Zero Dimensional Polariton Laser in a Sub-Wavelength Grating Based Vertical Microcavity

Semiconductor exciton-polaritons in planar microcavities form coherent two-dimensional condensates in non-equilibrium. However, coupling of multiple lower-dimensional polariton quantum systems, critically needed for polaritonic quantum device applications and novel cavity-lattice physics, has been limited due to the conventional cavity structures. Here we demonstrate full confinement of the polaritons non-destructively using a hybrid cavity made of a single-layer sub-wavelength grating mirror and a distributed Bragg reflector. Single-mode polariton lasing was observed at a chosen polarization. Incorporation of a designable slab mirror into the conventional vertical cavity, when operating in the strong-coupling regime, enables confinement, control and coupling of polariton gasses in a scalable fashion. It may open a door to experimental implementation of polariton-based quantum photonic devices and coupled cavity quantum electrodynamics systems.


INTRODUCTION
Semiconductor microcavity exciton-polaritons [1] have recently emerged as a unique, open system for studying non-equilibrium quantum orders [2][3][4]. Exciton-polaritons are formed via strong coupling between the excitons and photons. Due to the excitonic component, polaritons are massive, weakly interacting quasi-particles that feature strong nonlinearity and rich manybody physics [5]. Due to the mixing with the photon, polaritons have an effective mass 10 − 8 of the Hydrogen atom mass, and they are relatively insensitive to disorders or localization potentials in the active media. Hence polaritons exhibit quantum coherence over macroscopic scales at high critical temperatures. Polaritons in quantum-well (QW) microcavities couple out of the cavity at a fixed rate while conserving the energy and in-plane wavenumber, providing direct experimental access unavailable in typical manybody quantum systems. Hallmarks of non-equilibrium condensation and superfluidity have been widely observed in isolated two-dimensional polariton systems (Ref. [3] and references therein).
The foundational work on 2D polariton systems has inspired theoretical schemes for polariton-based quantum circuits [6][7][8], quantum light sources [9][10][11][12], and novel quantum phases [4]. Experimental implementation of these schemes requires control, con finement and coupling of polariton systems, which remain challenging with the conventional microcavity structure. Important features of a versatile experimental platform based on polaritons include: firstly, well defined 0D polaritons as building blocks of a coupled system, secondly, the establishment (i.e., survival) of non-equilibrium quantum phase in each 0D polariton cell typically manifested as polariton lasing, thirdly, controllable coupling among the 0D cells, and lastly, individual addressability and control of each cell. In conventional polariton-cavities, the thick mirrors, made of distributed Bragg re flectors (DBRs), make it difficult to confine or control the polaritons beyond the perturbative regime. Most existing methods to control the polaritons lead to a weak modulation potential that modi fies the system's properties without reducing its dimensionality from 2D to 0D. Examples include weakly confining the excitons via mechanical strain [13] and periodic modulation of the optical modes via surface patterning [14,15]. Advanced techniques have been developed to embed apertures inside the cavity [16,17], which has created 0D polariton cells but polariton lasing has not been reported so far. Alternatively, 0D polariton systems were also created via direct etching of the vertical cavity into pillars [18][19][20][21]. Using this method, two groups have achieved polariton lasing in the pillars recently [22][23][24], and thus satisfying the first two requirements. However, this approach requires a destructive plasma etching throughout the 4-6 µm tall cavity structure as well as the active media layers, which excludes coupling between separate pillars. It is also unclear if further control of the polariton modes in each pillar would be possible. In this work, we demonstrate a polariton system in an unconventional cavity that could ful fill all the four requirements. The new cavity structure replaces the top DBR with a slab photonic crystal (PC) (as shown in Fig. 1), which enables confinement and control of the polariton modes by design [25][26][27]. At the same time, there is no destructive interface in the active media layers or the main cavity layers, hence coupling among multiple low-dimensional polariton cells is unhindered. We demonstrate with the new cavity system zero-dimensional polariton lasing at a chosen polarization.

MATERIALS AND METHODS
A schematic of our hybrid cavity polariton device is shown in Fig. 1 There are 12 GaAs QWs distributed at the three central anti-nodes of the cavity. We create square gratings of 5-8 µm in length ( Fig. 1(b)) on the top layer via electron-beam lithography followed by a short plasma etching. A hydrochloric acid chemical etching was then applied to remove the sacrificial layer, followed by critical point drying. The fabricated gratings are ~80 nm thick, with a period of ~520 nm and a duty cycle of ~40%, and suspended on an air gap of ~300 nm. It is optimized as a high re flectance mirror for light polarized along the grating bar direction (TE-polarization). Figure 1 Optical measurements were performed to characterize the properties of the cavity system. The sample was kept at 10-90 K in a continuous flow liquid -helium cryostat. A pulsed Ti-Sapphire laser at 740 nm was used as the excitation laser, with a 80 MHz repetition rate and 100 fs pulse duration. It is focused to a spot size of ∼2 µm in diameter on the device from the normal direction with an objective lens of a numerical aperture of 0.55.
The photoluminescence signal was collected with the same objective lens, followed by real 4 space or Fourier space imaging optics, and sent to a 0.5 m spectrometer with an attached nitrogen cooled charge coupled device (CCD). The spectrally resolved real space and Fourier space distributions were measured by selecting a strip across the center of the Fourier space and real space distributions using the spectrometer's entrance slit. The resolution of the measurements was limited by the CCD pixel size to 0.3 /µ for Fourier space imaging and by the diffraction limit to 0.4 µm for real space imaging.

RESULTS AND DISCUSSION
Strong-coupling between excitons and TE-cavity modes were evident in the momentum space images of the emission from within the cavity, as shown in Fig. 2(a). Discrete lower polariton (LP) modes and a faint upper polariton (UP) branch were observed below and above the exciton energy, respectively, with dispersions distinct from that of the cavity photon (the red solid line). In contrast, the emission from outside the hybrid cavity region shows a flat, broad exciton band at the heavy hole exciton energy of Eexc =1.551 eV ( Fig.   2(b)). The energies of the polariton modes can be described as follows in the rotating wave approximation: Here is the inplane wavenumber, is the un-coupled cavity energy and 2ℏΩ is the The spatial profile of the confined LP modes are also measured via spectrally resolved real-space imaging, as shown in Fig. 2(c). The four lowest LP modes are well con fined within the SWG region, while higher excited states spread outside and form a continuous band. The variances of the k-space and x-space wavefunctions along the detected direction are ∆k =0.85 /µm and ∆x =1.01 µm. Their product is ∆x×∆k =0.86. It is slightly larger than the uncertainty limit of 0.5, which may be due to the diffusion of the LPs.
The absorption spectra of the modes were obtained via re flectance measurements. The spectrum measured normal to the sample (Fig. 2(d)) shows the three symmetric modes with the lowest mean inplane wavenumber: the UP ground state, the LP ground state, and the LP second excited states. Other polariton states have too small a spectral weight to be measured in reflectance. When measured at 3.5 • from the sample normal, the 1st excited state of LPs was also observed (Fig. 2(e)).
A further confirmation of the strong-coupling regime is the temperature tuning of the resonances, as shown in Fig. 2 Finally, we show that polariton lasing was achieved in the 0D hybrid cavity. As shown in Fig. 4 (a), the emission intensity I from the LP ground state increases sharply with the excitation power P at a threshold of Pth =∼ 5 KW/cm 2 , characteristic of the onset of lasing.
Interestingly, the emission intensity I varies with P quadratically both below and well above the threshold, except at very low excitation densities. This may be because the energy separation between the discrete modes is larger than kBT ∼ 0.8 meV. As a result, relaxation to the ground state through LP-phonon scattering is suppressed compared to LP-LP scattering. Accompanying the transition, a sharp decrease of the LP ground state linewidth was measured. The minimum linewidth of 0.24 meV may be limited mainly by the intensity fluctuation of the pulsed excitation laser [28]. The LP energy increased continuously with the excitation density due to exciton-exciton interactions. The blueshift shows a linear dependence below threshold, it is suppressed near threshold, and shows a logarithmic dependence above threshold [22,29]. The discrete energy levels are maintained across the threshold and remain distinctly below the uncoupled cavity energy.
The establishment of polariton lasing con firms the quality of the 0D-polariton system.
The threshold density is smaller or comparable to those measured in DBR-DBR pillar cavities [22,23]. The linewidth deduction and blueshift are all within an order of magnitude difference compared to reported values in DBR-DBR planar or pillar microcavities [1,22,23]. Unlike DBR-DBR cavities, however, the polariton lasing we demonstrated takes place in a priori defined polarization, independent of excitation conditions.

CONCLUSIONS
In conclusion, we have demonstrated the first hybrid cavity incorporating a slab PC mirror, operating in the strong coupling regime, supporting polariton lasing. Three dimensional confinement of the polaritons was achieved by using a finite size SWG, with the QWs and the main cavity layers untouched. Polariton lasing in the ground state was readily observed.
Unique to the hybrid SWG-cavity, the LP is linearly polarized, while the orthogonally polarized exciton mode remains in the weak-coupling regime. The PL of the weakly-coupled TM excitons provides direct access to the TE exciton reservoir that has not been available in conventional III-As cavities. It enables polarized polariton lasers [30][31][32][33][34] and simpli fies quantum photonic devices based on single-spin polaritons [10][11][12]35].
The integration of a slab PC mirror in a polariton system adds the flexibility to control