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Journal of the Physical Society of Japan

Photon Number Squeezing due to Two-Photon Absorption in Internal and External Fields of a Microcavity

Hiromi Ezaki

Published May 15, 1999• 4 citations
Publisher

Abstract

The amplitude and phase noise spectra of the internal and external field of a microcavity are calculated using the quantum mechanical Langevin equations. We assume that two-photon absorber works inside a cavity, which brings photon-number squeezing in the internal field as well as the external field. The individual frequency components of the output field have strong squeezing at cavity resonance due to the interference between the input and the cavity field, which is similar to the quadrature squeezing in a parametric oscillator and the photon number squeezing in a saturated laser oscillator. However, the degree of the squeezing is not perfect becuase the material fluctuation remains.

DOI
10.1143/jpsj.68.1562

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The amplitude and phase noise spectra of the internal and external field of a microcavity are calculated using the quantum mechanical Langevin equations. We assume that two-photon absorber works inside a cavity, which brings photon-number squeezing in the internal field as well as the external field. The individual frequency components of the output field have strong squeezing at cavity resonance due to the interference between the input and the cavity field, which is similar to the quadrature squeezing in a parametric oscillator and the photon number squeezing in a saturated laser oscillator. However, the degree of the squeezing is not perfect becuase the material fluctuation remains.
The amplitude and phase noise spectra of the internal and external fields of a laser oscillator are calculated using the quantum mechanical Langevin equations. The outgoing field spectra are demonstrated to be different from the internal field spectra. The outgoing photon flux\hat{N}from a laser oscillator operating at far above the threshold has a spectral density equal to the classical shot noise level,2\langle\hat{N}\rangle. On the other hand, the internal photon number spectrum is Lorentzian, and the variance is equal to the average photon number,\langle\hat{N}\rangle. The difference stems from the quantum mechanical interference between the transmitted internal field and the reflected zero-point fluctuation at the output coupling mirror. The relation between the present analysis and the previous noise theory of a laser is also discussed.
It is shown that a laser with a two-photon saturable absorber exhibits a phase instability similar to that of two-photon optical bistability. The authors calculate the spectrum of the intensity fluctuations in the output field under conditions of exact resonance between the amplifier and the absorber. In the bad-cavity limit the relevant part of the spectrum assumes a simple Lorentzian form; as the phase-instability threshold is approached, the reduction of quantum noise becomes perfect for small frequencies.
We apply the laser quantum Langevin equations derived in part I of this paper to the description of the laser intensity fluctuations when the external field entering the input - output port is in a squeezed vacuum state with finite bandwidth. We focus on the two opposite limits in which the detection time is much longer, or much shorter, than the inverse of the cavity linewidth. When there is detuning between the squeezed input and the laser frequency, the variance of the intensity fluctuations displays regular oscillations with frequency equal to the detuning. In the limit of small detection times there is the possibility of substantial reduction of the photon-number fluctuations using a squeezed input.
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.
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The theory of a two-mode nondegenerate parametric amplifier in a cavity is reformulated in terms of quadrature-phase-amplitude variables. The corrrespondence with a genuine classical stochastic linear process is found (non-negative-definite diffusion matrices) for the case of a cavity device immersed in thermal or ordinary (nonsqueezed) vacuum sources. A special kind of squeezing, i.e., quadrature squeezing [B. L. Schumaker, Phys. Rep. 135, 318 (1986)], is found to be characteristic of the internal steady state for the case of a cavity model subjected to an additional phase-sensitive noise source coupled to one of the two internal modes. Finally, the usual squeezing spectrum of the output field is calculated in both cases by means of an input-output formalism based upon a symmetric ordering scheme of noncommuting operators, well adapted for the quadrature-phase description of the fields involved in the interaction.