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Physical Review A

Quantum-limited phase-matching effect in a Λ -type laser system

Deshui Yu, Jingbiao Chen

Published Jun 29, 2011• 3 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.83.063846

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The theory of a quantum-limited phase-matching effect in a \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-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.
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.
It is shown that a laser with a two-photon saturable absorber exhibits a phase instability similar to that of two-photon optical bistability. The authors calculate the spectrum of the intensity fluctuations in the output field under conditions of exact resonance between the amplifier and the absorber. In the bad-cavity limit the relevant part of the spectrum assumes a simple Lorentzian form; as the phase-instability threshold is approached, the reduction of quantum noise becomes perfect for small frequencies.
Noninversion lasing is investigated in \ensuremath{\Lambda}-type three-level atomic systems that are coupled to two modes of the electromagnetic field. As a result of an external field driving the transition between the lower two closely spaced levels, laser action can be achieved in both modes simultaneously at arbitrarily small initial upper-level population (lasing without inversion) provided the pumping rate exceeds a certain threshold. The relative phase of the two modes is locked to a particular value controlled by the phase of the external field. In addition, new regimes of the laser operation arise when initial coherences between various atomic levels are also injected into the resonator. Firstly, laser action can be achieved in both modes at arbitrarily small pumping (no threshold). Secondly, the injected atomic coherence can control competition between the modes, and result in a variety of multistable steady-state behavior illustrating the very sensitive dynamics of the system.
The fundamental source of noise in laser and optical amplifier is spontaneous emission. However, it is possible to reduce this noise by preparing the gain medium (atoms) in coherent superposition of states. There are essentially two schemes for generating atomic coherence in optical amplifiers. \n \nFirst scheme involves the preparation of atoms in a coherent superposition of states before injecting them inside the cavity. In the other scheme atoms (initially pumped incoherently) are continuously driven by an external pump field inside the cavity. Almost all the studies concerning the quenching of spontaneous emission noise in optical amplifiers, based on the notion of atomic coherent superposition, ignore the finite bandwidth of the field that is responsible for generating coherence. In this dissertation, we have examined the effect of the finite bandwidth associated with the phase fluctuations of the driving field on a number of noise quenching schemes. \n \nIt is known that coherent preparation of atoms can, under certain conditions, lead to noise-free amplification and almost 50 percent phase squeezing in a two-photon correlated emission laser. We study the effect of phase fluctuations in the injected atoms on the phase noise of the field in these systems. We discuss the conditions under which squeezing is preserved in the two-photon linear amplifiers. We also show that, even for very large phase fluctuations in the injected atoms, almost 50 percent phase squeezing can be achieved. The corresponding gain is however significantly reduced. \n \nWe also study a system of phase-sensitive amplifier where atoms are prepared in a coherent superposition of states by a strong classical field. We study the role of pump phase fluctuations associated with the finite linewidth on the quantum statistical properties of the radiation field. A study of output field characteristics reveals that the presence of a weak pump field gives rise to equal variances in both the field quadratures which are independent of linewidth. On the other hand, the presence of strong pump field alters the output field characteristics with the generation of squeezing which is later on destroyed due to the presence of phase fluctuations
We show that it is possible to realize simultaneous Raman lasing at two different frequencies using a double-$\mathrm{\ensuremath{\Lambda}}$ system pumped by a bifrequency field. The bifrequency Raman lasers are phase-locked to one another and the beat-frequency matches the energy difference between the two metastable ground states. Akin to a conventional Raman laser, the bifrequency Raman lasers are expected to be subluminal. As such, these are expected to be highly stable against perturbations in cavity length and have quantum noise limited linewidths that are far below that of a conventional laser. Because of these properties, the bifrequency Raman lasers may find important applications in precision metrology, including atomic interferometry and magnetometry. The phase-locked Raman laser pair also represent a manifestation of lasing without inversion, albeit in a configuration that produces a pair of nondegenerate lasers simultaneously. This feature may enable lasing without inversion in frequency regimes not accessible using previous techniques of lasing without inversion. To elucidate the behavior of this laser pair, we develop an analytical model that describes the stimulated Raman interaction in a double-$\mathrm{\ensuremath{\Lambda}}$ system using an effective two-level transition. The approximation is valid as long as the excited states adiabatically follow the ground states, as verified by numerical simulations. The effective model is used to identify the optimal operating conditions for the bifrequency Raman lasing process. This model may also prove useful in other potential applications of the double-$\mathrm{\ensuremath{\Lambda}}$ system, including generation of squeezed light and spatial solitons.
The problem of the quantum-limited or intrinsic linewidth of a good-cavity laser is revisited. Starting from the Scully-Lamb master equation, we present a fully analytical treatment to determine the correlation function and the spectrum of the cavity field at steady state. For this purpose, we develop an analytical approximation method that implicitly incorporates the microscopic fluctuations of both the phase and intensity of the field, and, in addition, takes full account of the saturation of the nonlinear gain. Our main result is a simple formula for the quantum-limited linewidth that is valid from near to far above threshold and also includes the presence of thermal photons. Close to the threshold, the linewidth is twice as large as predicted by the standard phase-diffusion treatment neglecting intensity fluctuations, and even 50% above threshold the increase is still considerable. In general, quantum fluctuations of the intensity are present and continue to influence the linewidth as long as the photon-number distribution is not strictly Poissonian. This inherent relationship is displayed by a formula relating the linewidth and the Mandel Q parameter. More than 100% above treshold the linewidth is found to be smaller than predicted by the standard treatment, since the simple phase-diffusion model increasingly overestimates the rate of phase fluctuations by neglecting gain saturation. In the limit of a very large mean photon number the expected perfectly coherent classical field is obtained.