Enhanced Interactions between Dipolar Polaritons

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Enhanced Interactions between Dipolar Polaritons

Emre Togan, Hyang-Tag Lim, Stefan Faelt, Werner Wegscheider, and Atac Imamoglu

Phys. Rev. Lett. 121, 227402 – Published 26 November 2018

Abstract

Nonperturbative coupling between cavity photons and excitons leads to the formation of hybrid light-matter excitations, termed polaritons. In structures where photon absorption leads to the creation of excitons with aligned permanent dipoles, the elementary excitations, termed dipolar polaritons, are expected to exhibit enhanced interactions. Here, we report a substantial increase in interaction strength between dipolar polaritons as the size of the dipole is increased by tuning the applied gate voltage. To this end, we use coupled quantum well structures embedded inside a microcavity where coherent electron tunneling between the wells creates the excitonic dipole. Modifications of the interaction strength are characterized by measuring the changes in the reflected light intensity when polaritons are driven with a resonant laser. The factor of 6.5 increase in the interaction-strength-to-linewidth ratio that we obtain indicates that dipolar polaritons could constitute an important step towards a demonstration of the polariton blockade effect, and thereby to form the building blocks of many-body states of light.

Received 13 July 2018
Revised 16 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.227402

Physics Subject Headings (PhySH)

Exciton polariton Nonlinear optics Semiconductor microcavities Semiconductor quantum optics

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied PhysicsNonlinear Dynamics

Authors & Affiliations

Emre Togan¹, Hyang-Tag Lim¹, Stefan Faelt^1,2, Werner Wegscheider², and Atac Imamoglu¹

¹Institute of Quantum Electronics, ETH Zurich, CH-8093 Zurich, Switzerland
²Solid State Physics Laboratory, ETH Zurich, CH-8093 Zurich, Switzerland

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Vol. 121, Iss. 22 — 30 November 2018

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Images

Figure 1
(a) Schematic of the sample structure. The sample contains three pairs of ${In}_{0.04} {Ga}_{0.96} As$ coupled quantum wells (QWs) located at three separate antinodes of a $5 λ / 2$ cavity formed between two GaAs/AlAs distributed Bragg reflectors (DBRs). To ensure that electron tunneling for the lowest-energy electron states of the two QWs occur at finite electric field, we use QWs with different thicknesses; thus each pair consists of a 5-nm- and a 11-nm-thick QW. The thickness of the GaAs barrier between the two QWs is 13 nm. An electric potential $V_{G}$ applied between the $p$ (66 nm) and $n$ (66 nm) doped layers tunes the energy of the direct exciton (DX) and indirect exciton (IX) levels. See the Supplemental Material [23] for details on the sample structure and the fabrication process. (b) Reflection spectrum with zero in-plane momentum excitation ( $k_{in} = 0$ ) as a function of applied gate voltage $V_{G}$ . Changes in the energy levels of the bare DX (green dashed line) and IX (blue dashed lines) are extracted from a measurement of the reflection spectrum at a point where the top DBR has been etched (see the Supplemental Material [23]). Cavity resonance (orange dashed line) is constant as we vary $V_{G}$ . Changes in the energies of the three coupled states—upper polariton (UP), middle polariton (MP), and lower polartion (LP)—with $V_{G}$ are shown as red dashed lines. We use the calculated eigenstates associated with the red lines to estimate the DX, IX, and C (cavity) content at a particular sample position and $V_{G}$ .
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Figure 2
(a) Reflection spectrum obtained at $V_{G} = 1.1 V$ when scanning a weak ( $\sim 0.5 μ W$ ) linearly polarized probe laser across a LP resonance. The power of a second, orthogonally linearly polarized pump laser tuned to 1.45853 eV is varied (cyan: 0 mW, orange: 2.15 mW, purple: 7.2 mW). The polariton linewidth broadens as we increase the pump power: the $γ_{P}$ values are $80 μ eV$ , $116 μ eV$ , and $130 μ eV$ , respectively. (b) The left axis shows changes in the LP resonance energy, extracted from traces as shown in (a), as the power of the pump laser (horizontal axis) is varied. The right axis shows changes in the differential reflection of the pump laser tuned to 1.45853 eV as its power is varied. Differential reflection ( $d R$ ) is obtained by subtracting the reflection signal obtained at $V_{G} = 1.1 V$ from a reflection trace obtained at $V_{G} = 0 V$ . The red dashed line shows the calculated $d R$ signal using Eq. (2). The pump laser is off resonant with all polariton transitions at $V_{G} = 0 V$ . All reflection and pump-probe experiments are carried out using a pulse scheme to minimize the effects of light-induced slow changes to the polariton environment (see the Supplemental Material [23]).
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Figure 3
(a) Changes in polariton interaction strength $g_{P}$ extracted from differential reflection measurements similar to Fig. 2 as a function of $| x |^{2}$ . Different data points were obtained at $V_{G} = 1.4 V$ at different positions on the sample. The IX content remains $| y |^{2} \leq 0.004$ for all of the data. Changes in $g_{P}$ are in agreement with $g_{P} = (14 \pm 1) | x |^{4} g_{0}$ . The error bar for the parameter estimated in the model is based on the $1 σ$ confidence interval obtained in the fit. The error bars on data points are standard deviations of the extracted $g_{P}$ obtained at different repetitions of the experiment at different spatial positions that have the same $| x |^{2}$ content (See the Supplemental Material [23]). (b) Changes of the linewidth, in the linear regime, extracted from low-power ( $\leq 0.5 μ W$ ) reflection measurements using a single probe laser. The error bars are standard deviations of the extracted linewidth when repeating the experiment at different spatial positions that have the same $| x |^{2}$ content.
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Figure 4
(a) Changes in polariton interaction strength $g_{P}$ extracted from differential reflection measurements similar to Fig. 2 as a function of $V_{G}$ at a fixed position. The data match a simple model $g_{P} = a (| x |^{4} + b | y |^{4}) g_{0}$ with $a = 17.6 \pm 0.1$ , $b = 7.4 \pm 0.5$ for linearly polarized measurements (red dashed line) and $a = 27.7 \pm 0.1$ , $b = 8.1 \pm 0.3$ for circularly polarized measurements (blue dashed line). The error bars for the parameters estimated in the model are based on the $1 σ$ confidence interval obtained in the fit. For each $V_{G}$ value we repeat the experiment more than 10 times and fit a value for $g_{P}$ to each of these measurements. The error bars on the data points are standard deviations of the extracted $g_{P}$ ’s for these measurements. (b) Change in the particle weight as a function of $V_{G}$ . The dipole size of the polariton changes from 0.09 to 3.4 nm as $V_{G}$ changes from 1.4 to 0.95 V (see the Supplemental Material [23]). (c) Changes of the linewidth extracted from a reflection measurement similar to Fig. 2, in the linear regime, for each of the points. The error bars show the $1 σ$ confidence interval of the linewidth extracted from a fit of the reflection spectrum to a Lorentzian. (d) Change in the ratio of $g_{P} / γ_{P}$ for the data presented in (a) and (c).
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