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Comptes Rendus Physique
Volume 17, n° 8
pages 874-892 (octobre 2016)
Doi : 10.1016/j.crhy.2016.05.004
Polariton interactions in semiconductor microcavities
Interactions entre polaritons dans des microcavités semiconductrices
 

Fig. 1




Fig. 1 : 

Far-field emission from a planar semiconductor microcavity.


Fig. 2




Fig. 2 : 

Spatially resolved photo-luminescence of polaritons confined in cylindrical mesas of different sizes: (a) ≈3 μm, (b) ≈10 μm, and (c) ≈20 μm. The PL intensity is plotted in a normalized log color scale. Confined lower polariton states are visible below 1.484 eV. Confined upper polariton states are found between 1.485 eV and 1.490 eV. The two-dimensional excitonic-like lower-polariton energy is 1.4845 eV, and the two-dimensional photonic-like upper polariton energy is visible above 1.492 eV (from the PhD thesis of Gaël Nardin [43]).


Fig. 3




Fig. 3 : 

Schematics of the homodyne system. Pulses from a Ti:sapphire laser are split into two arms. One excites the sample at a given angle, given a well-defined speed to the polariton fluid. The light emitted by the sample is interfered with the second pulse from the laser. The interference fringes are then Fourier transformed so as to obtain the time-resolved density and phase of the fluid (from the PhD thesis of Gaël Nardin [43]).


Fig. 4




Fig. 4 : 

Schematics of the heterodyne four-wave mixing system. Pulses from a Ti:sapphire laser are split into three arms. All pulses are frequency shifted to allow for synchronous detection of the proper combination. Two of the pulses are used to excite the sample and the last one is a reference that is mixed with the signal to be detected. The excitation pulse can also be shaped to the proper energy width through a pulse (from the PhD thesis of Naotomo Takemura [49]).


Fig. 5




Fig. 5 : 

Principle of the excitation for optimal observation of bistability with a mesa. Left: emission spectrum, right: far-field emission and laser position (from [48]).


Fig. 6




Fig. 6 : 

Different bistable loops observed in a 3-μm mesa under an excitation with a laser detuning of 0.49 meV with different ellipticity values of the laser, indicated in each of the panels (from [51]); ρ =±1 corresponds to circular polarization, ρ =0 to linear polarization.


Fig. 7




Fig. 7 : 

Emission polarization degree ρ C versus the excitation polarization degree ρ p . At constant excitation power, ρ p is scanned from +0.5 to −0.5 and backwards. a. Polarization hysteresis. At high excitation power, narrow polarization hysteresis is observed for spin-up and spin-down polaritons. On the forward path (black), a first jump of spin-up polaritons out of their upper branch causes a decrease in ρ C to a value close to ρ p . Then a jump of spin-down polaritons to their upper branch brings ρ C to −1. On the backward path, the process is reversed with a hysteresis behavior. b. Effect of the excitation power. A decrease in the excitation power brings the polarization hysteresis cycles close to ρ p =0. c. Multistability. Further decrease of the power make the two polarization hysteresis loops merge. Three values of ρ C are allowed in the multistability region M. d. Spin amplification. At even lower excitation power, the overlap is complete. At the edge of the A region, a small variation of ρ p leads to a total spin-up/spin-down conversion. ρ C jumps from +0.97 to −0.97. (From the PhD thesis of Taofiq Paraiso [51].)


Fig. 8




Fig. 8 : 

Principle of multistability. The blue curves represent the spin conversion plateaus obtained in power-dependence experiments at different excitation polarization degrees ρ p =0.34, 0.17, −0.17, and 0.34. The sign of the plateau (±1) depends on the sign of the excitation polarization degree. We represent a case where the polarization conversion is symmetric with respect to the linearly polarized excitation axis and display mirrored curves for nearly linear excitation polarization. For instance, on the ρ p =±0.17 curve, the polarization is converted to ρ C ±1. Consider the system initially prepared in the yellow-cross state (fixed power) in the plateau of the ρ p =+0.34 curve. The black curve highlights what happens upon a continuous change of ρ p from +0.34 to −0.34. In fact, ρ C follows the plateaus, and, eventually, polarization hysteresis in the vicinity of ρ p =0 causes the right circular polarization ρ C =1 to be preserved beyond the linearly polarized excitation axis before switching to linear ρ C =0 and then to left circular ρ C =−1. Red curve: on the backward scan of ρ p (red curve), the opposite polarization ρ C =−1 is preserved by hysteresis, producing a multistability region (green circle) around ρ p =0, where three spin polarization states are admitted (green crosses). (Figure adapted from the PhD thesis of Taofiq Paraiso [51].)


Fig. 9




Fig. 9 : 

Co (blue) and counter (red) circularly polarized pump-probe spectra at the cavity detuning of δ =−1.5 meV. The spectra are plotted for three different pump intensities, as indicated in the figure. 1 mW would correspond to 1.51013 photons per pulse and per cm2. The probe spectra without pump and with pump pulse are respectively presented with dashed and solid lines. LP and UP respectively mean upper and lower polariton. From the PhD thesis of Naotomo Takemura [49].


Fig. 10




Fig. 10 : 

Energy shifts of lower (a) and upper (b) polariton resonances in co-circular configuration as a function of cavity detuning. The four different symbols represent different pump intensities. From the PhD thesis of Naotomo Takemura [49].


Fig. 11




Fig. 11 : 

Energy shifts of (a) lower and (b) upper polaritons in counter-circular excitation, as a function of cavity detuning. Four different symbols represent the different pump intensities. From the PhD thesis of Naotomo Takemura [49].


Fig. 12




Fig. 12 : 

Schematics of the pump-probe experiments around the Feshbach resonance. A population of spin-down polaritons is created by the pump pulse, then the probe introduces a few spin-up polaritons, which interact with the spin-down polaritons. The relative energy position with respect to the biexciton state determines the sign of interactions: from attractive (below the biexciton energy) to repulsive (above the biexciton energy). (From the PhD thesis of Naotomo Takemura [49].)


Fig. 13




Fig. 13 : 

Energy shifts (a, c) and absorption (b, d) of the pump spectrum as a function of cavity detuning. The intensities of pump polaritons are 51010 (a, b) and 1.61011 (c, d) polaritons/pulse/cm2. The blue dots are the experimental results, the solid and dashed lines are numerical simulations respectively with and without the biexciton effect. The green shaded areas represent the expected position of the biexciton resonance. For the numerical calculation, we use the parameters given in the text. (From the PhD thesis of Naotomo Takemura [49].)


Fig. 14




Fig. 14 : 

Experimental probe transmission spectrum as a function of energy and time delay between pump and probe pulse. The cavity detuning is set at 0.5 meV. The black dashed lines are the lower and upper-polariton peak energies without pump pulse. (From the PhD thesis of Naotomo Takemura [49].)


Fig. 15




Fig. 15 : 

Effect of the value of the background interaction constant on the quality of the fit reported in Fig. 13. The upper panel displays, as a function of cavity detuning, the computed energy shifts and the lower panel, the absorption strength. The experimental results are the blue dots. The orange and black lines report the numerical simulations with and without polariton–biexciton coupling, respectively. (From ref. [27], supplementary material.)


Fig. 16




Fig. 16 : 

Interaction (orange line) and absorption (blue line) ratios as a function of the cavity detuning. The interaction and absorption ratios are the ratios between the solid (with g bx 0) and dashed (g bx =0) lines extracted from Fig. 13. (From the PhD thesis of Naotomo Takemura [49].)


Fig. 17




Fig. 17 : 

Comparison of pump-probe spectra for different pump densities: the dashed curves correspond to a non-excited cavity. Figure (a) shows the low-pump case, where a redshift of the probe is observed, together with strong absorption. In (b), larger pump intensity is used and the spectrum shows a clear splitting that is reported as a function of detuning in Fig. 18. Here, cavity detuning is ±0.25 meV. From the PhD thesis of Naotomo Takemura [47].


Fig. 18




Fig. 18 : 

Energy shifts of the two peaks (green open circles and blue dots) shown in Fig. 17 as a function of cavity detuning. The solid lines and dashed lines are numerical simulations respectively with and without the biexciton coupling. From the PhD thesis of Naotomo Takemura [47].


Fig. 19




Fig. 19 : 

(a) Computed polariton energy shift for co-circular (blue) and opposite spins (red) as a function of the cavity detuning for a normalized pump polariton density of 0.2; (b) α 2 /α 1 ratio as a function of cavity detuning (from Ref. [53]).

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