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Physical Review A

Observation of Quantum Phase Fluctuations in Infrared Gas Lasers

Kenneth R. Manes, Anthony E.. Siegman

Published Jul 1, 1971• 63 citations
Publisher

Abstract

By heterodyning together the outputs from two stable He-Ne $3.39\ensuremath{-}\ensuremath{\mu}$ lasers, we have measured the power spectrum of the laser field over a wide range of output powers. By combining this high-gain laser transition with a very lossy laser cavity, the quantum phase noise contribution to the laser linewidth could be made dominant at low output powers. The laser spectrum was then found to be nearly Lorentzian with a bandwidth inversely proportional to output power, in good agreement with a modified form of the Schawlow-Townes laser linewidth formula. Weak quantum-noise-excited sidebands were also observed in the beat spectrum of a He-Xe $3.508\ensuremath{-}\ensuremath{\mu}$ laser. These were identified with a resonance in the He-Xe laser amplitude-fluctuation spectrum.

DOI
10.1103/physreva.4.373

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•Jan 1, 1995•1 citation
By heterodyning together the outputs from two stable He-Ne 3.39\ensuremath−\ensuremathμ3.39\ensuremath{-}\ensuremath{\mu}3.39\ensuremath−\ensuremathμ lasers, we have measured the power spectrum of the laser field over a wide range of output powers. By combining this high-gain laser transition with a very lossy laser cavity, the quantum phase noise contribution to the laser linewidth could be made dominant at low output powers. The laser spectrum was then found to be nearly Lorentzian with a bandwidth inversely proportional to output power, in good agreement with a modified form of the Schawlow-Townes laser linewidth formula. Weak quantum-noise-excited sidebands were also observed in the beat spectrum of a He-Xe 3.508\ensuremath−\ensuremathμ3.508\ensuremath{-}\ensuremath{\mu}3.508\ensuremath−\ensuremathμ laser. These were identified with a resonance in the He-Xe laser amplitude-fluctuation spectrum.
We perform a first-principles calculation of the quantum-limited laser linewidth, testing the predictions of recently developed theories of the laser linewidth based on fluctuations about the known steady-state laser solutions against traditional forms of the Schawlow-Townes linewidth. The numerical study is based on finite-difference time-domain simulations of the semiclassical Maxwell-Bloch lasing equations, augmented with Langevin force terms, and includes the effects of dispersion, losses due to the open boundary of the laser cavity, and non-linear coupling between the amplitude and phase fluctuations (α factor). We find quantitative agreement between the numerical results and the predictions of the noisy steady-state ab initio laser theory (N-SALT), both in the variation of the linewidth with output power, as well as the emergence of side-peaks due to relaxation oscillations.
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 study the linewidth of a one-photon laser through the approach of the two-time correlation function. Our numerical calculations cover the regions of below, near, and above threshold. Well below threshold, the laser linewidth decreases linearly with increasing linear gain. Near and above threshold, in comparison with the approximate linewidth given by the phase-diffusion coefficient at the mean photon number (which is inversely proportional to the laser intensity---the Schawlow-Townes formula), we find that the laser intensity fluctuations increase the laser linewidth and that the Schawlow-Townes formula is valid only when the mean photon number is large and the photon-number variance is much smaller than the square of the mean photon number. Near threshold, the laser linewidth can be twice as large as that given by the phase-diffusion coefficient at the mean photon number (i.e., twice as large as that given by the Schawlow-Townes formula).
We have measured the variance in fluorescence intensity and the spectrum of those fluctuations for two-level atoms in a phase-diffusing laser field. We compare our results with recent theoretical predictions that have been extended to include the effects of Doppler broadening and spatial variation of the laser intensity. Our study includes the effects of laser power, bandwidth, and shape (Lorentzian and non-Lorentzian) of the laser spectrum. At lower laser intensities, our measured variances versus detuning are in quantitative agreement with the theoretical predictions. At intensities above saturation, the variance is sensitive to inhomogeneities in the distribution of laser intensity in the interaction region, and only qualitative agreement is achieved. Asymmetries in the variance versus detuning resulting from correlated amplitude and phase noise have been observed. Spectra of the phase-noise-induced fluorescence-intensity fluctuations are shown to contain contributions from transients excited by the phase noise and are more sensitive to artifacts in the noise modulation process than the intensity spectrum of the laser field itself.
Measuring the phase dynamics of the beat note in the output of a HeNe Zeeman laser, we (i) unravel the interplay of phase locking and correlated spontaneous emission, (ii) observe the phase-diffusion noise reduced to 114\frac{1}{14}141​ of the Schawlow-Townes quantum level (the largest reduction of quantum noise reported so far), and (iii) show that balanced pumping of the two upper laser levels would achieve correlation of the laser phase noise with no locking at all. The resulting reduction in the phase noise of the beat note allows interferometric measurements of vastly enhanced sensitivity.
This thesis describes the phase and amplitude noise properties of semiconductor lasers subjected to weak, dispersive optical feedback. In the first half, experiments demonstrating reductions in the laser frequency noise power spectrum and spectral linewidth by several orders of magnitude are presented. Weak optical feedback is applied to the laser by an external cavity containing an atomic vapor. The presence of the vapor adds to the dispersion of the cavity and simultaneously locks the laser to a fixed frequency reference. The role of 1/f frequency noise in limiting the effectiveness of this linewidth reduction technique is investigated and 1/f noise is found to be the dominant contribution to the linewidth under strong optical feedback conditions. An electronic feedback scheme utilizing FM sideband locking is then implemented alongside the optical feedback, and an additional reduction in the low frequency 1/f frequency noise power spectrum by over two orders of magnitude is obtained. With both systems operating simultaneously, the spectral linewidth is narrowed from its free-running value of about 20 MHz to 1.4 kHz. Excellent absolute frequency stability is also achieved. In the second half, the effects of optical feedback on the quantum mechanical amplitude noise properties of the laser are examined. A fully quantum mechanical theory of amplitude and phase noise for a semiconductor laser with weak optical feedback is developed, and the nature and limits of the noise reduction using this technique are established. Particular attention is given to the feedback-induced enhancement of the amplitude squeezing which can be obtained in a pump-suppressed semiconductor laser: an improvement in the squeezing by 3 dB is predicted under moderate pumping. Somewhat larger noise reductions are expected when the laser is operating closer to threshold. Measurements performed on a laser biased close to threshold are then described and a reduction in the low frequency amplitude noise power spectrum by 7 dB is obtained. An experimental investigation of the effects of optical feedback on the amplitude squeezing in a semiconductor laser is then discussed. The low frequency squeezing in a room temperature device is increased from 3% below the standard quantum limit (SQL) under free-running conditions to 19% below the SQL with optimal feedback. The experimental results are found to agree poorly with the single-mode model and a multi-mode model including the effects of asymmetrical cross-mode non-linear gain is developed to explain the discrepancy. Finally, further experimental investigation into the generation of amplitude squeezed light is presented using a commercial laser with no intentional external modifications. Squeezing as large as 29% below the SQL is measured using a balanced homodyne detector with the laser operating near room temperature, corresponding to 41% below the SQL at the output facet of the laser.