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cavity polaritons are bound light - matter states that appear due to the strong coupling of 2d excitons and photons in semiconductor microcavities.@xcite the optically driven system of polaritons behaves like a weakly imperfect bose gas , which results in a spectacular row of polariton collective phenomena such as multistability,@xcite parametric scattering,@xcite pattern formation,@xcite self - organization effects,@xcite dynamical bose - einstein condensation.@xcite polariton multistability attracts much attention as a potential candidate for very fast picosecond range optical switching on a micron size scale.@xcite moreover , the sharp transitions in intra - cavity field , stemming from the multistability , can proceed concurrently with inter - mode parametric scattering , which determines interesting ways of polariton self - organization under pumping near the inflection point of the lower polariton branch ( the `` magic angle'').@xcite    the polariton bistability has recently been studied in the `` scalar '' approximation neglecting the spin degrees of freedom.@xcite because of the mutual interaction of polaritons , their energy effectively depends on the intra - cavity field magnitude . the repulsion between excitons leads to the blueshift of polariton energy . when the pump is itself blue - detuned from the polariton resonance , a strong positive feedback loop between the resonance energy and the field amplitude is created in a certain range of system parameters , resulting in sharp jumps in the intra - cavity field and , hence , in the cavity transmission . consequently , the transmission signal can exhibit a prominent hysteresis in the dependence on continuous - wave ( cw ) pump intensity.@xcite    the response of the optically excited polariton system becomes more complicated with allowance made for exciton spin degrees of freedom ( that corresponds to arbitrary optical polarization of the intra - cavity field ) . in the general case the system has up to four stable states under a given cw pump , whereas the actual state of the system is determined by the history of the excitation process.@xcite in critical points , where a number and/or stability of stationary solutions change , the system can exhibit sharp jumps in both the amplitude and polarization of the intra - cavity field . under a spatially inhomogeneous ( e.g. , gaussian shaped ) cw excitation the system can also exhibit a nontrivial spatial distribution of polarization of the luminescence signal , like the `` spin ring '' patterns,@xcite due to the same underlying phenomena . the strong multistability effect predicted in ref .   has recently been observed experimentally,@xcite including the sharp jumps in the cavity transmission under a smooth variation of the pump polarization degree . the spin ring patterns under gaussian shaped excitation have also been reported.@xcite all these experiments were carried out under the cw excitation . thus , one of the still remaining questions is the dynamical peculiarities of the transitions in a multistable system , which could only be traced using the time - resolved techniques . particularly , the characteristic switching times between different stability branches call for the experimental study , for they can have a crucial impact upon the practical implementations . another question concerns the theoretical approach allowing to describe the observed multistability effect in microcavities . traditionally , the multistability is considered in terms of the self - acting classical fields corresponding to macro - occupied coherent polariton modes which appear under a coherent resonant excitation.@xcite although such an approach is supposed to be sufficient to describe the bistability in a circularly polarized system,@xcite it gives wrong predictions for the general case of elliptically polarized excitation.@xcite most probably , the incoherent states of the exciton reservoir which are inevitably excited in optical experiments have a substantial impact on the decay rates and energies of polaritons . for instance , the nonlinear decay of polaritons with different circular polarizations was taken into consideration in order to explain the experimental data in ref .  . further , the nonequilibrium transitions reported in ref .   can only be reproduced in calculations taking into account the reservoir induced shifts of the polariton energy .    in the present work we report the experimental study of nonequilibrium transitions in the multistable cavity polariton system . unlike in recent refs . , we have studied the optically polarized system under a pulsed nanosecond - long excitation , which allowed us to trace the time - resolved dynamics of the intra - cavity field . the shifts in polariton energy were reflected by temporal variations in the transmission energy spectrum . thus , the employed technique is capable of visualizing the temporal correlations between the resonance energy and intensity of the intra - cavity field . we discuss in detail the time dependence of the transmission signal polarization , below as well as above the threshold , for several polarizations of the pump beam . the observed polarization behavior can not be reproduced within a semi - classical model based on the gross - pitaevskii equations considered in refs .  . the experimental results allowed us to develop a phenomenological model to describe a multistable polariton system with a proper regard to the exciton reservoir . the reservoir excitons shift the polariton energy that , in turn , influences the thresholds of nonequilibrium transitions . both the linear and nonlinear mechanisms of exciton scattering into the reservoir are found to be significant within a sub - nanosecond time scale . while the nonlinear decay of cross - circularly polarized excitons leads to the levelling of the @xmath0 and @xmath1 jump points ( which has also been found in refs .   in the cw pump regime ) , the linear decay mechanism leads to the temporal delay of the jumps with respect to the pump intensity peak . further , we apply the developed approach to simulate the parametric scattering under pumping at the magic angle . as we show , this model allows to explain self - consistently the temporal dependences of polarizations of both the driven mode and the scattering signal which appears at the polariton branch bottom . the paper is organized as follows . in sec . [ sec : theory ] the available models of the multistability effect are considered and compared with each other in view of the recent experimental results of refs .  . [ experimental ] references the experimental setup . sec . [ sec : experiment ] contains the experimental results and compares them with the calculations performed in the framework of the suggested model , for the cases of pumping at normal incidence ( sec . [ sec : normal ] ) and at the magic angle ( sec . [ sec : magic ] ) , with a brief reference to some of the still unresolved issues ( sec . [ sec : discussion ] ) . the results are summarized in conclusion ( sec . [ sec : conclusions ] ) . the multistability effects in microcavities were recently considered in the framework of gross - pitaevskii equations written for the macro - occupied polariton modes.@xcite these equations can also be written for the strongly coupled exciton and photon fields ( @xmath2 and @xmath3 respectively ) in the cavity active layer:@xcite @xmath4 ( in the @xmath5 basis ) . here , @xmath6 stands for the incident electric field that is usually treated as a plane wave : @xmath7 ; @xmath8 and @xmath9 are the eigenfrequencies and decay rates of the intra - cavity photon and exciton modes ; @xmath10 and @xmath11 are the cavity response coefficients , and @xmath12 is exciton polarizability ( so that @xmath13 equals rabi splitting ) ; @xmath14 are the matrix elements of the interaction between excitons with same ( @xmath15 ) and opposite ( @xmath16 ) circular polarizations .    for simplicity , eqs . ( [ ef_p][xp_m ] ) are written for only the driven polariton mode with zero quasi - momentum , although they can be easily generalized to the case of essentially many - mode system.@xcite in the latter case , the usage of the exciton - photon basis ( instead of the simplified polariton basis ) brings the advantage of taking account of the te / tm splitting effects as well as the angular dependence of the polariton interaction constants . as will be shown below , it is also convenient for taking account of the incoherent exciton reservoir . the multistability conditions are defined by the relation between exciton - exciton interaction constants , @xmath15 and @xmath16 . according to the study of polariton spin quantum beats in a gaas cavity,@xcite the cross - circularly polarized excitons exhibit attraction ( @xmath17 ) that is weaker than the repulsive interaction of co - circular excitons ( @xmath18 and @xmath19 ) . the fact that @xmath16 is negative is also confirmed by the rotation of polariton polarization direction during the process of parametric scattering.@xcite in the general case the processes of exciton - exciton interaction are mediated by biexciton and dark exciton states,@xcite hence the relation between the interaction constants of _ polaritons _ can be dependent on the exciton - photon detuning.@xcite more precisely , one should also consider the saturation of excitonic transitions as an additional nonlinear mechanism affecting the blueshift of polaritons under a sufficiently strong excitation.@xcite    if @xmath18 and @xmath20 ( as assumed in refs .   basing on the experimental estimations of ref .  ) , then the @xmath5-components of the intra - cavity field are almost uncoupled . if @xmath17 , then the threshold intensity @xmath21 . contrary to the above predictions , @xmath22 has been found to be slightly less than @xmath23 in the experiments using cw as well as time - resolved pumping techniques.@xcite@xmath24 was observed under normal incidence cw excitation in the 3@xmath25 m wide cavity mesa  @xcite and ( under the same cw pump conditions ) in ordinary ( spatially uniform ) microcavity structure.@xcite in the latter case , the negative sign of @xmath16 in a studied sample was proven by the observed rotation of the scattering signal polarization . in the case of weakly circularly polarized pump , the jumps in both @xmath0 and @xmath1 modes were found to occur simultaneously@xcite in the sense of cw excitation conditions with `` infinitesimally slow '' variations of pump intensity . in view of the gross - pitaevskii equations  ( [ ef_p])([xp_m ] ) , this looks like a manifestation of a large repulsion between polaritons with opposite pseudospins . at the same time , in a case when the pump energy is less than a half of biexciton energy , one expects an attractive interaction between excitons with different pseudospins,@xcite so they can not provide blueshift for each other ; it agrees with the observed indications of the negative sign of @xmath16.]in order to explain it , two theoretical approaches have been proposed . the first one@xcite presumes a repulsive interaction of polaritons with opposite pseudospins ( @xmath5 polarizations ) in the framework of gross - pitaevskii equations of type ( [ ef_p])([xp_m ] ) . the second approach@xcite considers the additional blueshift resultant from an exciton reservoir , which leads to @xmath26 without the necessity for a repulsive interaction between cross - circularly polarized excitons . ( a somewhat similar model has previously been proposed in ref . to describe the interaction of a `` spinless '' polariton condensate with a reservoir . )    in the present work we explore the second model accounting for the transitions of the optically driven excitons into the incoherent ( reservoir ) state in which the overall pseudospin is relaxed , so that the reservoir provides equal blueshifts for both polarization components of the coherent state.@xcite those transitions are introduced phenomenologically as non - radiative decays of bright excitons accorded with the rate of occupation of the optically inactive reservoir . the model for the intra - cavity electric field @xmath3 and exciton polarization @xmath2 coupled with the integral population of the reservoir @xmath27 can be written as @xmath28    \mathcal{p}_+ + a \mathcal{e}_+ , \label{xp_p_r } \\ i \dot{\mathcal{p}}_- & = \bigl [ \omega_\mathrm{x } + v_1    |\mathcal{p}_-|^2 + v_2    |\mathcal{p}_+|^2 + ( v_1 + v_2 ) \ , \mathcal{n}/2 - { } \nonumber\\    & i \left ( \gamma_\mathrm{x } + \gamma_\mathrm{xr } + v_\mathrm{r }      |\mathcal{p}_+|^2 \right ) \bigr ]    \mathcal{p}_- + a \mathcal{e}_- , \label{xp_m_r } \\    \dot{\mathcal{n}}~ { } & = -\gamma_\mathrm{r } \mathcal{n } + 2    \gamma_\mathrm{xr } \left ( |\mathcal{p}_+|^2 + |\mathcal{p}_-|^2    \right ) + { } \nonumber\\ & 4 v_\mathrm{r } |\mathcal{p}_+|^2    |\mathcal{p}_-|^2 . \label{res}\end{aligned}\ ] ] this model is a generalization of eqs . ( [ ef_p])([xp_m ] ) . here , @xmath29 is an additional decay rate of excitons that corresponds to the linear mechanism of light absorption , providing the term @xmath30 that provides an additional occupation of the reservoir ( @xmath31 stands for the reservoir own decay rate . and @xmath32 ) has been considered in ref .  . in such a case , the reservoir induced blueshifts are determined mainly by the ratio between reservoir s decay rate and the coupling constant @xmath33 . for instance , the calculations performed with different @xmath34 but constant @xmath35 and a sufficiently slow variation of the pump power lead to exactly same results for the cases of circular and linear pump polarizations . in this connection , the experiments carried out with time resolution using the nanosecond long pump pulses ( described in sec .  [ sec : experiment ] ) are capable of clarifying the characteristic lifetimes of the reservoir states , as well as the relation between linear and nonlinear mechanisms of polaritons scattering into the incoherent exciton reservoir . for instance , the former mechanism is expected to play a role irrespectively of pump polarization , affecting the dynamics of polariton energy and the time moments when the nonequilibrium transitions occur . ] microscopically , the nonlinear absorption of cross - circularly polarized excitons is resultant from the scattering of a pair of bright excitons with opposite spins ( @xmath36 and @xmath37 ) into dark excitons ( @xmath38 and @xmath39 ) , which is closely related to biexciton creation ( see ref .   for details ) . we do not consider the reverse transitions of incoherent ( reservoir ) excitons into the driven mode ; this approximation is valid as long as the occupation of the reservoir states is small enough . under resonant pumping at @xmath40 the energy mismatch of the pump with respect to free exciton makes the filling of reservoir quite ineffective , but it is still possible due to energy level broadening and non - zero temperature . the reservoir can accumulate excitation due to its comparatively long lifetime ( see sec . [ sec : experiment ] ) . equations  ( [ ef_p_r])([res ] ) can easily be generalized to the case of many - mode system , with exactly the same nonlinear interaction terms ( which are `` local '' in the real space ) , and a linear part being in the @xmath41-space the same as in ref .  . in the many - mode calculations represented below in figs . [ fig:2 ] , [ fig:3 ] , and [ fig:11][fig:13 ] , the cavity dispersion @xmath42 and response coefficients @xmath43 , @xmath44 for te and tm cavity modes are properly taken into account using the transfer matrix technique.@xcite     ( thin solid line ) . thick solid line shows the data calculated using eqs . ( [ ef_p_r])([res ] ) with @xmath45 , @xmath46 , and @xmath47 ( explicitly as in ref .  ) . dash - and - dot line represents the same dependence calculated using eqs . ( [ ef_p])([xp_m ] ) with @xmath45 ( this ratio was used in refs .  ) . dash line corresponds to the case of @xmath48 . the calculated data is time - averaged for each temporal point over 100 ps intervals , in order to eliminate the fast transitional effects which are not observable under the cw pump conditions . ( b - d ) the corresponding time dependences of the intra - cavity field intensity in @xmath5 polarization components . ]    ) ([res ] ) with @xmath49 , @xmath50 , and @xmath47 ( explicitly as in ref .  ) . the pump dcp is @xmath51 ( as in fig . [ fig:1 ] ) . panels _ a  e _ show the spatial distribution of intensity of the intra - cavity field in @xmath0 and @xmath1 polarization components ( solid and dashed lines , respectively ) , for several values of pump power  @xmath52 ; the pump distribution profile is shown by dotted lines . @xmath53 roughly corresponds to the threshold excitation density . panels _ d f _ represent the corresponding spatial distribution of the intra - cavity field dcp . ]     and @xmath54 . all other parameters coincide with those of fig . [ fig:2 ] . unlike fig . [ fig:2 ] , almost no ring structure appears in the cavity transmission dcp even at @xmath55 . ]    the two models , eqs . ( [ ef_p])([xp_m ] ) and ( [ ef_p_r])([res ] ) , can give similar predictions for the cases of circular and linear polarizations of excitation . in particular , the key experimental effect waiting for explanation  that the threshold of linearly polarized pump is smaller ( @xmath56)can be reproduced within the eqs . ( [ ef_p])([xp_m ] ) with @xmath57 . nonetheless , the transitional dynamics under the intermediate pump polarizations @xmath58 are completely different in the two systems , see an example in fig . [ fig:1 ] .    if @xmath17 and @xmath59 ( fig . [ fig:1]_a _ , solid line , and fig . [ fig:1]_b _ ) , the cavity transmission polarization increases with pump in the sub - threshold area , due to the dominant blueshift of the leading polarization component ( @xmath60 ) . on reaching the threshold , the leading component jumps up to the high - energy state , which causes a step - like increase in reservoir population and the blueshift of @xmath1 mode . consequently , the minor mode also enters the above - threshold area , and the degree of circular polarization ( dcp ) of transmission ( @xmath61 ) decreases down to the values smaller than the pump dcp . the same effect results in formation of the spin ring patterns under the gaussian shaped excitation@xcite in a close vicinity of the threshold pump power ( fig . [ fig:2 ] ) . as a matter of fact , the ring shaped pattern of dcp indicates that both polarization components reach the high - energy state at the center of the pump spot where , therefore , the transmission dcp is minimal . the spatial distribution of @xmath61 ( fig . [ fig:2]_d  f _ ) exhibits a well pronounced minimum at @xmath62 already when the threshold is surpassed by 1.5 times ( fig . [ fig:2]_e _ ) , in agreement with the experimental observations ( see fig.3 in ref . ) . this markedly differs from a prediction of the conventional theory based on gross - pitaevskii equations@xcite with @xmath63 ( see fig .  [ fig:3 ] ) which does not exhibit the rings even at @xmath64 for @xmath65 . the temporal dynamics for @xmath66 is shown in fig . [ fig:1]_a _ ( dash - and - dot line ) and in fig . [ fig:1]_c_.    in the opposite case , when @xmath67 and the system is `` purely coherent '' ( fig . [ fig:1]_a _ , dash line , and fig . [ fig:1]_d _ ) , which also corresponds to the right relation @xmath68 , the polarization dynamics is completely different . first , the transmission dcp decreases in the sub - threshold area , since an increase in the `` leading '' @xmath0 component provides a larger blueshift for @xmath1 , so that the difference in @xmath5 intensities weakens with increasing pump . on reaching the threshold , @xmath61 shows a minor step - like increase followed by the very weak changes with further increasing pump power . no prerequisites for the spin ring formation are satisfied in this case . thus , the observed phenomena  the disparity of thresholds , @xmath56 , together with the field polarization dynamics  cannot be reproduced within eqs .  ( [ ef_p])([xp_m ] ) using only two constants @xmath14 of exciton - exciton interaction even if a single polariton mode at @xmath69 is considered . the experiments revealing both the energy ( blueshift ) and polarization dynamics of the driven polariton mode under the nanosecond - long excitation pulses are described below in sec . [ sec : experiment ] . the microcavity structure grown by a metal - organic vapor - phase epitaxy technique has top ( bottom ) bragg reflectors composed of 17 ( 20 ) @xmath70 al@xmath71ga@xmath72as / alas layers . the @xmath73 gaas cavity contains six @xmath74 nm thick in@xmath75ga@xmath76as / gaas quantum wells . the rabi splitting is about @xmath77mev . a gradual variation of the active layer thickness along the sample provides a change in the photon mode energy @xmath78 and , accordingly , in the detuning @xmath79 between the exciton @xmath80 and photon @xmath81 mode energies . experiments are carried out in several regions of the same sample with @xmath82 ( sec . [ sec : normal ] ) and @xmath83 ( sec . [ sec : magic ] ) . the sample is placed into the optical cryostat with controlled temperature . to excite the cavity , we use a pulsed ti : sapphire laser producing picosecond long pulses at a repetition rate of 5  khz . prior to coming into the cryostat , the pulses pass trough a long multi - mode optical fiber and then through a monochromator . after the fiber , the pulses have a duration of about @xmath84ns , and after the monochromator they have spectral full width at half maximum ( fwhm ) of @xmath85mev . the excitation is performed either along the normal to the cavity plane ( @xmath86 ) or at the magic angle ( @xmath87 ) slightly above the lower polariton branch resonance , with various pump polarizations ( circular , linear , or elliptical ) . the main axis of pump polarization is directed along the @xmath88 axis of the structure . the pump beam is focused onto the spot with a diameter of @xmath89 m . the kinetics of the cavity transmission signal @xmath90 is detected at @xmath91k by the streak camera with spectral , angular , and time resolution of @xmath92mev , @xmath93 , and @xmath94ps , respectively , in various polarizations . the temporal dependences of the signal are averaged over @xmath95 pulses , for we have to collect the signal in order to eliminate noises . the information on the intra - cavity field kinetics is obtained from the cavity transmission measurements.@xcite the active region of the cavity is separated from a detector by the bragg mirror that does not introduce any nonlinearity and/or spectral selectivity . thus , the intensity of the transmission signal , @xmath96 , is proportional to the squared magnitude of the intra - cavity electric field @xmath97 , and the first momentum @xmath98 at @xmath99 reflects the time dependence of the average ( effective ) energy of excited mode @xmath100 .     for different pump powers @xmath52 ( _ b  d _ and _ f  h _ ) . the pump is polarized circularly . the normalized temporal shape of the excitation is shown at the left side ( white solid line ) ; the weighted mean value of the pump energy is shown by the vertical line . left and right panels represent the experimental and calculated data , respectively . the color scale is logarithmic . ] figures [ fig:4]_b  d _ show the measured time dependences of transmission signal @xmath101 under the excitation with circularly polarized ( @xmath0 ) light . the spectra are recorded in the same @xmath0 polarization ; the fraction of signal in the opposite polarization ( @xmath1 ) does not exceed a few percent . at low peak excitation density @xmath102kw/@xmath103 the maximum of the signal is found at the low energy side of the excitation , near the lower polariton eigenfrequency . although the blueshift in polariton energy remains relatively small , the time dependence of the signal differs markedly from that of the pump pulse . this indicates the onset of nonlinear processes at the red edge of pump spectrum . in particular , the maximum of the signal is delayed for a few hundred picoseconds with respect to the pump peak . nonlinearities in both the magnitude and spectral position of the signal increase with pump power : as the peak energy of the signal shifts up to the pump energy @xmath104 , ( i ) the signal intensity shows the superlinear ( threshold like ) increase and ( ii ) the time when the signal reaches its maximum value shifts backward to the onset of excitation pulse . the observed correlation between the energy blueshift and intensity of the signal is expected in the framework of the multistability model@xcite eqs . ( [ ef_p])([xp_m ] ) , however this model fails to explain the process of instability development . figures  [ fig:4]_e  h _ show that the observed time and spectral dependences can be qualitatively reproduced in simulations using eqs .   with appropriate time and energy shapes of the excitation ( see appendix ) . the chosen parameters of microcavity coincide with those used in the experiment ; the constants of interaction with reservoir are considered below .     and @xmath105 , resp . ) for different pump polarizations @xmath106 ( circular , elliptical , and linear polarizations ) . the top panels show the time shape of the exciting pulse . left and right panels represent the experimental and calculated data , respectively . in the experiment , @xmath107 . ]    ) . left and right panels represent experimental and calculated data , respectively . in the experiment , @xmath107 . ] components in the range of polarization instability ( experiment ) . weighted mean values of the energy @xmath108 are indicated by arrows . ] the temporal dependence of transmission under the excitation with linearly , elliptically and circularly polarized pulses ( dcps 0 , 0.2 , 0.6 , and 1 ) at @xmath109kw/@xmath103 is shown in fig . [ fig:5 ] . the temporal delay of the dominating @xmath0 and @xmath110 polarization components of the signal with respect to the pump peak is seen to be in the range of 150200ps , which is much larger than the lifetime of polaritons with @xmath111 . the `` anomalous '' increase in the intra - cavity field observed in the range of decreasing pump power ( after the pump peak is already passed ) can be explained by the blueshift in effective polariton energy . in turn , this blueshift could only be provided by the long - lived polariton states accumulated during the pulse . such an effect corresponds to the `` linear '' process of polariton scattering into the exciton reservoir , which is determined by the ratio between @xmath34 and @xmath29 in eqs . ( [ xp_p_r])([res ] ) . the experimental results are qualitatively reproduced in numerical simulations with @xmath112 , @xmath113 , @xmath114mev , and @xmath115mev . these parameters are chosen to meet the following conditions : ( i ) the overall occupation of the reservoir is comparable to that of the driven ( optically active ) polariton mode , so that @xmath56 , and ( ii ) the temporal peak of the signal can be delayed by hundreds of picoseconds with respect to the excitation peak even for @xmath116 . note the long decay times of the reservoir states , @xmath117ps . so long times are characteristic of excitons localized due to fluctuations of quantum well potential and/or free excitons with large lateral wave numbers . figures [ fig:5]_b _ and [ fig:5]_e _ reveal the transmission signal to be retaining both circular and linear pump polarizations ; in these cases only a weak depolarization of the transmitted light is observed . retaining of the circular polarization in agreement with the angular momentum conservation law is expected . measurements performed under linearly polarized pump in a wide range of @xmath118kw/@xmath103 ( not shown ) have revealed the magnitude of transmitted light depolarization to be within the limits of 1217% , almost independently of the pump power . on the other hand , under the elliptically polarized excitation ( @xmath119 ) the signal dcp does depend on the pump intensity due to the anisotropy in polariton - polariton interaction.@xcite accordingly , the ratio between both circularly and linearly polarized components of the signal intensity ( @xmath5 and @xmath105 , respectively ) varies with time ( fig .  [ fig:5]_c , d _ ) . the corresponding temporal dependences of the degrees of circular and linear polarizations of the signal are shown in fig . [ fig:6 ] . from comparison of figs . [ fig:5 ] and [ fig:6 ] , it is seen that the reaching of maximum signal intensity at @xmath120 is accompanied by a decrease in the signal dcp , in much the same way as the cw driven system behaves ( fig . [ fig:1 ] ) , though the latter system exhibits the expectedly sharper transitions . on the other hand , our experimental technique allows us to visualize the energies of intra - cavity field in addition to their intensities . the information on the energies is extracted from the transmission spectra as shown in fig . [ fig:7 ] since @xmath121 . the energies of intra - cavity field in @xmath0 and @xmath1 polarizations demonstrate a well pronounced blueshift with increasing polariton density and a well pronounced splitting . in particular it is seen in fig . [ fig:7 ] that in the range of maximum polarization the @xmath0 component of the field is markedly ( by 0.3 mev ) blue - shifted with respect to @xmath1 .    the basis in which shown degree of linear polarization ( dlp ) was measured is related to the pump polarization axis . we observe no linear polarization in the basis rotated by @xmath122 with respect to the former one . thus , the sum of squared stokes parameters per signal intensity is less than 1 , which means that the signal is partially depolarized ; this is because the signal polarization components are measured as averaged quantities . , under excitation with elliptically polarized pulses with @xmath123 . grey dotted line corresponds to the normalized temporal shape of excitation . left and right panels represent experimental and calculated data , respectively . ]     of the transmission energy in @xmath0 ( thick lines ) and @xmath1 ( thin lines ) polarization components ( _ d , h _ ) , for several values of the pump power @xmath52 . the pump dcp is @xmath124 . the mean value of pump energy , which exhibits minor variations in a close vicinity of @xmath125 , is shown by solid thin lines in panels ( _ d , h _ ) . left and right panels represent experimental and calculated data , respectively . ]     components of the signal with respect to the pump vs. pump power ( as defined by eq . ( [ eq : delay ] ) ) , for two pump polarizations , @xmath126 ( panels _ a , c _ ) and @xmath127 ( panels _ b , d _ ) . left and right sides of the figure represent experimental and calculated data , respectively . ]    in order to clarify the physics underlying the signal polarization transitions , let us consider the series of measurements performed under elliptically polarized pulses with @xmath123 and various pump intensities . [ fig:8 ] represents measured ( left side ) and calculated ( right side ) time dependences of the transmission signal in @xmath5 polarization components . from these series , the pump power dependence of the temporal delay between the signal and pump peaks is evidenced . the certain conditions for a switch in signal polarization depend on both the pump intensity and its temporal shape . in case of the very low pump densities , the intra - cavity field is insufficient for multistability to reveal ; on the other hand , if the pump density is increasing quickly enough then a jump into a high - energy state happens with no delay related to the long - lived reservoir , since most of the intra - cavity field is concentrated in the driven ( optically active ) polariton state . except the case of maximum @xmath52 , the dynamics shown in fig . [ fig:8 ] lies in the intermediate range of pump powers which all are insufficient to pull a polariton state by itself up to the threshold magnitude . instead of that , the non - equilibrium transitions proceed through the mediation of excitation accumulated by the reservoir . in such a case the development of instability in the leading polarization component ( @xmath0 ) always precedes the reservoir induced switch in signal polarization . figure  [ fig:9 ] , which also shows a series for two peak pump intensities at fixed @xmath123 , allows us to visualize the temporal correlations between the energy ( in both @xmath5 polarization components ) and polarization degree of the transmission signal . the overall process of the instability development is accompanied by blueshifts in @xmath5 energies . at the first stage ( which starts the earlier , the higher is pump density @xmath52 ) , the leading polarization component ( @xmath0 ) enters the region of positive feedback between its effective resonance energy @xmath128 and the @xmath0 field amplitude , so the difference in @xmath5 energies grows along with the dcp of transmission signal ( fig . [ fig:9]_b , d _ ) . accordingly , a well pronounced decrease in the dlp of transmission is observed at the same time interval ( fig . [ fig:9]_c _ ) . at approximately the half way through the energy growth ( see panel  _ d _ ) , the integral occupation of reservoir becomes sufficient to provide the shift in the minor component ( @xmath1 ) , which leads to decrease in both the energy difference @xmath129 and dcp , and to the corresponding increase in dlp . all these effects are qualitatively reproduced in calculations shown in fig . [ fig:9]_e  h_. thus , the observed dynamics confirm the effect of reservoir , though the energy broadening makes the transitions much smoother compared to the cw driven system ( fig . [ fig:1 ] ) . figure  [ fig:10 ] shows the time delay of the signal with respect to the excitation pulse in a wider range of pump powers @xmath52 ; it summarizes the consideration of the threshold effects in the cavity transmission . the value of the delay @xmath130 is determined as the difference between the moments the signal and the pump reach their half - maxima for the first time : @xmath131 at small @xmath52 the response is linear , and the delays @xmath130 are expectedly small . at threshold , the superlinear growth of the signal is observed with @xmath130 of about 150 to 200 picoseconds , i.e.at the back front of excitation . thus , this transition is induced by the reservoir as explained above . with further increasing @xmath52 , the optically active fraction of excitons grows , which lowers the system s intertness , and the delay of response decreases . note , that the minor ( @xmath1 ) polarization component exhibits the superlinear growth at the same _ peak _ power @xmath52 as @xmath0 , and the relative delay of @xmath0 and @xmath1 components , @xmath132 , remains nearly constant above the threshold . this is an extra evidence of the fact that the jump in the minor component is provided by the reservoir even at high @xmath52 . let us now consider the polarization properties of the signal of parametric scattering  generally referred to as cavity `` optic parametric oscillator '' ( opo ) signal@xcite  which appears at the branch bottom ( @xmath111 ) if pumping is at the magic angle ( @xmath134 ) . there are two points to discuss here . first , in the general case of elliptically polarized excitation the signal is expected to reflect variations in the dcp of the driven mode that , in turn , are shown to be strongly affected by the excitonic reservoir . second , if the pump is polarized linearly , the experiments show the @xmath135 rotation of the signal polarization axis;@xcite thus , we have to check if eqs . ( [ ef_p_r])([res ] ) can reproduce this effect in spite of the reservoir induced interaction between the cross - circularly polarized excitons . the experiments are carried out at negative detuning between the photon and exciton ( @xmath83 ) in order to have the pump frequency close to that employed for the normal incidence pumping considered in sec  [ sec : normal ] . the cavity and excitation parameters used in the simulations coincide with the experimental ones , whereas the nonlinear interaction constants as well as reservoir characteristics are the same as used in the previous section . ( _ d , j _ ) in two polarization components @xmath0 and @xmath1 ( thick and thin lines , resp . ) , opo signal intensity ( _ e , k _ ) and dcp ( _ f , l _ ) , for several values of the pump power @xmath52 . straight lines in panels _ c , i _ indicate the mean value of pump energy . left and right panels represent experimental and calculated data , respectively . ] polarized linearly along the tm cavity mode ( @xmath136 ) , for some different values of the pump power @xmath52 . left and right panels represent the experimental and calculated data , respectively . the temporal shape of excitation is indicated in panels _ a , c _ as a guide for eye . ]    . left and right panels represent experimental and calculated data , respectively . the temporal shapes of excitation are indicated in panels _ a , c _ as a guide for eye . in calculation , the te / tm splitting of the driven polariton mode equals to @xmath137mev . ] figure  [ fig:11 ] represents measured and calculated dynamics of intra - cavity field at @xmath138 ( which corresponds to the cavity transmission ) and @xmath111 ( opo signal ) under elliptically polarized excitation with @xmath139 and different pump powers  @xmath52 . when @xmath52 exceeds the critical value ( in the experiment @xmath140 ) , a well pronounced superlinear growth of the cavity transmission ( fig . [ fig:11]_b _ ) is observed at @xmath141 . near the threshold , a doubling of the pump power  @xmath52 leads to an order - of - magnitude growth of the opo signal intensity ( fig . [ fig:11]_e _ ) . the observed nonlinearities indicate the onset of parametric instability , being , however , by far not as sharp as under cw excitation.@xcite    the dynamics of the driven mode is similar to that under the pumping at normal incidence . the growth of the field amplitude , which continues with increasing pump density ( fig . [ fig:11]_b _ ) , expectedly leads to the growth of transmission dcp ( fig . [ fig:11]_c _ ) due to the dominantly repulsive exciton - exciton interaction . at @xmath142ns the transmission starts to behave strongly nonlinearly with respect to the driving field , and the peak of transmission becomes significantly delayed with respect to the peak of pump pulse . the latter indicates that the transition is assisted by the reservoir induced blueshift . accordingly , the jump in transmission dcp is immediately followed by dropping back as soon as the system enters the above - threshold region where the energies of @xmath5 components of intra - cavity field ( fig .  [ fig:11]_d _ ) become partially levelled due to the reservoir filling . the domination of the leading polarization component ( @xmath0 ) is strongly enhanced in the opo signal ( fig . [ fig:11 ] ) whose dcp reaches  0.85 at @xmath143ns . the subsequent lowering of dcp of the driven mode forces the opo signal , too , to partially loss its polarization . however , the signal restores a high dcp during the further evolution accompanied by the decrease in transmission intensity . the calculations performed on the basis of eqs . ( [ ef_p_r])([res ] ) , which are presented in the right panels of fig . [ fig:11 ] , reproduce the observed threshold - like behavior of intra - cavity field along with its polarization properties . however , a quantitative agreement is not achieved , partially due to a complicated spectral shape of the pump pulses ( see fig .  [ fig:4 ] ) and due to intrinsic limitations of the suggested theoretical model ( see discussion in sec .  [ sec : discussion ] ) . let us turn to the case of exactly linear polarization of the excitation at @xmath144 ( figs . [ fig:12 ] and [ fig:13 ] ) . in this case the opo signal depends on whether the pump excites a pure cavity state one of te and tm modes which are the eigenstates of 2d photon in the empty cavity  or a mixture of both the te and tm components . fig . [ fig:12 ] represents the dynamics of opo signal under the pump polarized along the tm cavity mode . in the range of high intensity of the signal , its degree of linear polarization ( dlp ) reaches 90% . the polarization axis is @xmath135 rotated with respect to the pump ( what corresponds to negative dlp values ) , which is well reproduced in the calculations .    on the other hand , if the pump is polarized in between the te and tm directions ( @xmath145 $ ] , fig .  [ fig:13 ] ) , the signal dlp does not exceed 30% in the range of a strong signal ( fig . [ fig:13]_e _ ) . the shown dlp values were measured ( and calculated ) in the basis of directions parallel and orthogonal to pump polarization ; there is no marked dlp in the te - tm basis as well . this effect is explained by the lifted degeneracy ( te - tm splitting ) of cavity modes which leads to the variation with time of the @xmath5 phase shift . accordingly , it causes the misbalance of @xmath0 and @xmath1 components of intra - cavity field , i.e.  a reduced dlp and non - zero dcp of the driven mode ( fig . [ fig:13]_a , b _ ) , which is seen in both measured and calculated data . due to permanent modification of the direction of signal polarization , the eventual opo signal appears to be significantly depolarized ( the sum of squared dcp and dlp is markedly less than  1 , fig . [ fig:13]_d , e _ ) . thus , the dynamics of the opo signal confirms the effect of reservoir . under elliptic excitation , the @xmath5 polarization components tend to be levelled by the reservoir . by itself , this effect could be assigned to a repulsion between cross - circularly polarized excitons ( @xmath146 ) . on the other hand , the axis of signal polarization is found inverted with respect to the pump , which restricts the sign of @xmath16 to be negative irrespectively of the reservoir induced blueshifts . since we have reproduced these effects within eqs . ( [ ef_p_r])([res ] ) , it is proven to provide a self - consistent description of the intra - cavity field polarization dynamics .      we have shown that the semi - phenomenological eqs . ( [ ef_p_r])([res ] ) explain the observed polarization dynamics in a good qualitative agreement with the experimental data . let us now consider the limitations of the suggested approach . its most important shortcoming is the absence of a feedback between the driven polariton modes and the exciton reservoir , as long as the latter is introduced using the integral occupation number  @xmath27 , neglecting the actual microscopic distribution of reservoir states . as a result , eqs . ( [ ef_p_r])([res ] ) do not describe , e.g. the establishing of equilibrium between coherent and incoherent exciton `` phases '' which would normally take place in a real system ; this process implies ( i ) the reverse transitions from the reservoir into the macro - occupied mode ( similar to bose - einstein condensation ) and ( ii ) dependence of the scattering rates ( @xmath29 and @xmath33 ) on the polariton density . these shortcomings lead to several visible discrepancies between the measured and calculated data . in particular , the superlinear drop in transmission intensity observed at the back front of exciting pulses , which is evident from comparison of left and right panels of fig . [ fig:8 ] , is not reproduced by the present model . note as well that the nonlinear scattering rate @xmath33 should depend on the energy of biexciton resonance which mediates the transitions of optically driven polaritons into the reservoir.@xcite accordingly , the actual relation between the multistability thresholds @xmath23 and @xmath22 would depend on the pump frequency as well as on the frequency detuning between photon and exciton modes .    as a result , we expect eqs . ( [ ef_p_r])([res ] ) to be qualitatively valid in the case of resonant excitation of the optically active cavity states . on the other hand , in the cases of comparably large pump wave numbers and/or non - resonant excitation conditions , when a much larger contribution of reservoir excitons is expected , the model is likely to become unsatisfactory . in the present work we have studied the non - equilibrium transitions in a multistable system of cavity polaritons under resonant nanosecond - long excitation . using the spectrally broadened pulses , we have visualized the temporal correlations between the effective resonant energy , intensity , and optical polarization of the intra - cavity field which all undergo the strong changes on reaching the threshold pump power . in the vicinity of the threshold , the dynamics of such system is strongly affected by the long - lived exciton reservoir ( excited due to polariton scattering ) which influences both the characteristic times of instability development and output signal polarization . the temporal behavior of the intra - cavity field is found to be not described in the conventional model based on the gross - pitaevskii equations written for purely coherent macro - occupied polariton states . most importantly , the observed phenomena can not be explained even qualitatively within a model with only the two exciton - exciton interaction constants ( @xmath14 ) allowed for . to explain the experiments , we have proposed the model for the macro - occupied polariton states coupled with an exciton reservoir . in spite of some limitations , this model provides a self - consistent description of the observed intra - cavity field dynamics under both pulse and continuous wave excitation conditions . authors thank m.s.skolnick for rendered samples , d.n.krizhanovskii for fruitful discussions , and a.v.larionov for assistance in the experiment . this work was supported by russian foundation for basic research and the russian academy of sciences . in attempt to reproduce the experimental pump spectrum , which is characterized by fwhm of about 0.8mev and , hence , has a lowered coherence , the modeled pump is ` broadened ' by means of the partial randomization of phases of different spectral harmonics . namely , the pump amplitude is defined as follows : @xmath147 here ,    * @xmath148 are real - valued amplitudes of the @xmath5 polarization components ; * @xmath149 defines the direction of the polarization axis ; * @xmath150 is the central pump frequency ; * @xmath151 ; * @xmath152 defines the width of the pump spectrum , @xmath153 ; * @xmath154 is a set of random uniformly distributed numbers within the interval @xmath155 . the spectral fwhm of the pump defined such a way approximately coincides with experimental one , and its coherence time is about 5 picoseconds . under these conditions the system is inevitably stochastic . hence , for each set of parameters eqs . ( [ ef_p_r])([res ] ) are solved a number of times ( 20100 ) with different @xmath156 until the averaged evolution of the signal intensity becomes independent on the number of realizations . this corresponds to the collection of numerous signals , which allows us to reduce noises . the degrees of polarization are then calculated using the _ averaged _ intensities . as a result , the transmission can be partially depolarized ( under elliptically polarized excitation ) due to small random differences in the individual pulses in much the same way as the measured signal . 33ifxundefined [ 1 ] ifx#1 ifnum [ 1 ] # 1firstoftwo secondoftwo ifx [ 1 ] # 1firstoftwo secondoftwo `` `` # 1''''@noop [ 0]secondoftwosanitize@url [ 0 ] + 12$12  & 12#1212_12%12@startlink[1]@endlink[0]@bib@innerbibempty link:\doibase 10.1103/physrevlett.69.3314 [ * * ,   ( ) ] @noop _ _ ( ,  ,  ) link:\doibase    10.1103/physreva.69.023809 [ * * ,   ( ) ] link:\doibase    10.1103/physrevlett.98.236401 [ * * ,   ( ) ] \doibase http://dx.doi.org/10.1038/nmat2787 [ * * ,   ( ) ] ,   link:\doibase 10.1103/physrevb.63.041303 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.63.193305 [ * * ,   ( ) ] http://stacks.iop.org/0295-5075/67/i=6/a=997 [ * * ,   ( ) ] link:\doibase 10.1103/physrevlett.104.126402 [ * * ,   ( ) ] \doibase    http://dx.doi.org/10.1038/nphys1668 [ * * ,   ( ) ] ,   link:\doibase    10.1103/physrevb.77.115336 [ * * ,   ( ) ] link:\doibase 10.1103/physrevlett.101.136401 [ * * ,   ( ) ] \doibase    http://dx.doi.org/10.1038/nature05131 [ * * ,   ( ) ] ,   link:\doibase 10.1103/physrevlett.100.116401 [ * * ,   ( ) ] link:\doibase 10.1103/physrevlett.101.016402 [ * * ,   ( ) ] link:\doibase 10.1134/s1063776110050146 [ * * , ( ) ] link:\doibase    10.1103/physrevlett.105.216402 [ * * ,   ( ) ] link:\doibase    10.1103/physrevlett.105.216403 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.81.035328 [ * * ,   ( ) ] link:\doibase    10.1103/physrevb.72.075317 [ * * ,   ( ) ] link:\doibase    10.1103/physrevb.73.073303 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.61.2863 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.76.045319 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.76.245324 [ * * ,   ( ) ] link:\doibase    10.1103/physrevb.82.075301 [ * * ,   ( ) ] link:\doibase    10.1103/physrevlett.79.1341 [ * * ,   ( ) ] link:\doibase 10.1103/physrevlett.105.116402 [ * * ,   ( ) ] @noop * * ( ) link:\doibase 10.1103/physrevlett.99.140402 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.66.045102 [ * * ,   ( ) ] link:\doibase 10.1103/physrevb.79.165308 [ * * ,   ( ) ]
the polarization dependence of nonequilibrium transitions in a multistable cavity - polariton system is studied under a nanosecond long resonant optical excitation at the normal and magic angle incidences with various polarizations of the pump beam . 
 the temporal correlations between the frequency , intensity , and optical polarization of the intra - cavity field , which all undergo sharp threshold - like changes due to the spin dependent interaction of cavity polaritons , are visualized . 
 the observed dynamics can not be reproduced within the conventional semi - classical model based on the gross - pitaevskii equations . to explain the observed phenomena , it is necessary to take into account the unpolarized exciton reservoir which brings on additional blueshift of bright excitons , equal in the @xmath0 and @xmath1 polarization components . 
 this model explains the effect of polarization instability under both pulsed and continuous wave resonant excitation conditions , consistently with the spin ring pattern formation that has recently been observed under gaussian shaped excitation .