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Annual Meeting Optical Society of America

Quantum noise of lasers with intracavity harmonic generation

Eugene Simon Polzik, В. Н. Горбачев

Published Jan 1, 1990• 0 citations

Abstract

We present new results for the quantum noise reduction owing to the mth harmonic generation (m = ½, 2, 3) in a laser. Study of such a source of light with noise beyond the quantum limit is now in progress.1,2 We consider this problem for both the laser with conventional random pumping and the laser with reduced pump noise, i.e., the sub-Poissonian laser. In the case of the laser with a conventional pump, the noise in the mth harmonic can be suppressed by m times as compared to the shot noise limit. For the sub-Poissonian laser, perfect noise reduction can be achieved in any harmonic mode. Cross correlations between the fundamental mode and the harmonic mode lead to the quantum noise interference effect, which manifests itself in the noise of the total photon flux from the laser. The system with two nonlinear crystals inside the laser cavity can serve as a source of two perfectly squeezed modes with divisible frequencies. The first crystal is driven by the external field of frequency 2ω. This field is downconverted in the crystal to the frequency ω, which is the frequency of lasing. In the second crystal the lasing field is again downconverted to the frequency ω/2. The lasing mode m and the subharmonic mode ω/2 from such a laser can be perfectly squeezed; that means complete quantumnoise reduction of these two modes if mixing with local oscillators of phase shifts π/2 is used.

DOI: 10.1364/oam.1990.mc5

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We present new results for the quantum noise reduction owing to the mth harmonic generation (m = ½, 2, 3) in a laser. Study of such a source of light with noise beyond the quantum limit is now in progress.1,2 We consider this problem for both the laser with conventional random pumping and the laser with reduced pump noise, i.e., the sub-Poissonian laser. In the case of the laser with a conventional pump, the noise in the mth harmonic can be suppressed by m times as compared to the shot noise limit. For the sub-Poissonian laser, perfect noise reduction can be achieved in any harmonic mode. Cross correlations between the fundamental mode and the harmonic mode lead to the quantum noise interference effect, which manifests itself in the noise of the total photon flux from the laser. The system with two nonlinear crystals inside the laser cavity can serve as a source of two perfectly squeezed modes with divisible frequencies. The first crystal is driven by the external field of frequency 2ω. This field is downconverted in the crystal to the frequency ω, which is the frequency of lasing. In the second crystal the lasing field is again downconverted to the frequency ω/2. The lasing mode m and the subharmonic mode ω/2 from such a laser can be perfectly squeezed; that means complete quantumnoise reduction of these two modes if mixing with local oscillators of phase shifts π/2 is used.

We consider lasers with intracavity nonlinear elements, e.g., two-photon absorption, second-harmonic generation, as a possible means to reduce the amplitude fluctuations in a laser. While amplitude squeezing up to 37% may be obtained for the internal field, only a modest amount of noise reduction (10% for two-photon absorption, effectively zero for second-harmonic generation) is found in the output field at the laser frequency. In the second-harmonic field an amplitude-noise reduction of 50% below the shot-noise level may be achieved.

Using an extension of the Scully—Lamb laser theory we show that by insertion of nonlinear elements in the cavity, laser light with nonclassical sub—Poissonian photon statistics can be generated. For an N—photon absorber in the limit of small saturation the variance of the photon number distribution can be reduced by a factor of (+1/N) compared to Poissonian limit of the usual laser. When we generalize the type of such nonlinear elements to the case of a nonlinear feedback or Raman type nonlinear transition, the noise in the laser intensity can be reduced even further and approach the ideal limit, characterized by a Mandel Q parameter of Q = —1. Furthermore we show how this noise reduction via nonlinearities can be combined with a regular pump mechanism, which recently has been sugessted as a way to generate sub—Poissonian light. It turns out that in certain configurations the effect of both methods can be combined. Finally we show how this nonclassical behaviour is also reflected in a reduction of the output intensity power spectra below the shot noise level.

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.

We have generated squeezed states of light by the process of second harmonic conversion within an optical cavity resonant at both fundamental and harmonic frequencies. The experiment consists of a standing-wave cavity containing a crystal of lithium niobate doped with magnesium oxide and driven by the field from a frequency-stabilized Nd:YAG laser (incident power, ~10 mW). The total field reflected from the cavity illuminates a pair of high quantum efficiency photodiodes, whose individual photocurrents are summed. Observations of squeezing are made by analyzing the spectral density of fluctuations for this sum photo-current while the cavity detuning is scanned through resonance. An intensity regulator holds the reflected light intensity constant during the scan by control of the incident light level. Reductions in photocurrent fluctuations of 12% relative to the vacuum-state or shot-noise level are achieved for frequency offsets near 4 MHz. Since significantly higher degrees of squeezing are predicted by our theoretical analysis, we discuss those processes that currently limit the observed noise reduction, including phase noise produced by the intracavity crystal in the absence of nonlinear conversion.

We show that the injection of an external field in a laser helps to improve amplitude squeezing and sub-Poissonian light generation close to threshold, but spoils quantum noise reduction for very high pumping rates. A general nonlinear theory is developed for the resonant case (no detunings), without any assumption on the relative magnitudes of field and atomic decay constants, thus encompassing a large class of lasers. Several possible pumping schemes are accommodated, ranging from regular to Poissonian. We carry out a detailed stability analysis of the general equations of motion, relating it to the noise-reduction problem. Both the photon-number variance inside the cavity and the homodyne spectra of the output are discussed.

The authors consider a laser with intracavity second-harmonic generation and injected signal at either the second-harmonic or the fundamental frequency. With a strong injected signal at the second-harmonic frequency, near-perfect phase squeezing at non-zero classical intensity is found. A weak injected signal at the second harmonic gives 50% intensity squeezing in the output at the second harmonic, at an adjustable frequency. A moderate injected signal at the fundamental gives 50% intensity squeezing at the second harmonic for a relatively small nonlinearity.