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Europhysics Letters (EPL)

Quantum Noise Reduction in Raman Lasers

Helmut Ritsch, Monika A. M. Marte, P. Zoller

Published May 1, 1992• 72 citations
Publisher

Abstract

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.

DOI
10.1209/0295-5075/19/1/002

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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 investigate the influence of pump bandwidth and pump intensity noise on the quantum-noise properties of lasers based on a Raman atomic-gain medium, which recently have been predicted to emit narrow-bandwidth, sub-shot-noise light. We show that, using finite-bandwidth pump light, the predicted limit to the laser bandwidth can still be well below the value given by the Shawlow-Townes formula and much smaller than the input bandwidth. The laser intensity noise is shown to be relatively insensitive to input phase noise as long as the Rabi frequency on the lasing transition is large compared to the bandwidth. On the other hand, even small amounts of pump amplitude noise tend to increase strongly the laser spectral bandwidth, especially in the high-intensity limit. Including dynamic pump-noise reduction through multilevel atomic cycling in our model leads to a Mandel Q parameter value even below Q=-1/2, together with a significant enhancement of the output intensity-noise squeezing.
We consider the problem of reducing the contributions of pump and spontaneous-emission noise to the output noise of a laser field. We consider two models based on an atomic medium, one analytic, the other involving numerical simulation of a sequence of pump cycles. The predictions of both models are shown to agree. For regular pump excitation the intensity fluctuations of a laser well above threshold may be reduced to zero at the cavity resonance frequency if the ratio of the lifetimes of the upper and lower lasing levels is sufficiently large that spontaneous emission is suppressed. When the atomic lifetimes are comparable, spontaneous emission reduces the amount of noise reduction. For example, for equal atomic lifetimes regular pump excitation will result in a maximum noise reduction in the output field of one-half the shot-noise limit.
We study the statistical properties of a three-level laser where cascade coherent excitation as a two-step process is used as a coherent pump and a laser field is generated on the upper transition. It is shown that the laser intensity fluctuations are suppressed up to 50% below the shot noise limit and that the laser linewidth is reduced below the Schawlow-Townes formula by more than one order of magnitude of the laser intensity. By transforming to the picture dressed by the coherent field on the upper transition, we identify a transfer of the lower coherent excitation to be responsible for the quantum noise reduction. Cascade coherent excitation turns out to be a new way in which one can create a pathway for recycling of active electrons and regularization of laser excitation process. The conditions for the physical realization of the Raman scheme (Ritsch et al 1992 Europhys. Lett. 19 7) as a limiting case is discussed.
The mechanism for quantum noise suppression in a multimode laser with a homogeneously broadened line is explained. It is shown that the spontaneous emission noise and pump noise contribution to the photon number fluctuations inside the laser cavity may be suppressed infinitely (up to their complete elimination) when the number of modes participating in the generation is increased. Low-frequency spectral squeezing for an individual output field mode in optimal conditions tends to 100% as the total number of modes increases. The low-frequency spectral squeezing for the total output field may reach 50% below the shot noise level under optimal conditions. The noise suppression of the laser light is explained by the saturation effect of an atomic transition and inter-mode correlation. A multimode laser is an accessible source of light with potentially fully suppressed quantum noise.
Based on the standard laser model of a large number N of model atoms resonantly coupled to a single lasing mode, we show that the nonlinear dynamics of the active atoms of the laser can lead to output-intensity fluctuations significantly reduced below the shot-noise level. We identify the multiple recycling of the active electron from the lower lasing level to the upper level through the pumping as the key process leading to this dynamic-pump-noise reduction. This process has been neglected in most of the standard treatments of the laser so far. We find that the results are closely related to recent calculations based on the assumption of an external regular pump. For the widely used four-level model of the active atoms, the intensity noise can be reduced 50% below the shot-noise level. Generalizing the model to an m-level system, we find a quantum-noise reduction by a factor of 1/2m/(m-1)(m\ensuremath{\ge}3), leading to perfect output-intensity noise reduction in the limit of a large number of intermediate steps in the recycling process of the active atoms. Finally, we demonstrate that the bandwidth of the noise reduction can be significantly enhanced using a nonlinear absorber in the cavity.
We investigate the effect of collisional broadening, of population trapping and repumping, and of detuning of the atomic levels on the quantum-statistical properties of Raman laser radiation. We find that under suitably chosen operating conditions the effect of such additional incoherent relaxation mechanisms for the atomic polarization and populations can be made very small. One obtains highly nonclassical values for the Mandel Q parameter and the output-intensity fluctuation spectrum S(\ensuremath{\omega}) for experimentally reasonable parameters. Including detuning of the laser and the pump light from the atomic levels in certain cases can lead to further narrowing of the intracavity photon number distribution, as compared to the resonant case, down to a Mandel Q parameter close to the optimum possible value of Q=-1. A subsequent preliminary analysis prevails that inhomogeneous Doppler broadening of the atomic lines, both for collinear and for counterpropagating pump and laser light, is not detrimental to the nonclassical intracavity state.