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Annual Meeting Optical Society of America

Tunable squeezed-light generation from twin beams using an optical-phase feed-forward scheme: a broadband calculation

Chonghoon Kim, Prem Kumar

Published Jan 1, 1991• 0 citations
Publisher

Abstract

Recently we analyzed an optical-phase feed-forward scheme to produce a squeezed-light beam from the twin beams generated by nondegenerate optical parametric amplification.1 Our interest in this scheme stems from the possibility it allows for the generation of tunable squeezed light. If the input signal beam to the parametric amplifier is tunable, a tunable squeezed output beam can be obtained for spectroscopic applications.2 In this paper we present a wideband model of this scheme. Noise characteristics of the homodyne detector, that measures squeezing properties of the phase-controlled output signal beam from the parametric amplifier, are analyzed in detail. To minimize the squeezed-noise power at an arbitrarily given sideband frequency, the optimal phase feed-forward transfer function is calculated. This feed-forward transfer function is achievable with a bandpass filter and an electronic amplifier. For certain frequency profiles of the gain and phase of the parametric amplifier, the squeezed-noise power spectral density can be minimized over the whole electronic bandwidth of the photodetector that is employed in homodyne detection.

DOI
10.1364/oam.1991.mbb2

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A Theoretical Study of the Generation of Squeezed-State Light via Degenerate Parametric Amplification

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This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.

•Nov 21, 2007•0 citations
Recently we analyzed an optical-phase feed-forward scheme to produce a squeezed-light beam from the twin beams generated by nondegenerate optical parametric amplification.1 Our interest in this scheme stems from the possibility it allows for the generation of tunable squeezed light. If the input signal beam to the parametric amplifier is tunable, a tunable squeezed output beam can be obtained for spectroscopic applications.2 In this paper we present a wideband model of this scheme. Noise characteristics of the homodyne detector, that measures squeezing properties of the phase-controlled output signal beam from the parametric amplifier, are analyzed in detail. To minimize the squeezed-noise power at an arbitrarily given sideband frequency, the optimal phase feed-forward transfer function is calculated. This feed-forward transfer function is achievable with a bandpass filter and an electronic amplifier. For certain frequency profiles of the gain and phase of the parametric amplifier, the squeezed-noise power spectral density can be minimized over the whole electronic bandwidth of the photodetector that is employed in homodyne detection.
Recently we analyzed an optical-phase feed-forward scheme to produce a tunable squeezed-light beam from the twin beams generated by means of nondegenerate parametric amplification [ Opt. Lett.16, 755 ( 1991)]. Here we present a wideband model of this scheme. The noise characteristics of the homodyne detector that measures squeezing properties of the phase-controlled output signal beam from the parametric amplifier are analyzed in detail. To minimize the squeezed-noise power at an arbitrarily given sideband frequency, we calculate the optimum phase feed-forward transfer function. This feed-forward transfer function is realizable through the use of a bandpass filter and an electronic amplifier. For certain frequency profiles of the gain and phase of the parametric amplifier, the squeezed-noise power spectral density can be minimized over the entire bandwidth of the electronic detector that is used in homodyne detection.
We analyze an optical-phase feed-forward scheme to produce a squeezed-light beam from intensity-correlated twin beams generated by nondegenerate parametric amplification. The quadrature measurement of the idler beam at the output of the parametric amplifier is linearly fed forward onto the output signal beam with an electro-optic phase modulator. The minimum available squeezing factor is shown to be 1/(2g - 1), where g is the parametric amplifier gain, and is equal to the nonclassical intensity-noise reduction factor of the original twin beams at the output of the parametric amplifier. By changing the frequency of the input signal beam, one can generate tunable squeezed light with this scheme for application in precision spectroscopy.
We analyze an intensity feedforward scheme to produce a sub-Poissonian (amplitude-squeezed) light beam from the intensity-correlated twin beams generated by a nondegenerate parametric amplifier. Photon-number measurement of the idler beam at the output of the parametric amplifier is linearly fed forward onto the output signal beam using an amplitude modulator. The minimum available Fano factor is shown to be 1/(2g-1), where g is the parametric amplifier gain, and is equal to the nonclassical intensity-noise-reduction factor of the twin beams at the output of the parametric amplifier. By changing the frequency of the input-signal beam, tunable sub-Poissonian light can be generated with this scheme for application in precision absorption spectroscopy.
Twin beams generated from a nondegenerate optical parametric amplifier (NOPA) of gaing possess1 an intensity correlation that falls below the quantum limit by (2g – 1). This occurs whenever the input idler to the NOPA is in the vacuum state. Such input is practically advantageous because it makes the NOPA output intensities phase insensitive. When a non-vacuum idler input state is chosen, the NOPA output intensities become phase sensitive. For a proper input state and a suitable pump phase the output intensity correlation falls below the quantum limit by ( g + g − 1 ) 2 , which is 3 dB superior to the vacuum-idler-input result for g >> 1 and is equivalent to the quantum-noise reduction obtainable from a squeezed state generated with the same gain. Thus the sensitivity improvement achievable with NOPA twin beams by using direct detection is equivalent to that obtainable with squeezed states by using homodyne detection. The above equivalence also provides a new scheme for the generation of pulsed squeezed light that, in addition to being simple, automatically generates a matched local oscillator2 for homodyne detection of the squeezed pulses.
Pulsed squeezed light and intensity-correlated twin beams are generated by means of a traveling-wave optical parametric amplifier (OPA) consisting of a type-II phase-matched KTiOPO4 crystal that is pumped by a Q-switched and frequency-doubled Nd:YAG laser. Q switching of the laser results in a high peak pump intensity and a large peak parametric gain. Squeezed light is generated by amplifying the vacuum input field to the OPA, and it is detected by a balanced homodyne configuration that uses the fundamental beam of the laser as a local oscillator.1 Twin beams are generated by supplying a small input signal to the OPA. The amplified signal and idler beams are direct-detected individually and yield quantum-noise reduction when the two photocurrents are subtracted.
This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.