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arXiv:quant-ph/0306046 · Physical Review A

Squeezing based on nondegenerate frequency doubling internal to a realistic laser

Ulrik L. Andersen, Peter Tidemand‐Lichtenberg, Preben Buchhave

Published Jan 15, 2004• 0 citations
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Abstract

We investigate theoretically the quantum fluctuations of the fundamental field in the output of a nondegenerate second-harmonic generation process occurring inside a laser cavity. Due to the nondegenerate character of the nonlinear medium, a field orthogonal to the laser field is for some operating conditions independent of the fluctuations produced by the laser medium. We show that this fact may lead to perfect squeezing for a certain polarization mode of the fundamental field. The experimental feasibility of the system is also discussed.

DOI
10.1103/physreva.69.013808

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We investigate theoretically the quantum fluctuations of the fundamental field in the output of a nondegenerate second-harmonic generation process occurring inside a laser cavity. Due to the nondegenerate character of the nonlinear medium, a field orthogonal to the laser field is for some operating conditions independent of the fluctuations produced by the laser medium. We show that this fact may lead to perfect squeezing for a certain polarization mode of the fundamental field. The experimental feasibility of the system is also discussed.
We discuss quantum-fluctuation characteristics of a second-harmonic generation system that uses an optical resonator to confine only the fundamental field. It was predicted that the available amount of squeezing is limited to 1.76 dB for the fundamental output and 9.54 dB for the second-harmonic output, respectively, irrespective of system parameters. However, these predictions are based on low-order perturbation theory and are unavailable if the nonlinear coupling between the fundamental and the second harmonic becomes large. We consider the spatial evolution of the fields and reveal that the maximum amount of squeezing depends on the cavity loss: Even an arbitrary amount of squeezing is possible for both the fundamental output and the second-harmonic output. We also consider the possibility of parametric oscillation of empty cavity modes pumped by the generated second harmonic and derive the following prediction: In a system that uses a type I phase-matched crystal, the oscillation of the side mode hardly occurs because of sum-frequency generation with the fundamental and scarcely imposes any limitations on squeezing. On the other hand, a system with a type II phase-matched crystal suffers from the oscillation of the polarization mode orthogonal to that of the fundamental input, and squeezing of the second-harmonic output is limited to 3 dB.
The classical behavior and the quantum fluctuations are analyzed for the system of nondegenerate second-harmonic generation inside a cavity, where two frequency degenerate but orthogonally polarized harmonic modes are coupled to a second-harmonic mode via a ${\mathrm{\ensuremath{\chi}}}^{(2)}$ medium. We consider the consequences of asymmetrically pumping the two harmonic modes. Asymmetric pumping causes large changes in the classical dynamical behavior of the system; the pitchfork bifurcation, predicted by Ou [Phys. Rev. A 49, 4902 (1994)] and Eschmann and Reid [Phys. Rev. A 49, 2881 (1994)] for symmetric pumping, is transformed into a saddle node for any antisymmetric pumping. This new dynamics brings about the possibility of the system reaching a Hopf and a saddle-node--Hopf bifurcation point. Squeezed-state production is investigated at the critical points of the system. Large squeezing is predicted at the saddle-node and Hopf bifurcation points. The wealth of squeezing predicted by this model at the pitchfork bifurcation point is interpreted in terms of the dynamics of the system. For symmetric pumping, this system is shown to be able to produce two coherent amplitude and phase correlated beams both above and below the pitchfork bifurcation point and so is a candidate for an Einstein-Podolsky-Rosen experiment. \textcopyright{} 1996 The American Physical Society.
We present the analysis of a laser in which an intractivity χ (2) -nonlinear element couples the lasing mode to its second harmonic. The cavity is resonant for both modes. We investigate the potential for squeezing in this system by linearizing the quantum fluctuations around the steady states of the problem. In principle, more than 50% noise reduction below the vacuum level is possible in the second-harmonic field outside the cavity. The maximum squeezing, which is neither pure amplitude nor pure phase squeezing, occurs at a finite frequency-offset from the cavity resonance.
We present a theoretical investigation of the potential for squeezing of a doubly resonant cavity that contains a laser medium as well as a ${\mathrm{\ensuremath{\chi}}}^{(2)}$ nonlinearity. If the lasing mode is coupled to its second harmonic, i.e., for a self-frequency-doubling laser, we find more than 60% squeezing in the up-converted mode outside the cavity. In the opposite case of a ``self-down-converting laser,'' i.e., when the lasing mode is coupled to its subharmonic, a perfectly squeezed vacuum in the down-converted mode develops into a less squeezed state with a nonvanishing coherent amplitude as the pump rate is increased. Our analysis extends beyond the first stable regime of the classical dynamics and compares results for different laser models.
By solving linearized wave equations of nonlinear polarization for a medium, we derive the input-output relationship for the propagation of the quantum fluctuations in single-pass second-harmonic generation with arbitrary interaction length. Spectra of quadrature-phase squeezing are calculated from the input-output relations. It is found that the intensity fluctuations of both harmonic and fundamental fields are squeezed below the vacuum fluctuation level. For large interaction length, an arbitrary amount of squeezing can be achieved for the fundamental field whereas only 50% squeezing is possible for the harmonic field. The bandwidth of squeezing is determined by the phase-matching condition and can be very broad in this case. The possibility of a quantum-nondemolition measurement in the process is discussed. Some interesting features in quantum fluctuations of the fields are presented.