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Physical Review A

Control-laser-induced subnatural linewidths and quenching of spontaneous emission

G. S. Agarwal

Published Nov 1, 1996• 38 citations
Publisher

Abstract

We show how control lasers lead to subnatural linewidths in spontaneous emission as well as to the quenching of the quantum noise. We trace this quenching to the dispersive contributions to the line shape. We obtain analytical expressions for linewidths that for $\ensuremath{\wedge}$ systems are half the natural linewidths with the possibility of much more reduction for detuned control laser. We further present a simple physical analysis in terms of a two-photon Fermi golden rule to understand cancellation of spontaneous emission. Finally, we relate our results to recent experiments.

DOI
10.1103/physreva.54.r3734

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We show how control lasers lead to subnatural linewidths in spontaneous emission as well as to the quenching of the quantum noise. We trace this quenching to the dispersive contributions to the line shape. We obtain analytical expressions for linewidths that for \ensuremath∧\ensuremath{\wedge}\ensuremath∧ systems are half the natural linewidths with the possibility of much more reduction for detuned control laser. We further present a simple physical analysis in terms of a two-photon Fermi golden rule to understand cancellation of spontaneous emission. Finally, we relate our results to recent experiments.
The problem of fundamental laser line broadening due to random spontaneous emission of radiation and amplification of thermal radiation noise is analyzed in terms of a classical fluctuating field phasor model. We derive a general expression for the intrinsic linewidth, given in terms of the spectral power of the radiation noise source, which can be classical or quantum mechanical in nature. In the case of a two-level atomic laser, we recover by the use of Einstein relations, the traditional linewidth formula of the Schalow-Townes form. In the case of the free-electron laser (FEL), using the explicit expression for the spontaneous emission, we present calculation of the laser linewidth by purely classical methods. The result agrees with the one obtained in the framework of a quantum-mechanical model. By using ``extended Einstein relations'' which are applicable to classical radiators, we show that a Schalow-Townes-type formula can also be obtained for the FEL. The theory predicts extremely narrow intrinsic linewidth ${(10}^{\mathrm{\ensuremath{-}}7}$ Hz) for cw FEL's with parameters similar to those of the FEL experiment of Elias et al.
Subnatural linewidth in a strongly-driven closed F→F′F \rightarrow F'F→F′ transition
We observe linewidths below the natural linewidth for a probe laser on a {\it two-level system}, when the same transition is driven by a strong control laser. We take advantage of the fact that each level is made of multiple magnetic sublevels, and use the phenomenon of electromagnetically induced transparency or absorption in multilevel systems. Optical pumping by the control laser redistributes the population so that only a few sublevels contribute to the probe absorption. We observe more than a factor of 3 reduction in linewidth in the D2D_2D2​ line of Rb in room-temperature vapor. The observations can be understood from a density-matrix analysis of the sublevel structure.
Abstract The Schawlow–Townes limit established spontaneous emission as the fundamental quantum mechanism defining the minimum linewidth of an ideal laser oscillator. According to this description, random phase perturbations introduced by spontaneous photons become progressively less significant as the intracavity photon population increases, resulting in a continuous narrowing of the emission linewidth with increasing optical power. Although this relation remains a cornerstone of laser physics, it represents an ideal limit in which other sources of phase instability are absent. Practical laser systems frequently deviate from this behaviour: after an initial power-dependent narrowing regime, the linewidth often approaches a residual value that cannot be removed by further increasing the optical power. Such saturation suggests that linewidth should be treated not only as a photon-statistical quantity, but also as a property of the complete laser system, including the active medium. In this work, we develop a phenomenological framework in which laser linewidth is described as the combined result of spontaneous-emission noise, pump-induced fluctuations, and medium induced phase perturbations. The proposed approach preserves the Schawlow–Townes limit as the fundamental quantum contribution while introducing an active-medium-dependent term associated with the finite spectral response and microscopic fluctuations of the gain medium. The physical origin of this residual contribution is analysed using optical line-shape theory, considering homogeneous broadening, inhomogeneous broadening and the role of local environments in solid-state gain media. Er³+-doped systems are considered as representative rare earth active media, since their shielded 4f–4f transitions remain sufficiently narrow to support coherent emission while still retaining measurable signatures of crystal-field splitting, host disorder and spectral broadening. The model provides a physical interpretation for linewidth saturation and highlights that the ultimate optimisation of laser coherence requires not only improved cavity design and pump stabilisation but also control of the microscopic stability of the active medium. This viewpoint reframes the linewidth floor as a system-level property emerging from the interaction between quantum fluctuations, excitation dynamics and the gain medium.
The laser linewidth manifests the spectral coherence of a lasing resonator mode. It is of fundamental importance, theoretically as much as practically. For more than half a century we have been told that the laser linewidth is a result of quantum fluctuations due to spontaneous emission, which induce amplitude and phase fluctuations, whereas stimulated emission occurs in phase with the incident field. Unfortunately, in such a scenario each emission process would violate the law of energy conservation. We show that a (spontaneous or stimulated) emission process occurs 90 degrees in lead of the incident field, converts one atomic excitation into one photon in the lasing mode and, therefore, conserves the energy, whereas the mentioned fluctuations are the result of vacuum energy and occur at an orders-of-magnitude faster time scale than an emission process.
As discussed in the last three chapters, the fundamental source of noise in a laser is spontaneous emission. A simple pictorial model for the origin of the laser linewidth envisions it as being due to the random phase diffusion process arising from the addition of spontaneously emitted photons with random phases to the laser field. In this chapter we show that the quantum noise leading to the laser linewidth can be suppressed below the standard, i.e., Schawlow–Townes limit by preparing the atomic systems in a coherent superposition of states as in the Hanle effect and quantum beat experiments discussed in Chapter 7. In such coherently prepared atoms the spontaneous emission is said to be correlated. Lasers operating via such a phase coherent atomic ensemble are known as correlated spontaneous emission lasers (CEL). An interesting aspect of the CEL is that it is possible to eliminate the spontaneous emission quantum noise in the relative linewidths by correlating the two spontaneous emission noise events. A number of schemes exist in which quantum noise quenching below the standard limit can be achieved. In two-mode schemes a correlation between the spontaneous emisson events in two different modes of the radiation field is established via atomic coherence so that the relative phase between them does not diffuse or fluctuate. In a Hanle laser and a quantum beat laser this is achieved by pumping the atoms coherently such that every spontaneously emitting atom contributes equally to the two modes of the radiation, leading to a reduction and even vanishing of the noise in the phase difference.