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Annalen der Physik

Intracavity Multi‐Photon‐Absorption and the Quantum Noise Spectrum of Light

Ulrike Herzog

Published Jan 1, 1991• 1 citation
Publisher

Abstract

Abstract The intensity noise spectrum is investigated quantum‐mechanically for incident coherent light passing through a resonator which is filled with a k‐photon‐absorber. For k⩽ 2 the noise of the outgoing light is reduced below the shot noise level the reduction being maximal for frequencies that are small in comparison to the cavity bandwidth. It turns out that the highest possible value of this low‐frequency noise reduction is obtained when the resonator losses due to transmission through the outcoupling mirror are 2k – 1 times as large as the k‐photon absorption losses. In this case the noise at zero frequency is reduced with respect to the shot noise level by a factor of k/(2k – 1).

DOI
10.1002/andp.19915030811

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Abstract The intensity noise spectrum is investigated quantum‐mechanically for incident coherent light passing through a resonator which is filled with a k‐photon‐absorber. For k⩽ 2 the noise of the outgoing light is reduced below the shot noise level the reduction being maximal for frequencies that are small in comparison to the cavity bandwidth. It turns out that the highest possible value of this low‐frequency noise reduction is obtained when the resonator losses due to transmission through the outcoupling mirror are 2k – 1 times as large as the k‐photon absorption losses. In this case the noise at zero frequency is reduced with respect to the shot noise level by a factor of k/(2k – 1).
Squeezing in both intracavity and travelling-wave multiphoton absorption is investigated theoretically for incident intense nearly coherent light. It is shown that after sufficiently strong travelling-wave k-photon absorption (k=2,3...) a squeezed state of the radiation field is reached that is not a minimum uncertainty state. In this state the inphase and quadrature variances of the normalized electric field strength approach the asymptotic values k/(4(2k-1)) and k/4, respectively. With the help of an approximate Heisenberg picture treatment of a continuous mode field travelling through a broad-band k-photon absorber an analytical expression is obtained for the evolution of the squeezing spectrum in dependence on the degree of absorption. For intracavity multiphoton absorption the spectrum of output squeezing is investigated with the help of the usual Langevin equation approach. It turns out that the squeezing bandwidth in intracavity and travelling-wave multiphoton absorption is determined by the cavity bandwidth and the absorber linewidth, respectively.
We present an exact nonlinear derivation of the spectrum of fluctuations in the difference of output intensities for the signal and idler beams generated by intracavity two-photon gain, when the cavity decay rates are the same for the two modes, and taking into account the atomic fluctuations. For the field inside the cavity, we show that the variance in the difference of intensities may be up to 50% below the shot-noise value. We also consider the case of different decay rates, and show that the noise in the output-intensity difference vanishes at zero frequency, for single-ported cavities, and as long as the only source of field decay is the transmission through the mirror. Within this general approach, we show that for the two-photon laser there is a strong correlation between signal and idler output beams when the relay-level detuning is larger than the power broadening. We calculate, in lowest order, the correction to the noise spectrum of the difference of intensities due to the population of the relay level.
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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.
This paper presents a theoretical analysis of the optical properties of an optical cavity with both one- and two-photon intracavity absorption loss, without saturation. The cavity two-photon absorption loss per pass is assumed to be small, but otherwise the analysis is general. Analytical results for the cavity transmission as a function of cavity parameters, linear and two-photon intracavity loss, and detuning from resonance are derived and limiting cases discussed. Extraction of the two-photon loss from both cavity ring-down and cavity-enhanced absorption spectroscopy methods is analyzed and the predicted shot-noise limited sensitivities derived and compared. Numerical results are computed using the parameters of a recent experimental intracavity measurement of two-photon absorption of nitrous oxide. The results will be useful in the design and interpretation of cavity-enhanced, two-photon absorption spectroscopy.