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Spontaneous symmetry breaking is central to our understanding of physics and explains many natural phenomena, from cosmic scales to subatomic particles. Its use for applications requires devices with a high level of symmetry, but engineered systems are always imperfect. Surprisingly, the impact of such imperfections has barely been studied, and restricted to a single asymmetry. Here, we experimentally study spontaneous symmetry breaking with two controllable asymmetries. We remarkably find that features typical of spontaneous symmetry breaking, while destroyed by one asymmetry, can be restored by introducing a second asymmetry. In essence, asymmetries are found to balance each other. Our study illustrates aspects of the universal unfolding of the pitchfork bifurcation, and provides new insights into a key fundamental process. It also has practical implications, showing that asymmetry can be exploited as an additional degree of freedom. In particular, it would enable sensors based on symmetry breaking or exceptional points to reach divergent sensitivity even in presence of imperfections. Our experimental implementation built around an optical fiber ring additionally constitutes the first observation of the polarization symmetry breaking of passive driven nonlinear resonators.
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The realization of spontaneous symmetry breaking (SSB) requires a system that exhibits a near perfect symmetry. SSB manifests itself through a pitchfork bifurcation, but that bifurcation is fragile, and perturbed by any asymmetry or imperfections. Consequently, exploiting SSB for real-world applications is challenging and often requires cumbersome stabilization techniques. Here, we reveal a novel method that automatically leads to symmetric conditions, and demonstrate its practical application in coherently-driven, two-mode, passive Kerr resonators. More specifically, we show that introducing a $pi$-phase defect between the modes of a driven nonlinear resonator makes SSB immune to asymmetries by means of a period-doubled dynamics of the systems modal evolution. The two-roundtrip evolution induces a self-symmetrization of the system through averaging of the parameters, hence enabling the realization of SSB with unprecedented robustness. This mechanism is universal: all symmetry-broken solutions of driven Kerr resonators have a period-doubled counterpart. We experimentally demonstrate this universality by considering the polarization symmetry breaking of several different nonlinear structures found in normal and anomalous dispersion fiber cavities, including homogeneous states, polarization domain walls, and bright vector cavity solitons.
We report results of the analysis of the spontaneous symmetry breaking (SSB) in the basic (actually, simplest) model which is capable to produce the SSB phenomenology in the one-dimensional setting. It is based on the Gross-Pitaevskii - nonlinear Schroedinger equation with the cubic self-attractive term and a double-well-potential built as an infinitely deep potential box split by a narrow (delta-functional) barrier. The barriers strength, epsilon, is the single free parameter of the scaled form of the model. It may be implemented in atomic Bose-Einstein condensates and nonlinear optics. The SSB bifurcation of the symmetric ground state (GS) is predicted analytically in two limit cases, viz., for deep or weak splitting of the potential box by the barrier. For the generic case, a variational approximation (VA) is elaborated. The analytical findings are presented along with systematic numerical results. Stability of stationary states is studied through the calculation of eigenvalues for small perturbations, and by means of direct simulations. The GS always undergoes the SSB bifurcation of the supercritical type, as predicted by the VA at moderate values of epsilon, although the VA fails at small epsilon, due to inapplicability of the underlying ansatz in that case. However, the latter case is correctly treated by the approximation based on a soliton ansatz. On top of the GS, the first and second excited states are studied too. The antisymmetric mode (the first excited state) is destabilized at a critical value of its norm. The second excited state undergoes the SSB bifurcation, like the GS, but, unlike it, the bifurcation produces an unstable asymmetric mode. All unstable modes tend to spontaneously reshape into the asymmetric GS.
We investigate competition between two phase transitions of the second kind induced by the self-attractive nonlinearity, viz., self-trapping of the leaky modes, and spontaneous symmetry breaking (SSB) of both fully trapped and leaky states. We use a one-dimensional mean-field model, which combines the cubic nonlinearity and a double-well-potential (DWP) structure with an elevated floor, which supports leaky modes (quasi-bound states) in the linear limit. The setting can be implemented in nonlinear optics and BEC. The order in which the SSB and self-trapping transitions take place with the growth of the nonlinearity strength depends on the height of the central barrier of the DWP: the SSB happens first if the barrier is relatively high, while self-trapping comes first if the barrier is lower. The SSB of the leaky modes is characterized by specific asymmetry of their radiation tails, which, in addition, feature a resonant dependence on the relation between the total size of the system and radiation wavelength. As a result of the SSB, the instability of symmetric modes initiates spontaneous Josephson oscillations. Collisions of freely moving solitons with the DWP structure admit trapping of an incident soliton into a state of persistent shuttle motion, due to emission of radiation. The study is carried out numerically, and basic results are explained by means of analytical considerations.
We study light-beam propagation in a nonlinear coupler with an asymmetric double-channel waveguide and derive various analytical forms of optical modes. The results show that the symmetry-preserving modes in a symmetric double-channel waveguide are deformed due to the asymmetry of the two-channel waveguide, yet such a coupler supports the symmetry-breaking modes. The dispersion relations reveal that the system with self-focusing nonlinear response supports the degenerate modes, while for self-defocusingmedium the degenerate modes do not exist. Furthermore, nonlinear manipulation is investigated by launching optical modes supported in double-channel waveguide into a nonlinear uniform medium.
The present matter content of our universe may be governed by a $U(1)_{B-L}$ symmetry -- the simplest gauge completion of the seesaw mechanism which produces small neutrino masses. The matter parity results as a residual gauge symmetry, implying dark matter stability. The Higgs field that breaks the $B-L$ charge inflates the early universe successfully and then decays to right-handed neutrinos, which reheats the universe and generates both normal matter and dark matter manifestly.
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