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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Creating highly squeezed vacua in Hybrid Laguerre-Gauss modes

Carlos Navarrete–Benlloch, Germán J. de Valcárcel, Eugenio Roldán

Published Jun 1, 2009• 0 citations
Publisher

Abstract

In this paper, we study the above threshold quantum properties of a degenerate optical parametric oscillator (DOPO) tuned to a given transverse mode family at the signal frequency. We will show that under this configuration DOPOs are versatile sources of nonclassical light, in which one could be able to generate highly squeezed vacua with the non trivial shapes of hybrid Laguerre-Gauss modes.

DOI
10.1109/cleoe-eqec.2009.5191615

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We theoretically describe the quantum properties of a large-Fresnel-number degenerate optical parametric oscillator (DOPO) with spherical mirrors that is pumped by a Gaussian beam and is tuned at the subharmonic frequency to a given transverse-mode family. We first analyze the classical problem and find that only the Laguerre-Gauss modes with lowest orbital angular momentum (OAM) are amplified above threshold. The transverse symmetry of the classically emitted signal field depends on the family index $f$. If $f$ is even the lowest available OAM is zero and emission occurs in a radially symmetric mode; on the contrary, if $f$ is odd the lowest available OAM is 1 and the emitted signal field has the shape of a hybrid Laguerre-Gauss mode (a linear combination of the two Laguerre-Gauss modes with OAM equal to $\ifmmode\pm\else\textpm\fi{}1$) that breaks the rotational invariance of the system. Next we focus on the squeezing properties of this DOPO model. As for the modes with lowest OAM we demonstrate that their quantum properties (in the linear approximation) are equal to the standard single-mode DOPO (for even $f$) or to the recently analyzed DOPO tuned to its first transverse-mode family [C. Navarrete-Benlloch, E. Rold\'an, and G. J. de Valc\'arcel, Phys. Rev. Lett. 100, 203601 (2008)]. Concerning the rest of (classically empty) modes (having larger OAM) we find that combinations of Laguerre-Gauss modes with opposite OAM (hybrid Laguerre-Gauss modes) exhibit quadrature squeezing. This property is independent of the even or odd character of the family index and hence has nothing to do with the symmetry of the classically emitted signal field. Noticeably the amount of squeezing does not depend on the pump level (it is thus noncritical squeezing) and can be arbitrarily large for the lower OAM nonamplified modes.

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Squeezing induced by spontaneous rotational symmetry breaking

Carlos Navarrete–Benlloch, Ferran V. García-Ferrer, A. Romanelli +2 more

This communication studies the phenomenon of quadrature squeezing generated via spontaneous rotational symmetry breaking. A degenerate optical parametric oscillator (DOPO) tuned to the first family of transverse modes at the signal frequency, and having perfectly spherical mirrors. When pumped above threshold with a Gaussian beam and within a classical description, it is easy to show that a TEM10mode with an arbitrary orientation emerges at the subharmonic, hence breaking the rotational symmetry of the system in the transverse plane.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2009•0 citations
In this paper, we study the above threshold quantum properties of a degenerate optical parametric oscillator (DOPO) tuned to a given transverse mode family at the signal frequency. We will show that under this configuration DOPOs are versatile sources of nonclassical light, in which one could be able to generate highly squeezed vacua with the non trivial shapes of hybrid Laguerre-Gauss modes.
We theoretically describe the quantum properties of a large-Fresnel-number degenerate optical parametric oscillator (DOPO) with spherical mirrors that is pumped by a Gaussian beam and is tuned at the subharmonic frequency to a given transverse-mode family. We first analyze the classical problem and find that only the Laguerre-Gauss modes with lowest orbital angular momentum (OAM) are amplified above threshold. The transverse symmetry of the classically emitted signal field depends on the family index fff. If fff is even the lowest available OAM is zero and emission occurs in a radially symmetric mode; on the contrary, if fff is odd the lowest available OAM is 1 and the emitted signal field has the shape of a hybrid Laguerre-Gauss mode (a linear combination of the two Laguerre-Gauss modes with OAM equal to $\ifmmode\pm\else\textpm\fi{}1$) that breaks the rotational invariance of the system. Next we focus on the squeezing properties of this DOPO model. As for the modes with lowest OAM we demonstrate that their quantum properties (in the linear approximation) are equal to the standard single-mode DOPO (for even fff) or to the recently analyzed DOPO tuned to its first transverse-mode family [C. Navarrete-Benlloch, E. Rold\'an, and G. J. de Valc\'arcel, Phys. Rev. Lett. 100, 203601 (2008)]. Concerning the rest of (classically empty) modes (having larger OAM) we find that combinations of Laguerre-Gauss modes with opposite OAM (hybrid Laguerre-Gauss modes) exhibit quadrature squeezing. This property is independent of the even or odd character of the family index and hence has nothing to do with the symmetry of the classically emitted signal field. Noticeably the amount of squeezing does not depend on the pump level (it is thus noncritical squeezing) and can be arbitrarily large for the lower OAM nonamplified modes.
We predict squeezed light generation through the spontaneous rotational symmetry breaking occurring in a degenerate optical parametric oscillator (DOPO) pumped above threshold. We show, within the linearized theory, that a DOPO with spherical mirrors, in which the signal and idler fields correspond to first-order Laguerre-Gauss modes, produces a perfectly squeezed vacuum with the shape of a Hermite-Gauss mode. This occurs at any pumping level above threshold; hence, the phenomenon is noncritical. Imperfections of the rotational symmetry, due, e.g., to cavity anisotropy, are shown to have a small impact.
We study the classical and quantum properties of a degenerate optical parametric oscillator (DOPO) tuned to the first family of transverse modes at the down-converted frequency, under the injection of a resonant TEM10{}_{10}10​ mode. Unlike the usual single-mode DOPO with injected signal, large levels of squeezing are predicted even for relatively large injections. We interpret these results in connection with the spontaneous symmetry breaking predicted for this system in the absence of injection and with the existence of a bifurcation giving rise to the switching on of the (noninjected) TEM01{}_{01}01​ mode.
A degenerate optical parametric oscillator (DOPO) in the above threshold regime is a prominent source of squeezed field. In this study, a driven DOPO whose pump mode is coupled to a thermal bath while the signal mode is coupled to a squeezed vacuum reservoir is explored to understand the effect of the external squeezed light and the thermal fluctuations on the squeezing properties of both the intracavity and output pump and signal modes. Our findings showed that the injected squeezed vacuum reservoir enables the intracavity squeezing to surpass the maximum squeezing limit of 50% attainable in a DOPO coupled to an ordinary vacuum reservoir. We also found that the maximum squeezing of the output signal mode shifts from resonance to off-resonance in the presence of the injected squeezed vacuum field. Furthermore, the output pump mode exhibits nearly perfect squeezing for a squeezing parameter of r=2. Unlike the output signal mode, the maximum squeezing of the output pump mode occurs at resonance in the presence of the injected squeezed vacuum reservoir. Moreover, a considerable amount of squeezing is observed even in the presence of thermal fluctuations, as they are counterbalanced by the external squeezed light. Notably, relative damping rate between the pump and signal modes is observed to be a parameter that significantly influences squeezing, indicating the importance of optimizing the amount of damping depending on the intended purpose of the DOPO.
High-Q cavities play a central role in quantum optics for the generation and study of novel quantum mechanical states of light like squeezed states. It is however not widely recognized that even low-Q cavities can produce such states. For example, a degenerate optical parametric oscillator (DOPO) with one nearly perfect mirror can produce perfectly squeezed output light regardless of the second mirror transmission, provided the DOPO is at oscillation threshold. Moreover, the squeezing bandwidth increases with increasing transmission of the second mirror.
This communication studies the phenomenon of quadrature squeezing generated via spontaneous rotational symmetry breaking. A degenerate optical parametric oscillator (DOPO) tuned to the first family of transverse modes at the signal frequency, and having perfectly spherical mirrors. When pumped above threshold with a Gaussian beam and within a classical description, it is easy to show that a TEM10mode with an arbitrary orientation emerges at the subharmonic, hence breaking the rotational symmetry of the system in the transverse plane.