Interaction-Induced ac Stark Shift of Exciton-Polaron Resonances

T. Uto, B. Evrard, K. Watanabe, T. Taniguchi, M. Kroner, and A. İmamoğlu

Phys. Rev. Lett. 132, 056901 – Published 29 January 2024

Abstract

Laser-induced shift of atomic states due to the ac Stark effect has played a central role in cold-atom physics and facilitated their emergence as analog quantum simulators. Here, we explore this phenomenon in an atomically thin layer of semiconductor ${MoSe}_{2}$ , which we embedded in a heterostructure enabling charge tunability. Shining an intense pump laser with a small detuning from the material resonances, we generate a large population of virtual collective excitations and achieve a regime where interactions with this background population are the leading contribution to the ac Stark shift. Using this technique we study how itinerant charges modify—and dramatically enhance—the interactions between optical excitations. In particular, our experiments show that the interaction between attractive polarons could be more than an order of magnitude stronger than those between bare excitons.

Received 30 May 2023
Revised 20 December 2023
Accepted 4 January 2024

DOI:https://doi.org/10.1103/PhysRevLett.132.056901

Physics Subject Headings (PhySH)

Biexcitons Excitons Optoelectronics Polarons Stark effect Trions

Hexagonal boron nitride

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

T. Uto ^1,2,*, B. Evrard ^1,*, K. Watanabe ³, T. Taniguchi³, M. Kroner¹, and A. İmamoğlu ¹

¹Institute for Quantum Electronics, ETH Zürich, CH-8093 Zürich, Switzerland
²Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
³Research Center for Electronic and Optical Materials, NIMS, 1-1 Namiki, Tsukuba 305-0044, Japan

^*These authors contributed equally to this work.

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Vol. 132, Iss. 5 — 2 February 2024

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Images

Figure 1
(a) Sketch of the pump-probe setup and the Van der Walls heterostructure. (b) Reflection spectrum of the measured device as a function of the electron density $n_{e}$ . To enhance visibility, the signal is multiplied by 10 for $E < 1.64 eV$ . (c) Schematic of the energy levels showing the usual ac Stark shift for the first two levels and the interaction-induced shift which increases with the exciton density. (d) Reflection spectrum at charge neutrality, as a function of the delay between the cocircularly polarized pump and probe pulses. From a fit (dashed line) we extract the amplitude of the light shift. The latter is shown in (e) as a function of the pump detuning from the exciton resonance ( $δ_{ex}$ ), and well fitted by $Δ_{ex} = B / δ_{ex}^{2}$ (solid line). Throughout the Letter, error bars show the statistical error corresponding to two standard deviations obtained from a set of a few repetitions of the experiment.
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Figure 2
ac Stark shift of the attractive polaron (AP) resonance for cocircularly polarized pump and probe lasers. In (a)–(c), we show the AP resonance as a function of the pump-probe delay $τ$ for increasing pump-laser intensity ( $I_{pk} \approx 0.7, 1.3, 2 GW / {cm}^{2}$ ). The shift at $τ = 0$ is plotted in (d) as a function of the intensity, showing deviation from a linear dependence in $I_{pk}$ (dashed line). Here the pump-laser detuning from AP is $δ_{AP} \approx 13 meV$ and the electron density is $n_{e} \approx 1.7 \times 10^{12} {cm}^{- 2}$ . In (e), we show the $δ_{AP}$ dependence of the shift, which is well fitted by $B / δ_{AP}^{2}$ , shown as a blue line. Here, $n_{e} \approx 0.17 \times 10^{12} {cm}^{- 2}$ and $I_{pk} \approx 0.4 GW {cm}^{- 2}$ so that the $I_{pk}$ dependence is within the linear regime.
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Figure 3
(a) Electron density dependence of the attractive polaron light shift for cocircularly polarized pump and probe beam. From these data and a measurement of the AP oscillator strength [33], the AP-AP interaction strength $U_{AP}$ is extracted and compared to the exciton-exciton interaction strength $U_{ex}$ in (b). Here, $δ_{AP} \approx 25 meV$ and $I_{pk} \approx 1.7 GW {cm}^{- 2}$ .
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Figure 4
Light shift of the attractive polaron for cross-circularly polarized pump and probe beam. (a) Detuning $δ_{AP}$ dependence of the light shift at an electron density of $n_{e} \approx 1.0 \times 10^{12} {cm}^{- 2}$ . For large $δ_{AP}$ (open symbols) we use the full bandwidth of the pump and $I_{pk} \approx 5.3 GW / {cm}^{- 2}$ . To approach the AP resonance, we reduce the bandwidth and consequently $I_{pk}$ by a factor of $\approx 0.4$ . We then rescale the data (full symbols), ensuring that the two measurements match at intermediate detunings ( $δ_{AP} \approx 25, 30 meV$ ). The data are well fitted by a $B / δ_{AP}^{2}$ law, shown as a blue line. (b) Time dependence of the line shift for various $n_{e}$ at $δ_{AP} \approx 25 meV$ . The red line is a fit, from which we extract the shift at $τ = 0$ . The latter is shown in (c) as a function of $n_{e}$ . (d) The ratio of the interaction between opposite-valley APs and that of same-valley excitons for $I_{pk} \approx 1.7 GW / {cm}^{- 2}$ .
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