Effect of optically induced potential on the energy of trapped exciton polaritons below the condensation threshold

Exciton-polaritons (polaritons herein) offer a unique nonlinear platform for studies of collective macroscopic quantum phenomena in a solid-state system. Shaping of polariton flow and polariton confinement via potential landscapes created by nonresonant optical pumping has gained considerable attention due to the flexibility and control enabled by optically induced potentials. Recently, large density-dependent energy shifts (blueshifts) exhibited by optically trapped polaritons at low densities, below the bosonic condensation threshold, were interpreted as an evidence of strong polariton-polariton interactions [Y. Sun et al., Nat. Phys. 13, 870 (2017)]. In this work, we further investigate the origins of these blueshifts in optically induced circular traps and present evidence of significant blueshifts of the polariton energy due to reshaping of the optically induced potential with laser pump power. Our work demonstrates the strong influence of the effective potential formed by an optically injected excitonic reservoir on the energy blueshifts observed below and up to the polariton condensation threshold and suggests that the observed blueshifts arise due to interaction of polaritons with the excitonic reservoir, rather than due to polariton-polariton interaction.

Figure 1

(a) Image of a reflected optical excitation intensity from a sample surface presenting the shape of the pump distribution for a ring of $45\mu \mathrm{m}$ in diameter. White dashed circle indicates the position and shape of the spatial filter. (b) A cross section through the middle of the intensity ring showing a clean center of the excitation pattern (the scattered light in the middle is about $<0.8\%$ of the light intensity at the ring maxima position). (c) Schematic diagram of the experimental setup.

Figure 2

Typical PL spectra recorded in the experiment in the case of photonic detuning $\mathrm{\Delta }=-12\mathrm{meV}$ and small trap $D=29\mu \mathrm{m}$ at a pump power of 17 mW. (a) Full real-space PL spectrum of confined energy states. (b) ${\mathbf{k}}_{\parallel }=0$ filtered real-space PL spectrum showing the contribution of the ground state (GS) and the classical turning points of excited states. (c) Real-space PL spectrum with imposed spatial filter ($10\mu \mathrm{m}$ diameter) in the center. (d) Resulting dispersion of the filtered area from (c). One can easily match the corresponding quantized states contributing to the ${\mathbf{k}}_{\parallel }=0$ signal, labeled 1 and 2. Dashed lines in (a) and (b) correspond to the deduced approximation of an effective potential. Solid line in (d) depicts the theoretical polariton dispersion.

Figure 3

Power-dependent density in the middle of large traps of $D=45\mu \mathrm{m}$ in the photonic and excitonic detuning cases showing the enormous difference in the efficiency of polariton generation inside the trap.

Figure 4

Analysis of the photonic detuning case in a small trap of $D=29\mu \mathrm{m}$, where $P_{th}\approx 20$ mW. (a) Series of power-dependent PL spectra of ${\mathbf{k}}_{\parallel }=0$ in the range from $P=0.02P_{th}$ to $0.95P_{th}$. (b) Example of a multiline fit to the PL spectrum at $P=0.84P_{th}$. We use three distinct energies for the fit, as this is what is observed in the experimental data. (c) Power dependency of extracted energies of the states contributing to the ${\mathbf{k}}_{\parallel }=0$ spectrum. (d) Lowest eigenstates calculated for a trap of different barrier heights. (e) Amplitudes of extracted peaks. (f) Spectral centroid of the ${\mathbf{k}}_{\parallel }=0$ experimental data representing the net blueshift.

Figure 5

Results of power-dependent blueshifts for the photonic detuning case in a large trap $D=45\mu \mathrm{m}$, where $P_{th}\approx 36$ mW. (a) Series of power-dependent PL spectra of ${\mathbf{k}}_{\parallel }=0$ in the range from $P=0.11P_{th}$ to $P=0.94P_{th}$. (b) Far-field dispersion of measured polariton emission at $P=0.77P_{th}$. (c) Real-space experimental PL spectrum of the confined states in the trap at $P=0.77P_{th}$. (d) Simulation of a polariton luminescence, based on 2D Schrödinger equation and assuming thermal population of the states.

Figure 6

Summary of experimental data analysis for excitonic detuning $\mathrm{\Delta }\approx +8\mathrm{meV}$ and two trap diameters $D=28\mu \mathrm{m}$ (purple) and $D=45\mu \mathrm{m}$ (orange). (a) Power-dependent density measurements. (b) ${\mathbf{k}}_{\parallel }=0$ energy shifts versus polariton density. Dependency of homogeneous (closed) and inhomogeneous (open circles) linewidths on the measured polariton density at $D=28\mu \mathrm{m}$ (c) and $D=45\mu \mathrm{m}$ (d) traps. Extracted potential energy shapes (e) $D=28\mu \mathrm{m}$ and (f) $D=45\mu \mathrm{m}$. Dashed line indicates the extracted local ground-state energy slope. At large excitonic detuning, the condensation threshold was beyond our experimental capabilities.

Figure 7

Schematics of a $k$-space integration geometry on top of the pixel array of the CCD camera showing the cut of an image with a spectrometer entrance slit. Symbols are explained in the text.

Figure 8

(a) Full far-field spectrum of low-density polaritons at excitonic detuning. (b) Recorded position and size of the ${\mathbf{k}}_{\parallel }\approx 0$ filter. (c) Recorded spectrum with the use of momentum filtering in the case of a large excitonic trap. (d) The same as in (c) after using the Lucy-Richardson deconvolution.