
Craig M. Savage
Professor of Physics
ANU

















Publications before 1994
mainly quantum optics
ResearcherID 
Publications from 19942003 
Publications from 2004now
Atomic waveguides and cavities from hollow optical fibers,
C. M. Savage, S. Marksteiner, P. Zoller, Fundamentals of Quantum Optics III
Lecture Notes in Physics Volume 420, pp 6074 (1993).
Springer Link
The analysis of hollow optical fiber atomic waveguides uses quite simple physics. On this basis we claim to have demonstrated their feasibility. The primary obstacles appear to be technical, such as how to couple light into the optical waveguide. The idea of an atomic waveguide appears to us to be sufficiently fundamental that interesting applications, pure and applied, will follow. We have speculated that they might be used to make atomic cavities, which are one element required for the construction of an ``atomic laser''. On a more practical level flexible mass transport alone may prove useful.
Linewidth prevents macroscopic quantum superposition generation by single atom dispersion,
Xiping Zheng, J.A. Gifford and C. Savage, Quantum Optics 5, 311 (1993).
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A method for generating macroscopically distinguishable superposition states via single atom dispersion was proposed by Savage et al. In that model, the atomic linewidth was not considered. However, including the atomic linewidth, we get two contradictory conditions for the generation of distinguishable superposition states. This shows that the atomic linewidth prevents the formation of macroscopically distinguishable superposition states by the proposed method.
High power quenching resulting from pump excitedstate absorption in an erbiumdoped fiber laser,
T. Ralph, A.J. Stevenson, C. Savage, and H.A. Bachor, Optics Lett. 18, 1162 (1993).
Optics Letters 
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We present an interesting theoretical prediction from semiclassical laser theory, namely, the quenching of laser action at high pump powers that results from the presence of excitedstate absorption of pump photons. Experimental results are shown from an erbiumdoped fiber laser that are consistent with our prediction.
Squeezing from conventionally pumped lasers; a rate equation approach,
T. Ralph and C. Savage, Quantum Optics 5, 113 (1993).
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We calculate the cavity photon statistics of conventionally pumped fourlevel lasers using a diagonal number state representation. The results are in agreement with those obtained from previous treatments using linearized FokkerPlanck equations and predict subPoissonian photon statistics at sufficiently high pump rates.
Producing squeezed light from conventionally pumped lasers,
T. Ralph and C. Savage, JOSA B 9, 1895 (1992).
Journal of the Optical Society of America B 
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We discuss the conditions under which intensity squeezing is predicted to be observed in the output of conventionally pumped multilevel lasers.
Parametric amplifiers in phase noise limited optical communications,
Yi Mu and C.M. Savage, JOSA B 9, 65 (1992).
Journal of the Optical Society of America B 
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Gordon and Mollenauer [Opt. Lett. 15, 1351 (1990)] have shown that the nonlinear Kerr effect limits the range of coherent communications systems using laser amplifiers. We show that parametric amplifiers avoid this limitation. Our method is novel in that we use quantumoptical master equations to model the communications systems. These are solved numerically for systems with either laser amplifiers or parametric amplifiers, with and without the nonlinear Kerr effect. Parametric amplifiers perform better because they preserve the signaltonoise ratio and decrease the phase noise.
Correlation effects in lightsources with high quantum efficiency,
H.A. Bachor, P. Rottengater, C.M. Savage, App. Phys. B 55, 258 (1992).
Applied Physics B 
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The noise properties of an LED with high quantum efficiency are investigated. Light with subPoissonian photon statistics is generated by driving the LED with a high impedance, well regulated current source. It is shown that it is necessary to distinguish between the measured total quantum efficiency and the optical quantum efficiency. In addition, the correlation between the fluctuations in the driving current and the fluctuations in the photocurrent is demonstrated, allowing a suppression of the shot noise after the measurement. The properties of this alternative noise reduction technique are discussed.
The quantum mechanics of a classically chaotic dissipative system,
C.M. Savage, Computers in Physics 6, 513 (1992).
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The quantum mechanical model of a dissipative system that is chaotic in its classical limit is solved numerically. The system is nonlinear optical second harmonic generation, and the model is the quantum optical master equation. The steadystate of the master equation is found and compared with the classical chaotic attractor. Computational methods appropriate for vector processors and for the connection machine are described.
Squeezed light from conventionally pumped lasers with nonuniform spatial structure,
C.M. Savage and T.C. Ralph, Phys. Rev. A 46, 2803 (1992).
Physical Review A 
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Spatial variations of the laser mode and pumping rate are incorporated into the theory of conventionally pumped lasers that produce squeezed light. Both a quantummechanical theory and a heuristic statistical model are used. While variations in the laser mode are found to have a negligible effect on squeezing, variations in the pumping rate are significant. The maximum attainable squeezing is always reduced compared with the spatially uniform case. However, resonantly enhancing a lowpower pump in a FabryPérot cavity, rather than a ring cavity, may give better squeezing.
One atom lasers,
Yi Mu and C.M. Savage, Phys. Rev. A 46, 5944 (1992).
Physical Review A 
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Oneatom lasers are important because their governing equations can be solved exactly, even with a quantized field.
Full abstract.
Oneatom lasers are important because their governing equations can be solved exactly, even with a quantized field. We present a fully quantummechanical treatment of oneatom lasers modeled by quantumoptical master equations. These are solved numerically without any significant approximations. We show that laser action is possible with one atom, and that it might be achievable experimentally. Laser action is characterized by the dominance of stimulated emission over spontaneous emission. We use the oneatom laser model to investigate, without approximation, some interesting generic laser phenomena. Under certain conditions lasers produce intensity squeezed light, and then the laser linewidth increases with the pumping rate, in contrast with standard lasers. We also report selfquenching behavior: lasers with incoherent pumping out of the lower laser level turn off when the pumping is sufficiently fast because the coherence between the laser levels is destroyed.
Quantum theory of interferometric length measurement with inefficient photodetectors,
J.A. Gifford and C.M. Savage, Phys. Rev. A 43, 1484 (1991).
Physical Review A 
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We find an upper bound for the sensitivity of FabryPérot interferometric length measurements using inefficient photodetectors.
Full abstract.
We find an upper bound for the sensitivity of FabryPérot interferometric length measurements using inefficient photodetectors. This bound applies to all possible quantummechanical states of the light entering the interferometer. It applies to standard photodetection, differenced photodetection, and homodyne detection. In the limit of large photon number we identify the optimal detection scheme and input states. They are homodyne detection with a coherent state in one input port, and a nonvacuum quadrature squeezed state in the other. No other quantum states of the input light give better sensitivity, provided that the interferometer output is measured by either photodetection or homodyning, and that the photodetectors are inefficient.
Squeezed light from conventionally pumped multilevel lasers,
T. Ralph and C. Savage, Opt. Lett. 16, 1113 (1991).
Optics Letters 
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We calculate amplitude squeezing spectra for the light from a variety of conventionally pumped three and fourlevel lasers. Hence we extend a recent prediction that a certain threelevel laser can generate nonclassical light without the need for rigged pumping.
Squeezed light from a coherently pumped fourlevel laser,
T.C. Ralph and C.M. Savage, Phys. Rev. A 44, 7809 (1991).
Physical Review A 
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We calculate the amplitude squeezing in the output of a coherently pumped fourlevel laser and compare it with that from a similar incoherently pumped laser. We find that squeezing may be considerably enhanced by pumping with coherent light. The squeezing in both types of laser is explained by a simple statistical model.
Macroscopic quantum superpositions by means of single atom dispersion,
C.M. Savage, S. Braunstein, and D. Walls, Opt. Lett. 15, 628 (1990).
Optics Letters 
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We show that macroscopic quantum superpositions of the electromagnetic field can be generated through amplification of microscopic quantum superpositions prepared in a single atom. Our scheme has the advantage that dissipation is negligible, and hence the superpositions are not rapidly destroyed.
See Linewidth prevents macroscopic quantum superposition generation by single atom dispersion.
Squeezedstate generation in a spatially varying field mode without adiabatic elimination,
D.M. Hope, D.E. McClelland, and C.M. Savage, Phys. Rev. A 41, 5074 (1990).
Physical Review A 
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We investigate the effect of a spatially varying field mode on the squeezing generated by twolevel atoms interacting with a single mode of an optical cavity.
Full abstract.
We investigate the effect of a spatially varying field mode on the squeezing generated by twolevel atoms interacting with a single mode of an optical cavity. The mode structure is incorporated into a quantum theory that does not employ adiabatic elimination of field or atomic variables. Thus we are able to consider the regime in which cavity and atomic decay rates are approximately equal as well as the good and badcavity limits. Calculations show that squeezing is reduced by the inclusion of a Gaussian transverse mode profile and a standingwave structure for a particular value of atomic cooperativity C. The model is consistent with recent measurements of squeezing. The degree of squeezing reduction depends on the ratio of cavity and atomic damping rates, in the regime where they are similar in size.
Quantum optics with one atom in an optical cavity,
C.M. Savage, J. Mod. Optics 37, 1711 (1990).
Journal of Modern Optics (abstract only)  Local PDF (9MB) 
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The quantum mechanical master equation for a single twolevel atom in a singlemode optical cavity is numerically solved in both the quantum and the semiclassical limits. The quantum limit of few cavity photons shows semiclassically forbidden behaviour such as steady state twolevel population inversion. Qualitatively new fluorescent spectra, having sidebands broadened by the cavity interaction, also occur. The quantum theory of the singleatom laser with injected signal is presented. At the interface between its quantum and semiclassical dynamics we elucidate the signature of semiclassical limit cycles.
The fluorescence spectrum of an atom strongly coupled to a cavity driven by squeezed light,
C. Savage, Quant. Opt. 2, 89 (1990).
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Squeezing a light beam incident on a cavity which is strongly coupled to a single atom is shown to change the width of the fluorescent sidebands of the atom. The sidebands are either broader or narrower than in the absence of squeezing depending on whether the driving field has excess or reduced amplitude fluctuations. Unlike previously reported effects the entire electromagnetic vacuum seen by the atom does not have to be squeezed for optimum effect. A single squeezed mode driving the cavity is sufficient.
Resonance fluorescence spectrum of an atom strongly coupled to a cavity,
Craig M. Savage, Phys. Rev. Lett. 63, 1376 (1989).
Physical Review Letters 
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The spectrum of the resonance fluorescence light from a single twolevel atom in a small, highquality, optical cavity is calculated. The coupling between the atom and cavity is made sufficiently strong compared to the dissipation that single quantum frequency splitting (vacuum Rabi splitting) occurs. Under high excitation qualitatively new fluorescent spectra are predicted. The usual threepeaked resonance fluorescence spectrum now has sidebands whose width is given by the JaynesCummings atomcavity coupling coefficient rather than by the system dissipation.
Modelling magnetooptical domain erasure without cylindrical symmetry,
C. Savage, M. Watson, and P. Meystre, J. Appl. Phys. 66, 1789 (1989).
Journal of Applied Physics 
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We describe a technique for modeling domain dynamics in the context of thermomagnetic magnetooptical recording. The new feature of our model is that no assumption of cylindrical symmetry is required. We illustrate the potential of our technique by applying it to domain erasure on a moving disk.
On quantum superpositions in dispersive optical bistability,
C. Savage and W. Cheng, Opt. Commun. 70, 439 (1989).
Optics Communications (abstract only)  Local PDF (4.2MB) 
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Dispersively bistable optical systems have two possible output states for certain ranges of their input parameters. We investigate this classical bistability in the context of quantised atoms and field. We find, in the small damping limit, that the classical bistable states appear as mixtures rather than as quantum superposition states.
Stationary twolevel atomic inversion in a quantized cavity field,
C.M. Savage, Phys. Rev. Lett. 60, 1828 (1988).
Physical Review Letters 
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A quantum mechanical analysis of a twolevel atom in a coherently driven optical cavity is shown to predict steadystate atomic population inversion. Semiclassically this is forbidden because of the factorization of operatorproduct expectation values. The full quantum theory is much richer and different field states may be correlated with different atomic states. One consequence is that damping of the cavity field allows atomic polarization to be transferred from higher to lower field states and thus steadystate inversion becomes possible.
Single atom optical bistability,
C. Savage and H. Carmichael, IEEE J. Quant. Electron. 24, 1495 (1988).
IEEE Journal of Quantum Electronics 
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Absorptive optical bistability is shown to exist for a single twolevel atom inside a resonant optical cavity. Solutions for the quantummechanical density operator are obtained numerically for a parameter regime at the interface between the quantum limit, in which quantummechanical noise invalidates the semiclassical prediction of bistability, and the classical limit, in which quantum noise is a negligible perturbation on semiclassical results. Bimodal photon number distributions and Q functions are obtained, and twostate transition rates are calculated
Steadystate twolevel atomic population inversion via a quantized cavity field,
Markus Lindberg and Craig M. Savage, Phys. Rev. A 38, 5182 (1988).
Physical Review A 
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A twolevel atom illuminated by a laser may be driven into a populationinverted steady state if it is coupled to a cavity.
Full abstract.
A twolevel atom illuminated by a laser may be driven into a populationinverted steady state if it is coupled to a cavity. This is a result of the quantum nature of the electromagnetic field and is forbidden by the semiclassical theory. We numerically and analytically analyze this inversion. We find the maximum possible inversion and determine the rate of approach to the steady state. The quantized cavity modifies the electromagnetic vacuum seen by the atom; this connects our work to that on cavityenhanced spontaneous emission and on dynamical line narrowing. Experimental signatures of the inversion and potential experimental difficulties are considered. For example, neither the presence of many atoms in the mode nor many modes in the cavity destroys the inversion.
Oscillations and quantized secondharmonic generation,
Craig M. Savage Phys. Rev. A 37, 158 (1988).
Physical Review A 
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We investigate quantummechanical secondharmonic generation for parameters such that classical electrodynamics predicts oscillations. Specifically we calculate the Q distribution function in a Gaussian approximation about the classical limit cycle. In the classical limit initial rapid collapse of the Q distribution into the neighborhood of the limit cycle is followed by diffusion around the limit cycle. The experimental significance of this quantum diffusion is discussed.
Direct overwrite in magnetooptical recording,
C.M. Savage, F. Marquis, M. Watson, P. Meystre, Appl. Phys. Lett. 52, 1277 (1988).
Applied Physics Letters 
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We have used a numerical model of thermomagnetic recording to investigate direct overwrite by domain destabilization in magnetooptical thin films. Our model includes a linear dependence of domain wall velocity on the net wall pressure due to the demagnetizing field and the wall energy density. Direct overwrite by domain destabilization can be accomplished in one step, without bias fields or prior reading or erasure.
Squeezing by parametric oscillation and intracavity fourwave mixing,
C.M. Savage, D.F. Walls, J. Opt. Soc. Am. B 4, 1514 (1987).
Journal of the Optical Society of America B 
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We present a unified quantum analysis of parametric oscillators and intracavity fourwave mixers. The squeezing spectra below and above threshold for the degenerate cases are compared. Similarities between the systems are discussed and the optimum operating regimes identified.
Quantum tunnelling in dispersive optical bistability,
H. Risken, C. Savage, F. Haake, D.F. Walls, Phys. Rev. A 35, 1729 (1987).
Physical Review A 
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Quantum tunneling times for the model of Drummond and Walls describing dispersive optical bistability are investigated for small cavity damping.
Full abstract.
Quantum tunneling times for the model of Drummond and Walls describing dispersive optical bistability are investigated for small cavity damping. Without damping the system can be described by an appropriate Hamilton operator. By expanding the density operator in eigenstates of this Hamilton operator the stationary solution as well as the lowest eigenvalues are obtained from a Pauli master equation for the diagonal elements of the density matrix for small cavity damping. The tunneling time follows from the lowest nonzero eigenvalue of this master equation. Expectation values as well as the Q function for the stationary case are also presented.
Inhibition of tunnelling in optical bistability by a squeezed vacuum,
C.M. Savage, D.F. Walls, Phys. Rev. Lett. 57, 2164 (1986).
Physical Review Letters 
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Tunneling times for absorptive optical bistability with a squeezed vacuum as input to the cavity are calculated. Using a squeezed input field to reduce the fluctuations in the critical quadrature, we show that the tunneling times may be increased. This may substantially improve the intrinsic stability of the device.
Master equation for a damped nonlinear oscillator,
Fritz Haake, Hans Risken, Craig Savage, Daniel Walls, Phys. Rev. A 34, 3969 (1986).
Physical Review A 
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We derive and discuss the dissipative effects of a heat bath on a nonlinear oscillator, excluding very low temperatures [kT <(level width )] such that a Markovian master equation holds. For temperatures high enough for excited states of the oscillator to acquire noticeable thermal population we find the nonlinearity to have a drastic influence on transition rates and level shifts.
Squeezing via twophoton transitions,
C.M. Savage, D.F. Walls, Phys. Rev. A 33, 3282 (1986).
Physical Review A 
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The squeezing spectrum for a cavity field mode interacting with an ensemble of threelevel lambdaconfiguration atoms by an effective twophoton transition is calculated.
Full abstract.
The squeezing spectrum for a cavity field mode interacting with an ensemble of threelevel lambdaconfiguration atoms by an effective twophoton transition is calculated. The advantage of the threelevel lambda system as a squeezing medium, that is, optical nonlinearity without atomic saturation, has recently been pointed out by Reid, Walls, and Dalton. We predict perfect squeezing at the turning points for dispersive optical bistability and good squeezing for a range of other cases. Threelevel ladder atoms interacting by an effective twophoton transition are also shown to give perfect squeezing in the dispersive limit.
Quantum coherence and interference of damped free particles,
Savage, Walls, Phys. Rev. A 32, 3487 (1985).
Physical Review A 
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We use a Markovian master equation to solve for the dynamics of a free particle damped by the coupling of its coordinate to a bath of harmonic oscillators.
Full abstract.
We use a Markovian master equation to solve for the dynamics of a free particle damped by the coupling of its coordinate to a bath of harmonic oscillators. In the coordinate basis the reduced density matrix for the free particle tends to be diagonalized. Considering the evolution of an initial superposition of two plane waves, we find that the interferencepattern fringe contrast is decreased by the damping. However, for fixed times and sufficiently large damping, the fringe contrast increases with increasing damping. Considering an initial coordinatespace Gaussian wave function, we find that for sufficiently large damping the coupling to the environment models a quantum measurement of the particles coordinate.
Damping of quantum coherence: the master equation approach,
C.M. Savage, D.F. Walls, Phys. Rev. A 32, 2316 (1985).
Physical Review A 
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We solve the master equation for the coordinatecoordinate damped harmonic oscillator for initial superpositions of coherent states.
Full abstract.
We solve the master equation for the coordinatecoordinate damped harmonic oscillator for initial superpositions of coherent states. In the zerotemperature case the solution remains a simple superposition of coherent states. While the underdamped oscillator evolves all initial superpositions into mixtures of coherent states the overdamped oscillator does so selectively. For finite temperatures coherent states are no longer preserved, and we find a decrease in the variance of the offdiagonal coordinatebasis densitymatrix elements below the coherentstate value. This variance decreases with increasing bath temperature. In the overdamped case there is negligible associated spreading of the diagonal coordinatebasis densitymatrix elements. Thus the coordinate basis is an example of Zureks pointer basis and the coordinate damped oscillator models the coordinatebasis densitymatrix diagonalization which occurs in a coordinate measurement.
A multimode quantum theory of a degenerate parametric amplifier in a cavity,
C.W. Gardiner, C.M. Savage, Optics Commun. 50, 173 (1984).
Optics communications (abstract only)  Local PDF (4.5MB) 
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We undertake a detailed treatment of a FabryPerot cavity containing a degenerate parametric amplifier (DPA).
Full abstract.
We undertake a detailed treatment of a FabryPerot cavity containing a degenerate parametric amplifier (DPA). Boundary conditions appropriate to the mirrors and DPA are applied to the Fourier components of travelling wave light fields inside and outside the cavity. Solving the resulting algebraic equations gives an expression for the output field in terms of the cavity input fields. Hencw we can calculate the squeezing in the output field. The maximum squeezing is found in a narrow frequency component of the field around the degeneracy frequency.
Optical chaos in secondharmonic generation,
C.M. Savage, D.F. Walls, Optica Acta 30, 557 (1983).
Optica Acta (became Journal of Modern Optics) 
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Instabilities leading to selfpulsing, period doubling and chaos are predicted to occur in two simple systems in nonlinear optics.
Full abstract.
Instabilities leading to selfpulsing, period doubling and chaos are predicted to occur in two simple systems in nonlinear optics. Namely, secondharmonic generation, inside a coherently driven optical cavity, and subharmonic generation internal to the laser cavity.
From optical tristability to chaos,
H.J. Carmichael, C.M. Savage, D.F. Walls, Phys. Rev. Lett. 50, 163 (1983).
Physical Review A 
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Numerical evidence is presented for period doubling and chaos at attainable laser powers in a model for optical tristability comprising two ringcavity modes coupled via a J=1/2 to J=1/2 transition.
Full abstract.
Numerical evidence is presented for period doubling and chaos at attainable laser powers in a model for optical tristability comprising two ringcavity modes coupled via a J=1/2 to J=1/2 transition. A sequence of periodic windows found embedded in the chaos for this model has also been found in the Lorenz equations. It is suggested that it begins an infinite sequence of a new perioddoubling type.
Optical multistability and selfoscillations in three level systems,
C.M. Savage, H.J. Carmichael, D.F. Walls, Optics Commun. 42, 211 (1982).
Optics Communications (abstract only)  Local PDF (4.4MB) 
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The steady state behaviour of two cavity modes of the electromagnetic field interacting with a three level atomic medium is studied.
Full abstract.
The steady state behaviour of two cavity modes of the electromagnetic field interacting with a three level atomic medium is studied. This system may display optical tri and quadrastability. The results of Kitano et al. appear as a limit of our solutions in the dispersive and unsaturated regime. With the inclusion of saturation in the dispersive limit the asymmetric steady state may become unstable and give rise to self oscillations, period doubling and a new form of "optical turbulence".
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