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arXiv:physics/0406049 · Optics Letters

Experimental evidence of spontaneous symmetry breaking in intracavity type II second-harmonic generation with triple resonance

Laurent Longchambon, Nicolas Treps, T. Coudreau, Julien Laurat, Claude Fabre

Published Feb 1, 2005• 12 citations
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Abstract

We describe a spontaneous symmetry-breaking phenomenon between the intensities of the ordinary and extraordinary components of the fundamental field in intracavity type II harmonic generation. It is based on a triply resonant cavity containing a type II chi(2) crystal pumped at fundamental frequency omega0. The pump beam generates a second-harmonic mode at frequency 2omega0 that acts as a pump for frequency-degenerate type II parametric downconversion. Under operating conditions symmetric with respect to the ordinary and extraordinary components of the fundamental wave, we show a breaking of the symmetry of the intensities of these two waves.

DOI
10.1364/ol.30.000284

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Physical Review A•May 1, 1994•33 citations
We describe a spontaneous symmetry-breaking phenomenon between the intensities of the ordinary and extraordinary components of the fundamental field in intracavity type II harmonic generation. It is based on a triply resonant cavity containing a type II chi(2) crystal pumped at fundamental frequency omega0. The pump beam generates a second-harmonic mode at frequency 2omega0 that acts as a pump for frequency-degenerate type II parametric downconversion. Under operating conditions symmetric with respect to the ordinary and extraordinary components of the fundamental wave, we show a breaking of the symmetry of the intensities of these two waves.
It is known1 that in type-I second-harmonic generation in a doubly resonant cavity where a subharmonic mode is coupled to a harmonio mode through a χ(2) process, self-pulsing may occur for high input fundamental power. Squeezing2 and QND measurements3 are possible near the self-pulsing threshold. For type-II harmonic generation, however, there are two sub-harmonic modes coupled to the harmonic mode through the same χ(2) process but with different arrangements of polarizations. The extra subharmonic mode will make the dynamics of the system totally different.
We investigate, theoretically, the generation of bright and vacuum-squeezed light as well as entanglement in intracavity, type II, phase-matched second-harmonic generation. The cavity in which the crystal is embedded is resonant at the fundamental frequency but not at the second-harmonic frequency. A simple model for the process using semiclassical theory is derived, and quadrature-squeezing spectra of the involved fundamental fields are deduced. The analysis shows that vacuum squeezing reminiscent of subthreshold optical parametric oscillator squeezing is present and, in the ideal case, perfect. Under slight modifications of the operational conditions, the system is shown to produce efficient bright, squeezed light. Furthermore, we investigate the degree of polarization squeezing and find that three Stokes parameters can be squeezed simultaneously. Finally, we gauge the process for possible entanglement.
Classical and quantum fluctuations are analyzed in the system of type-II harmonic generation where two frequency-degenerate subharmonic fields with orthogonal polarizations are required for the generation of a harmonic field. The two subharmonic fields as well as the harmonic fields are on resonance in a cavity. It is found that there is no self-pulsing behavior as predicted for the type-I case where the intensities of both the subharmonic and the harmonic fields undergo fast oscillation. Instead there exists a threshold that is identified as the onset of an optical parametric oscillator (OPO) formed by a subharmonic mode with its polarization orthogonal to the input polarization (not the original modes). When the loss for the harmonic field is small, most of the input power is converted to the output power of the OPO. Under this circumstance, quantum-nondemolition measurements of the input can be performed at certain frequencies. The spectra of squeezing are calculated for the two subharmonic modes and it is found that both modes are squeezed for a certain range of frequency. The output of the OPO is found to exhibit phase squeezing.
Quantum fluctuation and quantum entanglement in competing nonlinear processes of type II second-harmonic generation in a triple-resonant cavity is analyzed. Operating above threshold with intracavity loss, the mean amplitude and the entanglement of reflected subharmonic field as a function of pump and loss parameters are calculated. It is found that the two eigenmodes become unbalanced when internal loss intervenes. The dependence of the entanglement characteristics of two reflected subharmonic modes on output coupling efficiency µ_b/µ, pump parameter sigma, and normalized frequency Omega are discussed. Under appropriate conditions, this system can be exploited as a bright entanglement resource.
Quantum fluctuation and quantum entanglement of the pump fields reflected from an optical cavity for type-II second-harmonic generation are theoretically analyzed. The correlation spectra of quadrature components between the reflected subharmonic fields are interpreted in terms of pump parameter, intracavity losses, and normalized frequency. High correlation of both amplitude and phase quadratures can be accessed in a triple resonant cavity before the pitchfork bifurcation occurs. The two reflected subharmonic fields are in an entangled state with quantum correlation of phase quadratures and anticorrelation of amplitude quadratures. The proposed system can be exploited as a source for generating entangled states of continuous variables.
The interaction between two cavity resonant nonlinear processes in an intracavity ${\mathrm{\ensuremath{\chi}}}^{(2)}$ medium is studied, namely frequency doubling of a pump field of frequency ${\mathrm{\ensuremath{\omega}}}_{1}$ and subsequent down-conversion of the second harmonic to a pair of photons of frequencies ${\mathrm{\ensuremath{\omega}}}_{1}$\ifmmode\pm\else\textpm\fi{}\ensuremath{\Delta}. A closed set of semiclassical equations of motion for appropriately chosen quantities of the full system is derived and an explicit stationary solution is given. Its features and stability are discussed, the most striking being a stable plateau in the second harmonic, i.e., the field of frequency ${\mathrm{\ensuremath{\omega}}}_{2}$=2${\mathrm{\ensuremath{\omega}}}_{1}$ becomes independent of the pump field scrE1{\mathit{scrE}}_{1}scrE1​, provided scrE1{\mathit{scrE}}_{1}scrE1​ is larger than a certain threshold value. It is demonstrated that undamped self-pulsing can only prevail, if the ratio of the rates of second harmonic generation over and parametric down-conversion exceeds a value which depends solely on the relative damping rates of the second harmonic and fundamental, which yields a tentative theoretical explanation of the experimentally observed quenching of the self-pulsing.