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arXiv:0709.0212 · Physical Review Letters

Noncritically Squeezed Light via Spontaneous Rotational Symmetry Breaking

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

Published May 19, 2008• 42 citations
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Abstract

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.

DOI
10.1103/physrevlett.100.203601

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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 predict the generation of noncritically squeezed light through the spontaneous rotational symmetry breaking occurring in a Kerr cavity. The model considers a chi(3)cavity that is pumped by two Gaussian beams of frequencies omega1and omega2. The cavity configuration is such that two signal modes of equal frequency omegas=(omega1+omega2)/2 are generated, these signal fields being first-order Laguerre-Gauss modes. In this system, a spontaneous breaking of the rotational symmetry occurs as the signal field corresponds to a Hermite-Gauss TEM mode. This symmetry breaking leads to the perfect and noncritical (i.e., nondependent on the parameter values) squeezing of the angular momentum of the output TEM mode, which is another TEM mode spatially orthogonal to that in which bright emission occurs.
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.
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.
In a series of articles we studied the quantum properties of a degenerate optical parametric oscillator tuned to the first family of transverse modes at the subharmonic. We found that, for a cavity having rotational symmetry with respect to the optical axis, a TEM10{}_{10}10​ mode with an arbitrary orientation in the transverse plane is emitted above threshold. We proved then that quantum noise induces a random rotation of this bright TEM10{}_{10}10​ mode in the transverse plane, while the orthogonal mode, the so-called dark mode, has perfect quadrature squeezing irrespective of the distance to threshold (noncritical squeezing). This result was linked to the spontaneous rotational symmetry breaking which occurs when the bright mode is generated, and here we analyze how the squeezing of the dark mode is degraded when the cavity is not perfectly symmetric. We will show that large levels of squeezing are still attainable for reasonable values of this anisotropy, with the advantage that the orientation of the bright and dark modes is basically fixed, a very attractive situation from the experimental point of view.
In the last years we have proposed the use of the mechanism of spontaneous symmetry breaking with the purpose of generating perfect quadrature squeezing. Here we review previous work dealing with spatial (translational and rotational) symmetries, both on optical parametric oscillators and four-wave mixing cavities, as well as present new results. We then extend the phenomenon to the polarization state of the signal field, hence introducing spontaneous polarization symmetry breaking. Finally we propose a Jaynes-Cummings model in which the phenomenon can be investigated at the singlephoton- pair level in a non-dissipative case, with the purpose of understanding it from a most fundamental point of view.
The squeezed state, as an important quantum resource, has great potential applications in quantum computing, quantum communication and precision measurement. In the noncritically squeezed light theory, the predicted noncritically squeezed light can be generated by breaking the spontaneous rotational symmetry occurring in a degenerate optical parametric oscillator (DOPO) pumped above threshold. The reliability of this kind of squeezing is crucially important, as its quantum performance is robust to the pump power in experiment. However, the detected squeezing degrades rapidly in detection, because the squeezed mode orientation diffuses slowly, resulting in a small mode mismatch during the homodyne detection. In this paper, we propose an experimentally feasible scheme to detect noncritically squeezing reliable by employing the spatial mode swapping technic. Theoretically, the dynamic fluctuation aroused by random mode rotation in the squeezing detection can be compensated for perfectly, and 3 dB squeezing can be achieved robustly even with additional vacuum noise. Our scheme makes an important step forward for the experimental generation of noncritically squeezed light.