Bose Polaron Interactions in a Cavity-Coupled Monolayer Semiconductor

The interaction between a mobile quantum impurity and a bosonic bath leads to the formation of quasiparticles, termed Bose polarons. The elementary properties of Bose polarons, such as their mutual interactions, can differ drastically from those of the bare impurities. Here, we explore Bose polaron physics in a two-dimensional nonequilibrium setting by injecting ${\sigma }^{-}$ polarized exciton-polariton impurities into a bath of coherent ${\sigma }^{+}$ polarized polaritons generated by resonant laser excitation of monolayer ${\mathrm{MoSe}}_2$ embedded in an optical cavity. By exploiting a biexciton Feshbach resonance between the impurity and the bath polaritons, we tune the interacting system to the strong-coupling regime and demonstrate the coexistence of two new quasiparticle branches. Using time-resolved pump-probe measurements, we observe how polaron dressing modifies the interaction between impurity polaritons. Remarkably, we find that the interactions between high-energy polaron quasiparticles, which are repulsive for small bath occupancy, can become attractive in the strong impurity-bath coupling regime. Our experiments provide the first direct measurement of Bose polaron-polaron interaction strength in any physical system and pave the way for exploration and control of many-body correlations in driven-dissipative settings.

Popular Summary

When a particle or mobile impurity interacts with a bath of bosons or fermions, its elementary properties, such as its effective mass and excitation spectrum, can be modified. In generic scenarios such as an electron embedded in a solid with a bath of lattice vibrations, the electronic properties are changed in a fixed manner that is dictated by the nature of the material. Here, we show that by tuning the interaction strength between an impurity and the bath particles through a molecular resonance, we can not only tune and control the properties of individual impurities but also their mutual interactions.

In our case the impurity is a polariton, a part-light (photon) part-matter (exciton) quasiparticle, interacting with a bath of polaritons of opposite spin. We create these polaritons by resonant excitation with short laser pulses of opposite polarization in an atomically thin semiconductor strongly coupled to a tunable optical cavity mode. We perform spectroscopy to determine the modification of the interaction between two impurities, as we tune the bath density and the molecular resonance condition. Remarkably, we find that dressing the two impurities with the bath polaritons modifies not only the strength but also the sign of the interaction between the impurities, allowing us to turn repulsion into attraction simply by tuning the bath density.

Extending the observed polaron effects to a system where impurities are electrons may allow for attractive interactions between them, opening avenues for identifying new unconventional mechanisms of electron pairing.

Figure 1

(a) Schematic of the device structure. The semiconductor cavity consists of a van der Waals heterostructure deposited on a distributed Bragg reflector (DBR)-coated fused silica substrate. The substrate, along with a DBR-coated fiber with a concave facet on the core, forms a 0D cavity. The heterostructure consists of a molybdenum diselenide (${\mathrm{MoSe}}_2$) monolayer (red) encapsulated by hexagonal boron nitride (hBN) layers (light green) and a graphene layer (purple) which acts as a gate. We excite the system through the substrate and collect the transmitted light through the fiber. (b) Transmission spectrum of the exciton-polaritons as a function of piezo voltage controlling the cavity detuning $\delta ={\omega }_{\mathrm{C}}-{\omega }_{\mathrm{X}}$, measured with a broad band cw white light source. For illustration purposes, the maximum intensity of the spectrum is normalized to 1 for each piezo voltage. The bare exciton energy ${\omega }_{\mathrm{X}}$ and the cavity energy ${\omega }_{\mathrm{C}}$ are indicated by gray dashed lines. The biexciton resonance condition for a polariton in one valley in the presence of a polariton in the other is shown by the green dash-dotted line. The red dashed box indicates the detuning range around the resonance condition $2{\omega }_{\mathrm{LP}}=2{\omega }_{\mathrm{X}}-{\omega }_{\mathrm{XXB}}$, which is examined using pump-probe spectroscopy. (c) Energy-level diagram to illustrate the experimental scheme. A K-valley polariton bath is resonantly created with a ${\sigma }^{+}$-polarized (pump) laser field (red arrow). The presence of this population allows for a resonant creation of a ${\mathrm{K}}^{\prime }$-valley polariton impurity population using a ${\sigma }^{-}$-polarized (probe) laser field (green arrow) to form a biexciton state.

Figure 2

(a)–(c) Left panel: Normalized probe transmission as a function of time delay for ${\omega }_{\mathrm{LP}}-{\omega }_{\mathrm{X}}=-16.3\mathrm{meV}$, $-15.5\mathrm{meV}$, and $-14.6\mathrm{meV}$ at an estimated bath exciton-polariton density of $n_{\mathrm{b}}=6.3\times {10}^{11}{\mathrm{cm}}^{-2}$ and impurity density $n_{\mathrm{i}}=0.15\times {10}^{11}{\mathrm{cm}}^{-2}$ at zero time delay, respectively. At negative time delays, i.e., before the arrival of the pump pulse that creates the bath polaritons, the transmitted probe spectrum peaks at the lower exciton-polariton energy for all detunings. Starting from $-2\mathrm{ps}$ towards positive time delays, the probe population has significant temporal overlap with the pumped population, which leads to the formation of Bose polarons. At resonance, where ${\omega }_{\mathrm{LP}}-{\omega }_{\mathrm{X}}\approx -15.5\mathrm{meV}$, the attractive and repulsive branches have approximately equal weight. At red (blue) detuning, the attractive (repulsive) branch dominates. (a)–(c) Right panel: Line cuts of the normalized probe transmission spectrum at negative (orange) and zero (black) time delays. (d) Transmission spectrum as measured from the undressed exciton-polariton energy as a function of detuning at zero time delay exhibiting the attractive and repulsive polaron branches. At zero time delay, the bath density introduced by the pump pulse is estimated to be $n_{\mathrm{b}}=6.3\times {10}^{11}{\mathrm{cm}}^{-2}$. (e) Simulated Bose polaron spectrum with the fit parameters $n_{\mathrm{b},\mathrm{theo}}=2.5\times {10}^{11}{\mathrm{cm}}^{-2}$ and ${\gamma }_{\mathrm{XX}}=2.5\mathrm{meV}$.

Figure 3

(a) Normalized Bose polaron transmission spectrum for bath densities $n_{\mathrm{b}}=3.2\times {10}^{11}{\mathrm{cm}}^{-2}$ to $7.1\times {10}^{11}{\mathrm{cm}}^{-2}$ at $\tau =0\mathrm{ps}$, and impurity density $n_{\mathrm{i}}=0.15\times {10}^{11}{\mathrm{cm}}^{-2}$. At low bath densities, the splitting between the two branches is much smaller than their linewidths. As the bath density is increased, the attractive and repulsive branches become clearly distinguishable as the splitting grows. The spectra for different bath densities are offset for clarity. (b) Peak energies of the repulsive (attractive) branch in blue (red) circles as a function of bath density. The energies are obtained from Lorentzian fits to the measured spectrum. (c) Comparison of the measured (green) and calculated (orange) energy splittings between the attractive and the repulsive branch as a function of bath density. (d) Impurity-bath interaction strength $g_{\mathrm{ib}}$ of the repulsive (attractive) branch in blue (red) circles as a function of detuning. The purple triangles correspond to the polariton-polariton interaction strength [$g_{\mathrm{ii}}(n_{\mathrm{b}}=0)$] measured in linear polarization as a function of the detuning.

Figure 4

Top panel: Normalized impurity density-dependent polaron [(a) attractive and (b) repulsive] spectrum in black lines ($\tau =0\mathrm{ps}$) and the corresponding undressed exciton-polariton spectrum (measured at $\tau =-50\mathrm{ps}$) in orange lines. The bath density is $n_{\mathrm{b}}=2.6\times {10}^{11}{\mathrm{cm}}^{-2}$. The spectra for different impurity densities are plotted with an offset for clarity. Middle panel: Impurity-impurity interaction shift of the repulsive (c) and attractive (d) branches as a function of the ratio between impurity and bath density, at $n_{\mathrm{b}}=2.6\times {10}^{11}{\mathrm{cm}}^{-2}$. Bottom panel: Experimentally (e) and theoretically (f) obtained impurity-impurity interaction strengths as a function of the bath density. In both cases, the values for the attractive (repulsive) polaron are given by the red (blue) dots. The interaction strength has been measured with respect to the undressed polariton spectrum, which includes polariton-polariton interactions in the same valley, implying that the interaction strength values above the gray shaded area are repulsive. The inset in panel (e) symbolizes the repulsive interactions between impurities (green dots) repulsively dressed by excitations of bath particles (red dots).

Figure 5

(a) Contrast-enhanced optical microscope image of the sample as viewed from the top. The individual layers are outlined and labeled. The ${\mathrm{MoSe}}_2$ layer is contacted via graphene contacts. The graphene layers (the contacts and the gate) are in turn contacted by $\mathrm{Ti}/\mathrm{Au}$ leads, which were defined by optical lithography. (b) Transfer matrix simulation of the sample in the cavity. For simplicity, a $\lambda /2$ cavity was considered. Both the substrate and the fiber facet are coated with identical DBR mirror coatings of alternating layers of ${\mathrm{Nb}}_2{\mathrm{O}}_5$ and ${\mathrm{SiO}}_2$. The coating was designed such that the optical electric field has a node at the surface. The vdW heterostructure was deposited on the DBR-coated substrate. It has the graphene backgate as the bottommost layer, which therefore lies at the node of the electric field (red line), while the thicknesses of the hBN layers were chosen to ensure the position of the ${\mathrm{MoSe}}_2$ close to the antinode of the electric field. The refractive index ($n$) profile of the DBR layers and the vdW structure are plotted with the blue line. The two dashed black lines indicate the position of the graphene and the ${\mathrm{MoSe}}_2$ monolayers. (c) Zoom-in of panel (a) at the position of the vdW heterostructure.

Figure 6

Impurity-density-dependent transmission spectra, as in Figs. 4 and 4 but not normalized, for the attractive and repulsive polaron in panels (a) and (b), respectively. The blue lines correspond to the polaron spectrum at $\tau =0\mathrm{ps}$. The data are multiplied by the indicated factor for clarity. The orange lines represent the reference transmission spectra of the probe laser at $\tau =-50\mathrm{ps}$. The insets show the extracted resonance energies of the probe laser transmission spectra as a function of the impurity density $n_{\mathrm{i}}$. The blue dots are obtained from fitting the polaron spectrum (at $\tau =0\mathrm{ps}$), the orange dots from the reference spectrum ($\tau =-50\mathrm{ps}$), and the green dots from the probe laser transmission spectrum with the pump laser blocked from reaching the sample. The resonance energies are plotted with respect to the exciton energy ${\omega }_{\mathrm{X}}$.