Trembling Motion of Exciton Polaritons Close to the Rashba-Dresselhaus Regime

Single-crystalline CsPbBr3 can sustain stable polariton fluids with long-range propagation and spontaneous coherence at room temperature.

“The single-crystalline CsPbBr 3 , as demonstrated in our earlier studies, can sustain stable polariton fluids with long-range propagation and spontaneous coherence at room temperature [27-30].”

• cites [27] R. Su, J. Wang, J. Zhao, J. Xing, W. Zhao, C. Diederichs, T. C. H. Liew, and Q. Xiong, Room temperature longrange coherent exciton polariton condensate flow in lead halide perovskites, Sci. Adv. 4 , eaau0244 (2018). https://doi.org/10.1126/sciadv.aau0244 sourcePartly supported

  The Abstract reports a CsPbBr3 exciton-polariton condensate at room temperature, and the Results report interference fringes above threshold as evidence of macroscopic coherence. The Results describe the condensate as localized to about 5 μm; our copy does not establish long-range propagation or stability of a polariton fluid, or specify that the microplate is single-crystalline. (LLM, conf=0.85)

  Experimental — accuracy not yet measured
• cites [28] R. Su, S. Ghosh, J. Wang, S. Liu, C. Diederichs, T. C. H. Liew, and Q. Xiong, Observation of exciton polariton condensation in a perovskite lattice at room temperature, Nat. Phys. 16 , 301 (2020). sourceDisputed

  The Results (‘Strong light-matter coupling’; page unavailable) identify the studied material as polycrystalline 2D PEPI, not single-crystalline CsPbBr3. The Discussion (page unavailable) describes electrically tunable Berry curvature at room temperature, not long-range propagation or spontaneous coherence of polariton fluids. (LLM, conf=0.84)

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured
• cites [29] J. Feng, J. Wang, A. Fieramosca, R. Bao, J. Zhao, R. Su, Y. Peng, T. C. H. Liew, D. Sanvitto, and Q. Xiong, All-optical switching based on interacting exciton polaritons in self-assembled perovskite microwires, Sci. Adv. 7 , eabj6627 (2021). sourcePartly supported

  The Introduction and Conclusion report room-temperature CsPbBr3 polariton-condensate flow with long-range propagation and spontaneous spatial coherence. The Results and Discussion describe the CsPbBr3 microwire microcavity and stable excitons, but our copy does not establish that the microwire was single-crystalline or demonstrate stability of the polariton fluid itself. (LLM, conf=0.81)

  Experimental — accuracy not yet measured
• cites [30] R. Su, A. Fieramosca, Q. Zhang, H. S. Nguyen, E. Deleporte, Z. Chen, D. Sanvitto, T. C. H. Liew, and Q. Xiong, Perovskite semiconductors for roomtemperature exciton-polaritonics, Nat. Mater. 20 , 1315 (2021). sourcePartly supported

  The paper reports room-temperature polariton condensation with long-range spatial coherence in a cesium lead halide perovskite lattice (conclusion and Fig. 4 discussion; page not provided). It also describes earlier work on long-range coherent condensate flow (introductory discussion). Our copy does not identify the material specifically as single-crystalline CsPbBr3 or demonstrate long-range propagation of a stable polariton fluid in this lattice. (LLM, conf=0.83)

  Experimental — accuracy not yet measured

The successful introduction of liquid crystal molecules into microcavities sustains synthetic spin-orbit coupling with broad tunability and realization of the RD Hamiltonian.

“More recently, the successful introduction of liquid crystal (LC) molecules into microcavities has been shown to sustain synthetic spinorbit coupling with broad tunability and realization of the RD Hamiltonian [23-26].”

• cites [23] K. Rechcińska, M. Król, R. Mazur, P. Morawiak, R. Mirek, K. Łempicka, W. Bardyszewski, M. Matuszewski, P. Kula, W. Piecek, P. G. Lagoudakis, B. Piętka, and J. Szczytko, Engineering spin-orbit synthetic Hamiltonians in liquid-crystal optical cavities, Science 366 , 727 (2019). sourceCould not verify

  The paper’s p. 1 discussion proposes a semiconductor spin-field-effect transistor with Rashba and Dresselhaus coupling. Our copy does not address liquid-crystal molecules in microcavities, synthetic spin-orbit coupling in that setting, or its claimed broad tunability; searches for those terms returned only semiconductor-device passages. (LLM, conf=0.75)

  Experimental — accuracy not yet measured
• cites [24] M. Król, K. Rechcińska, H. Sigurdsson, P. Oliwa, R. Mazur, P. Morawiak, W. Piecek, P. Kula, P. G. Lagoudakis, M. Matuszewski, W. Bardyszewski, B. Piętka, and J. Szczytko, Realizing optical persistent spin helix and Stern-Gerlach deflection in an anisotropic liquid crystal microcavity, Phys. Rev. Lett. 127 , 190401 (2021). sourcePartly supported

  The paper discusses a Rashba–Dresselhaus Hamiltonian for a two-dimensional electron gas and says the Rashba coupling may be tuned with an applied electric field (p. 1). It does not report introducing liquid crystals into microcavities or demonstrating tunable synthetic spin-orbit coupling in that setting. (LLM, conf=0.86)

  Experimental — accuracy not yet measured
• cites [25] Y. Li, X. Ma, X. Zhai, M. Gao, H. Dai, S. Schumacher, and T. Gao, Manipulating polariton condensates by Rashba-Dresselhaus coupling at room temperature, Nat. Commun. 13 , 3785 (2022). sourceNot checked — no full text of the source
• cites [26] K. Łempicka-Mirek, M. Król, H. Sigurdsson, A. Wincukiewicz, P. Morawiak, R. Mazur, M. Muszyński, W. Piecek, P. Kula, T. Stefaniuk, M. Kamińska, L. D. Marco, P. G. Lagoudakis, D. Ballarini, D. Sanvitto, J. Szczytko, and B. Piętka, Electrically tunable Berry curvature and strong light-matter coupling in liquid crystal microcavities with 2D perovskite, Sci. Adv. 8 , eabq7533 (2022). sourcePartly supported

  The paper describes a liquid-crystal-filled microcavity whose voltage-controlled anisotropy allows modes to be brought into resonance; it reports Rashba–Dresselhaus spin-orbit coupling and gives an effective Hamiltonian (passages [3] and [5], section labeled Abstract; page unavailable). It supports tunability, but does not establish the claimed broad range of tunability. (LLM, conf=0.83)

  Experimental — accuracy not yet measured

The paper experimentally emulates Zitterbewegung of exciton polaritons in a perovskite microcavity at room temperature.

“We report the experimental emulation of trembling quantum motion, or Zitterbewegung , of exciton polaritons in a perovskite microcavity at room temperature.”

• Also stated in: § Trembling Motion of Exciton-Polaritons Close to the Rashba-Dresselhaus Regime · p. 1 · boosted

  “In this study, we demonstrate the experimental emulation of trembling motion, or Zitterbewegung , of exciton polaritons with electrical tunability at room temperature.”

• Also stated in: § Trembling Motion of Exciton-Polaritons Close to the Rashba-Dresselhaus Regime · p. 4 · boosted

  “In summary, we have unambiguously demonstrated the observation of exciton polariton Zitterbewegung in a LC-filled perovskite microcavity at room temperature.”

The spatial distribution of S2 and S3 resembles interlocked fingers for spinor components, indicating spin precession during polariton propagation.

“As shown in Fig. 3(c,d), the spatial distribution of S 2 and S 3 resembles interlocked fingers for spinor components, indicating spin precession during the polariton propagation.”

Under resonant excitation, the polariton fluid exhibits trembling motion perpendicular to its flowing direction.

“Under a resonant excitation, the polariton fluid exhibits clear trembling motion perpendicular to its flowing direction, accompanied by a unique spin pattern resembling interlocked fingers.”

• Also stated in: § Trembling Motion of Exciton-Polaritons Close to the Rashba-Dresselhaus Regime · p. 1 · boosted

  “Under a continuous-wave resonant excitation at high momentum states, the polariton fluid exhibits an oscillatory trajectory and the spin precession in the real space, providing the unequivocal evidence of polariton ZB.”

• Also stated in: § Trembling Motion of Exciton-Polaritons Close to the Rashba-Dresselhaus Regime · p. 4 · plain

  “Under a resonant excitation, the injected polariton fluids exhibit long-range and ultrafast propagation with a counterintuitive trembling motion perpendicularly to its propagation direction.”

By tuning energy gaps with external electrical voltages, the authors observe continuous transition of polariton Zitterbewegung from relativistic (small gaps) to non-relativistic (large gaps) regimes.

“Furthermore, leveraging on the sizable tunability of energy gaps by external electrical voltages, we observe the continuous transition of polariton Zitterbewegung from relativistic (small gaps) to non-relativistic (large gaps) regimes.”

• Also stated in: § Trembling Motion of Exciton-Polaritons Close to the Rashba-Dresselhaus Regime · p. 1 · plain

  “By modulating the electrical voltages for tuning the RD Hamiltonian, we further observe the continuous transition of polariton ZB from relativistic dynamics to nonrelativistic dynamics.”

• Also stated in: § Trembling Motion of Exciton-Polaritons Close to the Rashba-Dresselhaus Regime · p. 4 · plain

  “Furthermore, leveraging on the sizable tunability in our platform, we continuously tune the energy gap between spinor states and realize continuous transition of polariton Zitterbewegung from relativistic to non-relativistic regimes.”

The energy gap ε between the two spinor polariton states increases monotonically with applied voltage from ∼8 meV at 2.7 V to ∼22.6 meV at 3.05 V.

“We further extract the energy gap ε as a function of the applied voltage [Fig. 2(b)], showing a monotonic increase trend from ∼ 8 meV at 2.7 V to ∼ 22 . 6 meV at 3.05 V.”

• Also stated in: § Trembling Motion of Exciton-Polaritons Close to the Rashba-Dresselhaus Regime · p. 3 · plain

  “As displayed in Fig. 2(a), the energy gap ε between the two spinor polariton states exhibits an increasing trend with growing of the applied voltage beyond 2.60 V.”

The polariton fluid exhibits a spin pattern resembling interlocked fingers.

“accompanied by a unique spin pattern resembling interlocked fingers”

• Also stated in: § Trembling Motion of Exciton-Polaritons Close to the Rashba-Dresselhaus Regime · p. 3 · hedged

  “As shown in Fig. 3(c,d), the spatial distribution of S 2 and S 3 resembles interlocked fingers for spinor components, indicating spin precession during the polariton propagation.”

• Also stated in: § Trembling Motion of Exciton-Polaritons Close to the Rashba-Dresselhaus Regime · p. 4 · boosted

  “We also observe unique spin textures during the polariton propagation, resembling interlocked fingers for opposite spinor components which serves as the compelling evidence of interference between spinor states.”

By introducing liquid crystal molecules into the microcavity, the authors achieve spinor states with synthetic Rashba-Dresselhaus spin-orbit coupling and tunable energy splitting.

“By introducing liquid crystal molecules into the microcavity, we achieve spinor states with synthetic Rashba-Dresselhaus spin-orbit coupling and tunable energy splitting.”

• Also stated in: § Trembling Motion of Exciton-Polaritons Close to the Rashba-Dresselhaus Regime · p. 1 · plain

  “By integrating birefringent LC into CsPbBr 3 perovskite microcavities, we achieve the synthetic RD Hamiltonian with broad tunability, which allows to continuously modulate the polariton band structures and the energy gap between two orthogonal spinor states.”

• Also stated in: § Trembling Motion of Exciton-Polaritons Close to the Rashba-Dresselhaus Regime · p. 2 · plain

  “We further fill the perovskite microcavity with birefringent LC and achieve synthetic spin-orbit coupling.”

ZB becomes unobservable at 3.15 V.

“ZB becomes unobservable at 3.15 V (Fig. S8)”

Under applied voltages from 2.65 V to 3.05 V, the polariton trajectories show distinct behaviors in periodicity and amplitude of oscillatory motion.

“As shown in Fig. 4(a) and Fig. S8, we collect the polariton trajectories under applied voltages ranging from 2.65 V to 3.05 V, where we experimentally observe distinct behaviors in terms of the periodicity and amplitude of the polariton oscillatory motion.”

Clear evidence of interference between spinor components is experimentally observed for the first time.

“It is noteworthy that such clear evidence of interference between spinor components is experimentally observed for the first time, thanks to the long-range polariton propagation and the tunable energy gap for sustaining a proper amplitude and frequency of ZB.”

With increasing voltage and energy gap, the oscillations become weaker with continuous decreases in period and amplitude.

“With the further increase of the voltage and the energy gap, the oscillations become weaker and weaker with continuous decreases in period and amplitude and ZB becomes unobservable at 3.15 V (Fig. S8), suggesting the transition from relativistic to weak-relativistic and eventually to non-relativistic regimes.”

The spin precession behavior directly correlates ZB to interference between two spinor components.

“This spin precession behavior directly correlates ZB to the interference between two spinor components, in line with previously predicted spin patterns in planar microcavities with TE-TM splitting [32] and our theoretical simulations (Fig. S6).”

• cites [32] E. S. Sedov, Y. G. Rubo, and A. V. Kavokin, Zitterbewegung of exciton-polaritons, Phys. Rev. B 97 , 245312 (2018). sourceNot checked — no full text of the source

The non-trivial drift of the polariton fluid perpendicular to its propagation direction strongly evidences the existence of ZB.

“ular to its propagation direction strongly evidences the existence of ZB.”

The presence of the shift allows precise detection of small values of the gap, restricted only by the polariton lifetime, which limits the observation time.

“The presence of the shift allows precise detection of small values of the gap, restricted only by the polariton lifetime, which limits the observation time.”

The tunable energy gap between two spinor states serves as the key ingredient to simulate trembling motion from relativistic to non-relativistic regimes.

“This tunable energy gap between two spinor states in our system, serves as the key ingredient to simulate the trembling motion of exciton polaritons from the relativistic (small gaps) to the non-relativistic (large gaps) regimes.”

The perturbed RD Hamiltonian couples the motion in only one direction to the spin precession.

“The perturbed RD Hamiltonian couples the motion in only one direction to the spin precession, and the realization of ZB with liquid-crystal filled microcavities underscores the potential of exciton polaritons as a solid-state platform for emulations of relativistic quantum physics in the 1+1 dimensions in the presence of an artificial magnetic flux.”

The observation of trembling polariton motion provides precise detection of the SU(2)-symmetry state, since small deviations from the RD Hamiltonian lead to significant deviations of the mean polariton trajectory from the straight path.

“The observation of trembling polariton motion in our work provides precise detection of the SU(2)-symmetry state, since small deviations from the RD Hamiltonian lead to significant deviations of the mean polariton trajectory from the straight path.”

The shift and ZB become most pronounced at σε/2α∼1.

“The shift and ZB become the most pronounced at σε/ 2 α ∼ 1 .”

Perturbation of the RD Hamiltonian leads to the opening of a gap in the energy spectrum.

“Perturbation of the RD Hamiltonian leads to the opening of a gap in the energy spectrum.”