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Physical Review A

Optical bistability with symmetry breaking

T. Yabuzaki, Taishi Okamoto, Masao Kitano, T. Ogawa

Published Apr 1, 1984• 36 citations
Publisher

Abstract

It is shown that a simple system without a cavity exhibits optical bistability with no hysteresis but with symmetry-breaking or pitchfork bifurcation. The optical system is composed of a cell containing atoms with spin in the ground state, a $\frac{\ensuremath{\lambda}}{8}$ plate and a mirror, and an incident light beam linearly polarized and nearly resonant with the atomic absorption line. The system has a positive-feedback loop for the rotation of polarization through competitive optical pumping by ${\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}$ circularly polarized components. When the intensity of the incident light exceeds a critical value, symmetry breaking occurs and its polarization is subject to rotation in the clockwise or anticlockwise sense. Correspondingly, atomic spin polarization is produced spontaneously in a direction parallel or antiparallel to the incident beam. This new type of optical bistability is found to be explained well in context with the cusp catastrophe, as well as the ordinary one with hysteresis. It is also found that, in the presence of a transverse magnetic field, self-sustained spin precession occurs, which results in the steady-state modulation of the light polarization at about the Larmor frequency. Experimental evidence of the symmetry breaking and pitchfork bifurcation is obtained by using sodium vapor.

DOI
10.1103/physreva.29.1964

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It is shown that a simple system without a cavity exhibits optical bistability with no hysteresis but with symmetry-breaking or pitchfork bifurcation. The optical system is composed of a cell containing atoms with spin in the ground state, a \ensuremathλ8\frac{\ensuremath{\lambda}}{8}8\ensuremathλ​ plate and a mirror, and an incident light beam linearly polarized and nearly resonant with the atomic absorption line. The system has a positive-feedback loop for the rotation of polarization through competitive optical pumping by \ensuremathσ\ifmmode±\else\textpm\fi{\ensuremath{\sigma}}_{\ifmmode\pm\else\textpm\fi{}}\ensuremathσ\ifmmode±\else\textpm\fi​ circularly polarized components. When the intensity of the incident light exceeds a critical value, symmetry breaking occurs and its polarization is subject to rotation in the clockwise or anticlockwise sense. Correspondingly, atomic spin polarization is produced spontaneously in a direction parallel or antiparallel to the incident beam. This new type of optical bistability is found to be explained well in context with the cusp catastrophe, as well as the ordinary one with hysteresis. It is also found that, in the presence of a transverse magnetic field, self-sustained spin precession occurs, which results in the steady-state modulation of the light polarization at about the Larmor frequency. Experimental evidence of the symmetry breaking and pitchfork bifurcation is obtained by using sodium vapor.
The dynamical behavior of a Fabry-Perot cavity filled with atoms having Zeeman sub-levels in the ground state is investigated. Such a system is known to exhibit optical tristability, where the atomic spins are oriented parallel or antiparallel to the optical axis even for the linearly polarized incident light. It is found that, when a static magnetic field is applied transversely to the optical axis, self-sustained precession of the spin polarization occurs. Correspondingly, the ${\ensuremath{\sigma}}_{+}$ and ${\ensuremath{\sigma}}_{\ensuremath{-}}$ components of the transmitted light are modulated at about the Larmor frequency. We also show that the Bloch equation describing the motion of the spin polarization in the cavity can be reduced to van der Pol's equation.
We study a theoretical model that describes an optically pumped Fabry–Perot cavity filled with sodium vapor as a nonlinear absorptive medium. The nonlinear medium is subjected to a static magnetic field. A difference of population is built up between Zeeman sublevels of the ground state when the pump exceeds a threshold. This gives rise to a nonsymmetrical absorption of the two circularly polarized components of the incident light. The emphasis of this paper is on the derivation of analytic results. We show that the system can exhibit a self-pulsing behavior and that in a suitable domain of parameters the system has two or more steady states. This is known as optical bistability or optical multistability.
A theoretical investigation is reported of the interaction of light with a system of two films which contain two-level centres and whose thickness is less than the incident radiation wavelength. It is shown that when light of the same intensity is incident from both sides of the films, symmetry-breaking bifurcation is possible, i.e. the transmitted fields are different for the opposite directions. The relationship between symmetry-breaking bifurcation and optical bistability is determined. If the distance between the films represents an odd number of the optical half-wavelengths symmetry breaking occurs at a lower value of the parameter representing the interaction nonlinearity than that corresponding to the onset of bistability. The opposite is true when an even number of half-wavelengths can be fitted between the films. The supression of symmetry-breaking bifurcation is illustrated for various intensities of the incident optical field.
We describe a simple nonlinear optical device which transforms an ingoing cw light beam into a periodically modulated one. The mechanism of operation is due to a spin precession in the ground state of optically pumped atoms with a J=(1/2)\ensuremath{\rightarrow}J'=(1/2) transition in the presence of a static transverse magnetic field. With optical feedback from a resonator, this magnetically induced spin precession can be self-sustained and then can give rise to a self-pulsing of the transmitted light at roughly the Larmor frequency. A detailed theoretical description of the system is presented and stability criteria are considered. In contrast to earlier work, our calculations take into account the resonator round-trip time, an optical detuning from the atomic resonance, and absorptive losses within the resonator. New signal features are predicted: These include a complicated structure of the initial transient as well as a precipitation to a stationary state. Our theoretical model is confirmed by measurements which are performed by means of a Fabry-Perot resonator containing sodium vapor. The behavior of the device is studied for a wide range of experimental parameters; threshold powers for oscillation (\ensuremath{\gtrsim}5 mW) and the oscillation frequency and its tuning range (140 kHz--13 MHz) are investigated as well as the dynamics of the system following a step input of light.
We exploit polarization self-rotation (PSR) in atomic rubidium vapor to observe spontaneous symmetry breaking and bistability of polarization patterns. We pump the vapor cell with horizontally polarized light while the vertical polarization, which is initially in the vacuum state, is resonated in a ring cavity. Microscopic field fluctuations in this mode experience cumulative gain due to the compound action of amplification due to the self-rotation and feedback through the resonator, eventually acquiring a macroscopic magnitude akin to an optical parametric oscillator. The randomness of these fluctuations results in a bistable, random macroscopic polarization pattern at the output. We propose utilizing this mechanism to simulate an Ising-like interaction between multiple spatial modes and as a basis for a fully optical coherent Ising machine (CIM).
We report the observation of transverse optical bistability (TOB) in a sodium-filled Fabry-P\'erot resonator, pumped by circularly polarized light, nearly resonant with the D1{\mathit{D}}_{1}D1​ line, in the presence of a buffer gas, for low vapor density. A sequence of circularly symmetric patterns, ascribable to superpositions of resonator modes, is obtained. The appearance of TOB can be explained in terms of a self-induced intensity-dependent lens formed in the medium by the interaction with the laser light. A simple model that considers the transverse diffusion of the atoms inside the cell provides predictions in good qualitative agreement with the observations.