally ordered variances (quantum-noise quenching) of Hermitian operators corresponding to the relative phase and the relative amplitude.
The quantum noise properties of atomic and semiconductor lasers are compared. The intensity fluctuation spectrum of the output field is calculated for the case of regularly, i.e., sub-Poissonian, pumped lasers. The effects of spontaneous emission on the output amplitude fluctuations may be suppressed in regularly pumped atomic lasers by requiring the lifetime of the lower lasing level to be short in comparison with that of the upper laser level. The output amplitude fluctuations then tend to zero at the laser frequency. In regularly pumped semiconductor lasers, net stimulated emission of photons dominates over spontaneous emission because of the combination of pumping and rapid intraband thermalization due to Coulomb scattering.
We demonstrate that the intensity fluctuations of a laser with a Raman gain medium, described by a large number of independent 3-level atoms, can drop well below the shot noise level. In the limit of a good cavity, where one can adiabatically eliminate the atoms, we find an optimum Mandel Q parameter of Q ≈ −1/2 over a large range of parameters, when the laser is operated well above threshold. This leads to a strong suppression of the low-frequency quantum fluctuations in the laser output. In addition we find that due to suppression of spontaneous emission into the lasing mode, the spectral linewidth of the emitted light can be reduced below the Schawlow-Townes limit by more than one order of magnitude.
We show that the nonlinear dynamics of the active atoms in conventionally pumped multilevel laser systems can lead to output intensity fluctuations significantly below the shot noise level1,2 (see also Refs, 3-5). Our calculations are based on the standard model of the laser which assumes a large number of atoms resonantly coupled to a single lasing mode. We identify the multiple recycling of the active electron from the lower lasing level to the upper level through pumping as the key process leading to this dynamic pump noise reduction. It is required that (i) the pump rates be comparable to the decay rates of the atom, and (ii) we have a closed repumping cycle, and a constant number of atoms. We find that the results are closely related to recent calculations based on the assumption of an external regular pump6 (for noise reduction in semiconductor lasers, see Ref. 7).
Nonlinear Heisenberg-Langevin equations are solved analytically by operator Fourier expansion for the laser in the light-emitting diode (LED) regime. Fluctuations of populations of lasing levels are taken into account as perturbations. The spectra of operator products are calculated as convolutions, preserving Bose commutations for the lasing field operators. It is found that fluctuations of population significantly affect spontaneous and stimulated emissions into the lasing mode, increase the radiation rate, the number of lasing photons, and broaden the spectrum of a bad cavity threshold-less and the superradiant lasers. The method can be applied to various resonant systems in quantum optics.