Quantum hydrodynamics of a single particle

Abstract

Semiconductor devices are strong competitors in the race for the development of quantum computational systems. In this work, we interface two semiconductor building blocks of different dimensionalities with complementary properties: (1) a quantum dot hosting a single exciton and acting as a nearly ideal single-photon emitter and (2) a quantum well in a 2D microcavity sustaining polaritons, which are known for their strong interactions and unique hydrodynamic properties, including ultrafast real-time monitoring of their propagation and phase mapping. In the present experiment, we can thus observe how the injected single particles propagate and evolve inside the microcavity, giving rise to hydrodynamic features typical of macroscopic systems despite their genuine intrinsic quantum nature. In the presence of a structural defect, we observe the celebrated quantum interference of a single particle that produces fringes reminiscent of wave propagation. While this behavior could be theoretically expected, our imaging of such an interference pattern, together with a measurement of antibunching, constitutes the first demonstration of spatial mapping of the self-interference of a single quantum particle impinging on an obstacle.

Keywords: Polaritons; Quantum optics.

Fig. 1. Generation, injection and detection of single polaritons; second-order correlation function for the pumping photons.

a Schematic of the experiment: a pulsed laser pumps a QD to generate single photons that are injected inside a semiconductor microcavity. An image of the single polariton propagation is acquired with an EMCCD. b Second-order correlation function of QD emission when multiplexing the pump pulse rate to 320MHz; The antibunching value of g⁽²⁾(0) = 0.16 ± 0.05 is an unequivocal signature of single-photon emission from these QDs

Fig. 2. Single polariton propagation measured in reflection configuration.

a Energy dispersion of the microcavity-quantum well system at the point of incidence of photons in the reflection configuration compared with the emission spectrum of the pumping QD, shown in (b). At k_y ≈ 1.1μm⁻¹, the exciton energy is in resonance with the LPB, allowing resonant polariton injection into the microcavity; polaritons injected with this in-plane momentum propagate with a group velocity v_g ≈ 2.1µm/ps, as deduced in the Supplementary Material; c Real space image of the single polariton propagation. d Energy-resolved propagation in c, evidencing how only the QD exciton peak couples into the system and propagates. e To obtain a better image of the propagation, the noncoupled reflected light is blocked by a spatial filter; polariton propagation distances are measured up to ~400µm. f At a different microcavity-quantum well detuning, the QD exciton is not in resonance with the polariton dispersion, and indeed, no propagation is evidenced in this situation

Fig. 3. Single polariton propagation measured in transmission configuration.

a Energy dispersion in the microcavity at the photon injection point in the transmission configuration compared with the emission spectrum of the selected QD, shown in panel b; note that the exciton energy of the QD coincides with the state of the LPB with in-plane momentum k_y ≈ 0.28 µm⁻¹; this allows resonant pumping of the microcavity with single photons from the QD; the second-order correlation function in Fig. 1b is precisely obtained for this QD emission spectrum; Single-polariton propagation obtained by matching the polariton dispersion in (a) with the single photons corresponding to (b). c, d Single-polariton propagation across a defect naturally occurring in the microcavity; an interference pattern appears due to the self-interference between the incoming wavefunction and its scattering against the defect; the red circle indicates the position of the structural defect

Fig. 4. Self-interference of individual polaritons.

a Numerical spatial distribution of the electric field of an incoming plane wave, and (b) that for a circular wave, as it could be used to model the light scattered from a point defect in the microcavity. c Experimental density map from Fig. 3d with superimposed numerical simulations of the single-polariton self-interference; red lines are contour lines with the same intensity calculated by making the wavefront interfere with the circular wave in b; the numerical simulations are obtained by assuming an incoming polariton with in-plane momentum k = 0.28 µm⁻¹, as in the experiment