## Introduction

Quantum fluids, from superconducting electrons1 to superfluid helium2, from ultracold atoms Bose–Einstein condensation (BEC) on optical lattices3 to the cosmological-scale superfluid core in neutron stars4, embody exotic quantum behaviors emblematic of particles or excitations with bosonic statistics. The hydrodynamics of quantum fluids has been the source of tremendous interest in a multitude of many-body systems1,2,3,5,6. In particular, exciton-polaritons, quasiparticles composed of a superposition of the confined photons and excitons in a semiconductor microcavity, recently emerged as a unique driven-dissipative system for quantum fluid research7. These exciton-polaritons possess an ultra-small effective mass (~10−5 electron mass) from their photonic component and also inherit strong nonlinearity from their excitonic component. Thus, compared to ultracold atoms, polaritons can undergo BEC at elevated temperatures8,9, ultimately limited by the exciton binding energy. Indeed, a series of exciting observations of rich macroscopic quantum fluid phenomena were reported in exciton-polaritons condensation with the GaAs or CdTe quantum well microcavities at cryogenic temperatures, such as frictionless superfluidity and Čerenkov supersonic flow10,11, quantized vortices12,13, and soliton formation14,15. However, due to the small Wannier–Mott exciton binding energy of the III-V or II-VI materials, these experiments must still be performed at liquid helium temperatures. The low-temperature operation and expensive molecular-beam epitaxy materials growth significantly limit the accessibility and practical applications. Although high exciton binding energy materials such as GaN, ZnO, and two-dimensional semiconductors show great potential for room-temperature polaritonics16,17,18,19, they unfortunately still have limitations to overcome for studying the quantum fluid hydrodynamics.

Moreover, as a non-equilibrium system, some discussions were also involved in the research of polariton fluids20,21,22. Specifically, under continuous-wave (CW) coherent driving below the optical parametric oscillation (OPO) threshold3, recent theoretical work21 shows polariton fluids can only preserve some superfluid-like properties due to the phase locking and are better to be understood as a rigid state instead of superfluidity. In this aspect, pulsed-laser pumping work, where the phase of the system can subsequently evolve freely after excitations, has certain advantages12,13,23, in quantum fluids study and recently even shown polariton superfluidity at room temperature in non-crystalline organic microcavities24. However, the intrinsically small interactions of Frenkel excitons in organics, short polariton lifetimes, and structural inhomogeneity have hampered the observation of the Čerenkov wave pattern in the supersonic regime in accordance with the Landau criterion of superfluidity. Furthermore, due to the small polariton-polariton interactions in organics, the pumping power is also close to the material damage threshold25,26, making the system impossible to address higher density behavior at room temperature.

Recently, a new family of semiconducting materials, the lead halide perovskites with a composition of ABX3 (where A is commonly CH3NH3+ (MA+) or Cs+; B is Pb2+; X is Cl, Br, and I), have attracted much attention because of their excellent optical performance in solar cells27 and optoelectronic devices28,29, thanks to the defect-tolerance, large carrier mobility, long lifetime, high photoluminescence (PL) efficiency, tunable bandgap, and simple single crystal growth processes30,31,32. Furthermore, single-crystalline bromide and chloride perovskites show excellent Wannier–Mott exciton properties for room-temperature polaritonics33, such as large exciton binding energy33, strong exciton photon coupling strength34, and high room-temperature nonlinear interaction strength35. With the chemical vapor deposition (CVD), small single crystal inorganic halide perovskites have demonstrated polariton condensation at room temperature34. Additionally, in contrast to conventional Wannier–Mott excitons materials like GaAs and CdTe, the intrinsic large and tunable splitting between transverse electric and transverse magnetic modes in perovskite cavities36,37 behaves as a winding in-plane magnetic field on the photon spin, enabling rich physics such as the Rashba–Dresselhaus Hamiltonians38,39,40,41, and spin textures39,42,43. However, the hallmark frictionless flow of nonlinear superfluidity and Landau criterion demonstration in halide perovskites, the foundation for studying rich spin-orbital coupled quantum fluid phenomena, remain elusive.

In this work, using large and extremely homogenous solution-grown halide perovskites40, we report the observation of polariton superfluidity in a Wannier-Mott exciton system at room temperature under resonantly pulsed excitations. Specifically, we demonstrate transitions from a normal fluid to superfluidity and supersonic fluid in both one- and two-dimensional cases in halide perovskite microcavities. In the one-dimensional case, we show that back-reflection can be fully suppressed outside the superfluidity healing length when the polariton superfluid hits a hard potential wall under the critical velocity. In the two-dimensional case, we demonstrate landmark zero-viscosity superfluid and a Čerenkov supersonic wave pattern at room temperature, on par with low-temperature cases11. The experimental data are also in quantitative agreement with our theoretical modeling using non-equilibrium Gross-Pitaevskii equations. Lastly, by comparing the simulations and experimental real-space images, the polariton-polariton nonlinear interaction strength from the inorganic perovskite’s Wannier-Mott exciton was also extracted to be more than two orders of magnitude higher than the Frenkel exciton in organics24. Our work reveals that halide perovskites microcavities can enable previously inaccessible complex quantum fluid behaviors at room temperature. It also creates a transformative room-temperature polariton playground with Rashba-like dispersion39 for exciting topological quantum fluid studies.

## Results

Our microcavity samples40 were made by directly solution-synthesizing the CsPbBr3 (exciton binding energy ~36 meV44) single crystals inside the prefabricated empty optical cavities, which were formed by a unique wafer-bonding process. Chemical synthesis under nanometer-size confinement enables highly homogenous single-crystalline perovskite microwires and plates with substantial sizes (Fig. 1), without any sample degradation due to the top DBR fabrication.

Firstly, a one-dimensional perovskite microwire was used to study superfluidity. The recent one-dimensional experiment in GaAs emulated the black hole and Hawking radiation with polariton superfluidity at low temperature45. However, despite its importance in polariton experiments17,46,47, there are no previous demonstrations of the one-dimensional superfluidity at room temperature. Figure 1b shows a long CsPbBr3 single-crystal microwire. Figure 1d shows the angle-resolved PL of a perovskite microwire with a width of 1.85 μm. Along the long x-axis, the angle-resolved photoluminescence shows the two continuous lower polariton branches (The details of the fitting are shown in Supplementary Note 1), which are split at k|| = 0 due to the optical birefringence from the orthorhombic phase of CsPbBr3. In contrast, the lateral confinement along the short y-axis induces discrete energy levels in the dispersion (Fig. 1d). More interestingly, the mode splitting can lead to tunable Rashba-like dispersions39,40,41, highly desired for synthetic non-Abelian gauge fields and topological physics studies.

Here, a linear-polarized pulsed laser was used to only excite one polariton branch resonantly to inject polariton fluid flowing along the long x-axis toward the edge of the microwire in a transmission configuration (Fig. 1 and Supplementary Fig. 4). The resonant excitation can easily generate propagating polariton fluid with designed in-plane momentum k|| compared with the non-resonant excitation and the triggered optical parametric oscillator10,23. In Landau’s theory of superfluidity, spontaneous energy dissipation or scattering can occur in quantum fluids only if it can reduce the energy of the moving fluid. Robust superfluidity with zero viscosity can exist if the quantum fluid’s group velocity vp is smaller than the critical speed vc of the system (Landau criterion vp < vc). As for a polariton fluid, the critical velocity vc is the polariton speed of sound $${c}_{s}=\sqrt{g|{\psi }_{p}{|}^{2}/m}$$11,48. Experimentally, the injected polariton fluid group velocity $${v}_{p}=\hslash {k}_{p}/m$$ can be tuned by adjusting the in-plane wavevector kp, i.e., changing the incident angle (Supplementary Fig. 4). In these two expressions, g describes the polariton-polariton interaction, $$|{\psi }_{p}{|}^{2}$$ is the polariton density, m is the polariton effective mass, and $$\hslash$$ is the reduced Planck constant. A small kp = 2.3 µm−1 was first chosen to satisfy the subsonic requirement of cs > vp. By tuning the polariton densities with the pumping power, the speed of sound can be tuned to fulfill the subsonic condition of superfluidity. At low excitation power, where the polariton density is low, the polariton fluid was clearly reflected back by the edge (a “hard” potential wall for the polariton fluid). As a result, the interference fringes between the incoming fluid and reflected fluid can be observed (Fig. 2a-I), accompanied by bright back reflection signals in momentum space at kx = 2.3 µm−1 (Fig. 2a-III). At high excitation power, the system enters the superfluidity regime (due to the increased speed of sound), and interestingly, the interference fringes in real space and the back reflection signals in momentum space disappear (Fig. 2a-II, a-IV). Since the polariton superfluid cannot go through the microwire’s end, the back reflection from the end will inevitably occur. In a microscopic picture, this back-reflection will eventually be suppressed through the polariton-polariton nonlinear interaction (Supplementary Fig. 6) outside the superfluidity healing length region (Supplementary Fig. 7 for CW excitation case). All the excitations only occur inside the healing length region where the bulk superfluidity condition breaks down. Thus, we can extract from the experimental data (Fig.  2c, d) that the healing length is ~3 µm in the fs laser pump case (similar for CW case as shown in Supplementary Fig. 7). These results and physical picture are also in quantitative agreement with our Gross-Pitaevskii equations modeling (Supplementary Note 2, Supplementary Fig. 7) both in real-space (Fig. 2b-I, b-II, c, d) and momentum space (Fig. 2b-III, b-IV). Lastly, the small non-uniform intensity profile and residual interference fringes at the superfluidity condition outside the healing length region are also due to the Gaussian shape fs-pulsed excitation, time-average imaging, the mode broadening induced by non-resonant excitation49, as well as small sample inhomogeneities.

When the polariton fluid is injected at a high kp (4.6 µm−1) to fulfill supersonic condition cs < vp, superfluidity will be destroyed based on the Landau criterion. Even at a very high polariton density, the interference fringes in real space and back-reflection signals in momentum space can always be ambiguously observed (Fig. 3a). Meanwhile, due to the increased nonlinear interactions between polaritons at high density, the wavenumber of the polariton fluid flow k decreases slightly to 4.2 µm−1 at high pumping intensity, as indicated by the increasing interference fringe distances (Fig. 3c, d). A similar decreased k effect was also reported in the previous black hole and Hawking radiation experiments at low temperature45. The Gross-Pitaevskii equations simulations again confirm these observations nicely, as shown in Fig. 3b–d.

Another evidence of the polariton fluid supersonic regime is the increasing Mach cone angle with Čerenkov wave pattern when polariton fluid flows across a defect in a two-dimensional configuration (Fig. 1c). However, in previous work with organics24, the linear Čerenkov wave pattern was not demonstrated when the polariton fluid was excited at a large kp. Moreover, a clear change of the scattering cone with increasing density was not observed due to the limited range of powers achievable in that system (Supplementary Fig. 15). Here, with the perovskite microcavities, parabolic wavefronts due to the interference around the defect were clearly observed at low polariton density (kp = 4.2 μm−1, Fig. 4a-I), accompanied by a bright Rayleigh scattering ring in momentum space (Fig. 4a-III). With increased pumping power, the parabolic wavefronts across the defect became linear, and the aperture angle gradually increased (Fig. 4a-II and Supplementary Fig. 8). The Mach cone is formed due to the polariton density modulation downstream (Fig. 4a-II), which was also well reproduced in the simulation nearly perfectly (Fig. 4b-I, a-II). Meanwhile, the scattering ring in the momentum space was heavily modified, as shown in Fig. 4a-III, a-IV. This observation of the Čerenkov pattern at room temperature can directly prove the existence of a well-defined sound velocity in the polariton fluid with perovskite in contrast to previous organics cases. The averaged sound velocity was also extracted as cs = 10.4 μm ps−1 from Fig. 4a-II by $$\sin (\phi )={c}_{s}/{v}_{p}$$, where $$\phi$$ is the half Mach cone angle11,50. Lastly, the two dark streaks in the wake of a defect (Fig. 4a-II, b-II) are most likely caused by oblique dark solitons7,14, an effect that has never been observed at room temperature and is worthy of further investigation.

Finally, the superfluidity in two-dimensional perovskite microcavity was also observed with a smaller injection momentum at kp = 2.3 μm−1 (Fig. 4c). At high polariton density (Figs. 4c-II, c-IV and 5b), the interference parabolic wavefront and the Rayleigh scattering ring were strongly suppressed, illustrating a “frictionless” superfluidity behavior. The simulations in Fig. 4d match the experiment very well.

The complex polariton fluid behaviors in superfluid and Čerenkov regimes can also be qualitatively understood by the Bogoliubov excitation spectra analysis49 (Fig. 5c, d). It is also worth noting that pulsed excitation rather than the CW excitation was chosen in this experiment. Since there is no stationary state under pulsed pumping, the observation of polariton fluid evolution is a time-averaged effect of different Bogoliubov states. Nevertheless, the main feature of the superfluidity and the Čerenkov state can be qualitatively captured by the Bogoliubov excitation spectra. For the superfluidity case in Fig. 5c, at low pumping power, the dispersion shows a parabolic shape (the solid red line), and the injected polariton can be elastically scattered to the same energy states as indicated by the yellow dashed lines. At high pumping power with high polariton density, the polariton-polariton interaction induces a strong blueshift and tilts the dispersion at high k, and a discontinuity emerges in the excitation spectrum (the solid blue line). As a result, there will be no states available to be scattered at the energy of the injected polariton. Thus, the elastic scattering vanishes, and the system enters the superfluidity regime. While for the Čerenkov case in Fig. 5d, at high pumping power, though strong blueshift reappears, there are still states with energy at and below the pumping energy as indicated by the yellow dashed lines. As a result, the system is in the supersonic case and shows a Čerenkov wave pattern.

## Discussion

It is worth noting that, the phase-locking effect in the CW resonant excitation21 does not exist in pulsed excitation cases because the polariton can freely evolve for a significant proportion of its life after the laser pulse excitation (Supplementary Fig. 13). Furthermore, the generation and flow of vortex pairs can be observed behind the defect in the supersonic regime in previous experimental reports12,13,24, a signature of phase evolution after the laser pulse. On the other hand, pulsed excitation also helps to reduce harmful thermal effects on the perovskite samples. Therefore, the observations were a time-averaged effect of the evolutions of different states (Supplementary Figs. 7 and 13).

We emphasize that strongly interacting polaritons are crucial for defining the sound velocity and stabilizing the polariton condensation and superfluidity (Supplementary Fig. 6). The interaction constant g in these experiments can be extracted (Supplementary Note 2) as gxx ~ 4 μeV μm2 (between excitons) and gpp ~ 0.5 μeV μm2, (between polaritons) from real-space images fittings as well as the sound velocity formula in the Čerenkov experiment cs. The polariton-polariton interaction strength is thus more than two orders of magnitude higher than organics24, and is also comparable with those in the low-temperature GaAs51 and other perovskite works at room temperature35,52. This suggests an intrinsic strong polariton-polariton interaction and high nonlinearity attributable to the Wannier-Mott exciton. In contrast, weakly interacting Frenkel excitons in organics demand a much stronger excitation laser pulse, which is close to the organic material’s photo-damaging threshold or has to go beyond it24,25,26. Lastly, our room-temperature two-dimensional experimental image quality is comparable to the low-temperature MBE-grown GaAs case11, which further justifies the excellence of the halide perovskite platform.

To conclude, we report the room-temperature polaritonic quantum fluid behaviors in solution-synthesized halide perovskites microcavities in both one- and two-dimensional cases. Room-temperature polaritonic quantum fluid phase transitions from a normal fluid to both superfluid and (Čerenkov, if two-dimensional) supersonic fluid were demonstrated. Our work established a robust room-temperature quantum fluid platform with strongly interacting polaritons and paved the way for a transformative playground for studies, such as non-equilibrium topological physics53,54, non-Abelian gauge fields39, and non-equilibrium collective excitation spectrum55,56,57. The quantum fluid study presented here can also guide future quantum fluid theory work on pulsed laser excitation cases and the development of other room-temperature polariton experiments such as layered perovskite materials35, and other types of cavities like DBR-free open cavity configurations58,59. The strong nonlinearity originating from halide perovskites’ Wannier–Mott excitons could also lead to other device applications, such as topological polaritonic laser and non-Hermitian photonic devices60.

## Methods

### Fabrication of optical cavity and nanocavity

#### Fabrication of distributed Bragg reflector (DBR) wafer

Quartz wafers were cleaned by heated piranha baths followed by deionized water washes. The cleaned wafers were loaded into a vacuum chamber for SiO2/Ta2O5 deposition by electron beam evaporation with an advanced plasma source. As a result, nine pairs of the SiO2/Ta2O5 DBR mirror were deposited at 300 °C. The elevated temperature and high-kinetic energy plasma bombardments produced an enhanced optical quality of the DBR mirrors.

#### Thermal compression wafer-wafer bonding of DBR wafer with patterned gold pillar

A two-dimensional array of squared gold pads was deposited on the surface of DBR wafers by electron beam evaporation. Then two gold-patterned wafers were loaded into the wafer bonder. The wafers were aligned according to the gold pads, followed by a thermal compression bonding process. Finally, the bonded wafer was diced into small chips for crystal growth. Bonded DBR chips are shown in Supplementary Fig. 1.

### Synthesis of halide perovskites

#### Growth of all CsPbBr3 crystals in the nanocavity

We used a inverse temperature crystallization (ITC). Dimethyl sulfoxide (DMSO) was added into cesium bromide and lead bromide powder mixture in a vial. All chemicals were purchased from Sigma-Aldrich Chemical and used as received. The prepared solution was dropped at the edge of the fabricated DBR nanocavity, and the cavity space was fully filled by the solution through capillary force. The DBR nanocavity with CsPbBr3 precursor solution was put on a hotplate for crystal growth. After that, the DBR nanocavity with crystals was put in a vacuum chamber to remove possible residual solvent.

### Characterizations of halide perovskites

#### Atomic force microscopy (AFM) measurements

Nanocavities were opened by brute force with tweezers to expose perovskite crystals before AFM measurements. The AFM images and height profiles of crystals were taken with Park Systems AFM in tapping mode and analyzed with the XEI software.