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Physical Review A

Broadband squeezing via degenerate parametric amplification

David D. Crouch

Published Jul 1, 1988• 25 citations
Publisher

Abstract

We show that parametric amplification is capable of generating squeezed light over a wide band if materials with large ${\ensuremath{\chi}}^{(2)}$ nonlinearities can be found, and that the squeezing bandwidth can be enhanced considerably by phase matching away from degeneracy. We compare our results with similar results recently found for four-wave mixing in an optical fiber.

DOI
10.1103/physreva.38.508

Related papers

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.

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Analysis of amplitude-squeezed light generation with Gaussian-beam degenerate optical parametric amplifiers

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Summary form only given. The generation of quantum states of light, such as squeezed states, often relies on degenerate optical parametric amplification. The input signal in a degenerate optical parametric amplifier (DOPA) may be amplified or deamplified depending on the phase of the signal field relative to that of the pump field (/spl Delta//spl phi/=/spl phi//sub pump/-2/spl phi//sub signal/). We present the results of an accurate numerical DOPA model for the generation of amplitude-squeezed light with Gaussian pump and signal beams. We find that the widely accepted 3-dB limit imposed by the Gaussian beam profiles can actually be exceeded in the tight focusing regime.

Quantum Electronics and Laser Science Conference•May 12, 2000•1 citation
We show that parametric amplification is capable of generating squeezed light over a wide band if materials with large \ensuremathχ(2){\ensuremath{\chi}}^{(2)}\ensuremathχ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced considerably by phase matching away from degeneracy. We compare our results with similar results recently found for four-wave mixing in an optical fiber.
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.
Squeezed states have been produced by degenerate parametric amplification and four-wave mixing[1−5]. In all these cases the squeezing was narrowband, because the mechanisms employed are inherently bandlimited. It would be desirable to construct a squeezing apparatus that is broadband, because then it could be applied to short optical pulses. Aside from the fact that optical pulses with reduced phase or amplitude noise are interesting in their own right, the use of optical pulses in experiments can eliminate many sources of noise that prevent effective squeezing of quasi cw excitations.
Optical parametric amplification generates squeezed light in device-specific sets of time-frequency eigenmodes, and it has been widely accepted that detection and utilization of squeezing must comply with this modal constraint. We show that this constraint can be considerably relaxed under the continuous-wave pump and broadband phase-matching approximation, where the modal decomposition is non-unique. Specifically, any time-frequency mode with “self-conjugated” spectral symmetry can approximate a squeezing eigenmode, and partial homodyne detection can herald squeezing in arbitrary time-frequency modes. We demonstrate this using a high-efficiency, low-loss all-fiber source, measuring 4.38 ± 0.11 dB and 0.88 ± 0.09 dB squeezing on partially coherent and chaotic self-conjugated modes, respectively. Using a bichromatic self-conjugated mode with reduced local-oscillator noise, we achieve 7.50 ± 0.12 dB squeezing, which represents the highest level reported for fully guided-wave squeezing sources based on χ(2) and χ(3) nonlinearities. Squeezed light enhances precision in quantum technologies. Here, authors demonstrate an all-fiber source achieving 7.5 dB squeezing in self-conjugated modes, enabling reconfigurable quantum light in arbitrary time-frequency modes using standard telecom components.
We demonstrate broadband phase-sensitive amplification (PSA) measurement of squeezed light generated by a waveguide optical parametric amplifier (OPA) with external dispersion compensation. In broadband systems, group velocity dispersion (GVD) induces a frequency-dependent rotation of the squeezing axis, which limits the observable bandwidth in PSA measurements. To overcome this limitation, we introduce external dispersion compensation between two OPAs and suppress the quadrature rotation over a wide frequency range. As a result, we observe a maximum squeezing of 5.9 dB near the carrier frequency and more than 5 dB of squeezing up to a frequency offset of 4.5 THz from the carrier. Furthermore, squeezing below the shot-noise level is confirmed up to a frequency offset of 6 THz from the carrier, corresponding to the accessible phase-matching bandwidth of the waveguide OPA. Our results establish a practical method for broadband characterization of squeezed light and provide a key step toward ultrafast continuous-variable quantum information processing.
The standard process for the production of strongly squeezed states of light is degenerate optical parametric amplification (OPA) below threshold in nonlinear dielectric media such as LiNbO3 or periodically poled potassium titanyl phosphate (KTP). Here, we present a graphical description of squeezed-light generation via OPA, visualizing the interaction between the nonlinear dielectric polarization of the medium and the electromagnetic quantum field. We explicitly focus on the transfer from the field's ground state to a squeezed vacuum state and from a coherent state to a bright squeezed state by the medium's second-order nonlinearity, respectively. Our pictures illustrate the phase-dependent amplification and deamplification of quantum uncertainties and give the phase relations between all propagating electromagnetic fields as well as the internally induced dielectric polarizations. The graphical description can also be used to describe the generation of nonclassical states of light via higher-order effects of the nonlinear dielectric polarization such as four-wave mixing and the optical Kerr effect.
Summary form only given. The generation of quantum states of light, such as squeezed states, often relies on degenerate optical parametric amplification. The input signal in a degenerate optical parametric amplifier (DOPA) may be amplified or deamplified depending on the phase of the signal field relative to that of the pump field (/spl Delta//spl phi/=/spl phi//sub pump/-2/spl phi//sub signal/). We present the results of an accurate numerical DOPA model for the generation of amplitude-squeezed light with Gaussian pump and signal beams. We find that the widely accepted 3-dB limit imposed by the Gaussian beam profiles can actually be exceeded in the tight focusing regime.