Polariton-polariton Interactions Research Articles

Magnetic field control of polarized polariton condensates in rectangular microcavity pillars

The influence of a magnetic field on a spinor exciton polariton condensate has been investigated in rectangular GaAs microcavity pillars. The condensate has been found to demonstrate an elliptical polarization that changes with its density. The effect is attributed to the competition between the magnetic-field-induced circular polarization buildup and the spin-anisotropic polariton-polariton interaction which favors linear polarization resulting in a reduction of Zeeman splitting. The spin polarization of the condensate in rectangular pillars has been found to be close to equilibrium in contrast to that in planar microcavities that they are made of.

Stimulated polariton-polariton scattering and dynamic Bose-Einstein condensation of polaritons in GaAs microcavities under excitation near the exciton resonance

The dynamics of formation of the macroscopically occupied polariton mode at the bottom of the polariton band E LP(k = 0) and its spin polarization under the quasiresonant pulse excitation of excitons (E = E X ) with large values of quasi-momentum have been studied in planar GaAs microcavities. It has been found that the growth in the depth E X − E LP(k = 0) of the polariton band leads to the change in the formation mechanism for the k = 0 condensate state from the direct parametric decay of the photoexcited mode (due to the polariton-polariton interaction) to the dynamic condensation of polaritons, which results from the multiple scattering of polaritons by both phonons and polaritons. At the same time, in microcavities with E X − E LP(k = 0) > 3.5 meV, the direct decay of the photoexcited mode does not disappear, becoming an efficient mechanism for the filling of the states located at the k-space ring, corresponding to the energies E LP(k) ≈ E X − 2.6 meV.

Black holes and wormholes in spinor polariton condensates

We propose a new system for the study of event horizons and black holes - a Bose-Einstein condensate of exciton-polaritons. Hawking radiation from a closed horizon in 2D is observed in numerical experiments. We simulate inter-Universe and intra-Universe wormholes capitalizing on the spinor nature of polariton condensates and on the spin dependence of polariton-polariton interactions.

Effect of Coulomb interaction on exciton-polariton condensates in GaAs pillar microcavities

The effect of Coulomb interaction on exciton-polariton condensates in GaAs pillar microcavities with lateral size of the order of 10 $\ensuremath{\mu}$m has been investigated by means of a nonresonant excitation with various spot sizes. A local excitation with a small laser spot has been shown to allow for control of the spatial potential of the lower polariton branch in the pillar and manipulation of the polariton condensate wave function, polarization, and energy. Contributions to the blueshift of the condensate mode resulting from interactions within the condensate and from those of condensed polaritons with the photoexcited exciton reservoir have been separated, and the constant of polariton-polariton interaction in the condensate has been evaluated experimentally and compared with the results of the theoretical model.

Density-matrix approach for an interacting polariton system

Using the Lindblad approach we develop a general formalism for theoretical description of a spatially inhomogeneous bosonic system with dissipation provided by the interaction of bosons with a phonon bath. We apply our results to model the dynamics of an interacting one-dimensional polariton system in real space and time, analyzing in detail the role of polariton-polariton and polariton-phonon interactions.

Interactions in Confined Polariton Condensates

We investigate the effect of interactions in zero-dimensional polariton condensates. The shape of the condensate wave function is shown to be modified by repulsive interactions with the reservoir of uncondensed excitons. In large micropillar cavities, when uncondensed excitons are located at the center, the condensate is ejected toward the pillar edges. The same effect results in the generation of optical traps in wire cavities. Once polariton condensates are spatially separated from the excitonic reservoir, spectral signatures of polariton-polariton interactions within the condensate are evidenced.

Polarized Nonequilibrium Bose-Einstein Condensates of Spinor Exciton Polaritons in a Magnetic Field

The effect of a magnetic field on a spinor exciton-polariton condensate has been investigated. A quenching of a polariton Zeeman splitting and an elliptical polarization of the condensate have been observed at low magnetic fields B<2 T. The effects are attributed to a competition between the magnetic field induced circular polarization buildup and the spin-anisotropic polariton-polariton interaction which favors a linear polarization. The sign of the circular polarization of the condensate emission at B<3 T is negative, suggesting that a dynamic condensation in the excited spin state rather than the ground spin state takes place in this magnetic field range. From about 2T on, the Zeeman splitting opens and from then on the slope of the circular polarization degree changes its sign. For magnetic fields larger than the 3 T, the upper spin state occupation is energetically suppressed and circularly polarized condensation takes place in the ground state.

Spin Rings in Bistable Planar Semiconductor Microcavities

A remarkable feature of exciton-polaritons is the strongly spin-dependent polariton-polariton interaction, which has been predicted to result in the formation of spin rings in real space [Shelykh, Phys. Rev. Lett. 100, 116401 (2008)]. Here we experimentally demonstrate the spin bistability of exciton polaritons in an InGaAs-based semiconductor microcavity under resonant optical pumping. We observe the formation of spin rings whose size can be finely controlled in a spatial scale down to the micrometer range, much smaller than the spot size. Demonstration of optically controlled spin patterns in semiconductors opens way to the realization of spin logic devices and spin memories.

Polarization Bistability and Resultant Spin Rings in Semiconductor Microcavities

The transmission of a pump laser resonant with the lower polariton branch of a semiconductor microcavity is shown to be highly dependent on the degree of circular polarization of the pump. Spin dependent anisotropy of polariton-polariton interactions allows the internal polarization to be controlled by varying the pump power. The formation of spatial patterns, spin rings with a high degree of circular polarization, arising as a result of polarization bistability, is observed. A phenomenological model based on effective semiclassical equations of motion provides a good description of the experimental results. Inclusion of interactions with the incoherent exciton reservoir, which provides spin-independent blueshifts of the polariton modes, is found to be essential.

Polarization of exciton-polariton condensates in lateral traps

The Gross-Pitaevskii equation for Bose-Einstein condensates of exciton polaritons in two-dimensional traps is solved analytically accounting for spin-dependent polariton-polariton interactions. We show that the ground state of the condensate is characterized by a nonuniform vector polarization. Also, an analysis of the polarization degree of the condensate is performed as a function of the number of polaritons in the trap.

Master equation approach for interacting slow- and stationary-light polaritons

A master equation approach for the description of dark-state polaritons in coherently driven atomic media is presented. This technique provides a description of light-matter interactions under conditions of electromagnetically induced transparency (EIT) that is well suited for the treatment of polariton losses. The master equation approach allows us to describe general polariton-polariton interactions that may be conservative, dissipative, or a mixture of both. In particular, it enables us to study dissipation-induced correlations as a means for the creation of strongly correlated polariton systems. Our technique reveals a loss mechanism for stationary-light polaritons that has not been discussed so far. We find that polariton losses in level configurations with nondegenerate ground states can be a multiple of those in level schemes with degenerate ground states.

Polariton-polariton interaction constants in microcavities

Resonant transmission of light through a microcavity in the strong coupling regime is used to estimate the strength of the interaction between polaritons with parallel $({\ensuremath{\alpha}}_{1})$ or antiparallel $({\ensuremath{\alpha}}_{2})$ spins. The ratio ${\ensuremath{\alpha}}_{2}/{\ensuremath{\alpha}}_{1}$ is found to be strongly dependent on the detuning between exciton and photon modes. From negative to zero detuning it changes from about 0 to less than $\ensuremath{-}1$. Our observations indicate that at certain conditions the polaritons might rather condense in the real space than form a Bose-Einstein condensate. We analyze theoretically different mechanisms of polariton-polariton interaction including the mean-field electrostatic interaction, the direct exchange interaction, the Van-der-Waals interaction and the indirect exchange interaction via dark exciton and biexciton states.

Polarization instability in a polariton system in semiconductor microcavities

The kinetics of a field on a quantum well in the active region of a planar microcavity with strong exciton-photon coupling has been investigated under the conditions of resonance pulse excitation by a small degree of circular polarization. It has been shown that the system of polaritons at the early stage of the development of instability induced by polariton-polariton interaction tends to transit to a circularly polarized state, but does not reach 100% circular polarization and returns to a polarized state whose polarization is close to the pump polarization. It has been shown that the observed effects are caused by the excitation of an unpolarized reservoir of excitons in quantum wells, which leads to fast relaxation of the difference between the effective resonance frequencies of excitons with different circular polarizations.

Effect of Interactions on Vortices in a Nonequilibrium Polariton Condensate

We demonstrate the creation of vortices in a macroscopically occupied polariton state formed in a semiconductor microcavity. A weak external laser beam carrying orbital angular momentum (OAM) is used to imprint a vortex on the condensate arising from the polariton optical parametric oscillator (OPO). The vortex core radius is found to decrease with increasing pump power, and is determined by polariton-polariton interactions. As a result of OAM conservation in the parametric scattering process, the excitation consists of a vortex in the signal and a corresponding antivortex in the idler of the OPO. The experimental results are in good agreement with a theoretical model of a vortex in the polariton OPO.

Higher order coherence of exciton-polariton condensates

The second- and third-order coherence functions ${g}^{(n)}(0)$ ($n=2$ and 3) of an exciton-polariton condensate are measured and compared to the theory. Contrary to an ideal photon laser, deviation from unity in the second- and third-order coherence functions is observed, thus showing a bunching effect, but not the characteristics of a standard thermal state with ${g}^{(n)}(0)=n!$. The increase in bunching with the order of the coherence function, ${g}^{(3)}(0)&gt;{g}^{(2)}(0)&gt;1$, indicates that the polariton condensate is different from a coherent state, a number state, or a thermal state. The measurement of third-order coherence has the advantage, compared to the second-order one, that the difference between a thermal state and a coherent state is more pronounced. The experimental results are in agreement with the theoretical model where polariton-polariton and polariton-phonon interactions are responsible for the loss of temporal coherence.

Kinetics of stimulated polariton scattering in planar GaAs microcavities resonantly excited with a linearly polarized light

Nonequilibrium transitions in the cavity polariton system are investigated under nanosecond-long pulsed excitation with linearly polarized light (TE or TM modes) near the magic angle. The main objective is to clarify the influence of the polarization-dependent properties of the polariton-polariton interaction on (i) instabilities in a driven lower polariton mode and (ii) the temporal hysteresis effects in the kinetics of the scattered polariton population. The driven mode retains the polarization of the exciting pulse and exhibits instabilities typical of the scalar (``spinless'') polariton system excited with circularly polarized light. No increase in the instability threshold for the driven mode and, as a consequence, no polarization multistability discussed for the spinor polariton system [N. A. Gippius et al., Phys. Rev. Lett. 98, 236401 (2007)] is observed. Polarization of the scattering signal at the zero wave vector and that of the driven mode are mutually perpendicular, due to the polarization dependence of the exciton-exciton interaction. At the same time, at pump intensities well above the threshold of stimulated scattering, the signal exhibits a markable decrease (up to 25%) of the polarization degree during the pulse transmission.

Chaotic Josephson oscillations of exciton-polaritons and their applications

We consider Josephson oscillations between two coupled, quasiresonantly pumped exciton-polariton (polariton) modes. We analyze the regions of stability and periodic oscillations of such a system and show that the spin degree of freedom allows a chaotic behavior. We show that two spatially separated polariton Josephson junctions can be synchronized and used for data encryption and transfer. Due to the strong nonlinearity of polariton-polariton interactions, chaos communication at rates up to 50 Gb/s is possible, which is at least ten times faster than the results obtained for other systems.

Stochastic polarization formation in exciton-polariton Bose-Einstein condensates

We demonstrate theoretically the spontaneous formation of a stochastic polarization in exciton-polariton Bose-Einstein condensates in planar microcavities under pulsed excitation. Below the threshold pumping intensity (dependent on the polariton lifetime), the average polarization degree is close to zero, while above threshold the condensate acquires a polarization described by a (pseudospin) vector with random orientation, in general. It is shown that the polariton-polariton interaction leads to suppression of the linear polarization degree of the condensate due to the self-induced Larmor precession of the pseudospin. We establish the link between the second-order coherence of the polariton condensate and the distribution function of its polarization. We examine also the mechanisms of polarization dephasing and relaxation.

Time dependence of the ground-state population statistics of condensed microcavity polaritons

The semiclassical approach consisting of Boltzmann equations for the excited states and the ground state supplemented by a Master equation for the probability distribution of the condensate population is solved for picosecond pulsed microcavity polaritons. With the simple birth- and death-type Master equation for the condensate population that disregards the condensate phase, one gets results, which, compared to quasistationary solutions, are in better agreement with the experiments. First, the time-dependent solutions show the influence of the change to the coherent state already at pump powers close above the condensate threshold. Second, and even more important for the interpretation of corresponding pulsed experiments, the time-dependent solution give results for the second-order correlation function with seemingly larger correlations above threshold, although no polariton-polariton interaction in the ground state has been included.

Polarization phenomena in resonantly pumped disordered semiconductor microcavities

We analyze the spatial distribution of the intensity of photoluminescence and its polarization in resonantly pumped semiconductor microcavities. The strong spin anisotropy of polariton-polariton interactions leads to the spontaneous formation of domains with strong circular polarization in real space under a uniformly polarized elliptical pump. These domains can serve as an experimental map of the disorder profile present in the system.