3D micro-printing: An enabling technique for arbitrary potential landscapes for photonic quantum-gases

TL;DR

Problem: Realizing versatile potential landscapes for photonic quantum gases in ambient conditions to study open driven-dissipative quantum systems. Approach: Employ direct laser writing to deposit sharp polymer structures on high-finesse cavity mirrors, enabling box, double-well, curved, and SSH lattice potentials with sub-wavelength control. Contributions: Demonstrated a $10\,\mu\mathrm{m}$ box potential with ground-state macroscopic occupation, tunnel couplings up to $J\approx2\,\mathrm{THz}$ in double wells, and a $20$-site SSH lattice with mid-gap edge states and a central band gap of approximately $2\,\mathrm{THz}$. Significance: Opens avenues for exploring lattice physics and open quantum thermodynamics with photonic quantum gases and may enable solving complex ground-state problems like the XY-model, while preserving high cavity finesse and reconfigurability.

Abstract

Photonic quantum gases explore the physics of open driven-dissipative quantum systems under ambient conditions and thus open access to thermodynamics and transport phenomena in quantum gases in the weakly interacting regime. Here we introduce the technology of 3D micro-printing to create potential landscapes for photonic quantum gases in dye-filled micro cavities, which surpass the current state of the art in terms of potential size and definition, potential depth, coupling strength, and number of coupled potentials by at least an order of magnitude. We realize as demonstration of the capabilities box potentials with rectangular side walls, anisotropic harmonic potentials, double-well potentials with dimensions on the scale of the wavelength of light as well as potential lattices with topological non-trivial properties. This approach paves the way for experimentally studying the physics of open quantum systems on lattices and might find applications in solving complex ground-state problems like the XY-model.

Figures (5)

• Figure 1: Photon gas spectroscopy of a box potential. a Sketch of the cavity in the Photon BEC setup. A polymer structure has been direct laser written on one of the cavity mirrors. b Microscope image of a polymer box potential. c Position space spectrum of the light from the cavity for a box potential. The light is confined to the width of the box marked by the straight orange lines. d Momentum space spectrum of the light from the cavity for a box potential. The orange parabola shows the dispersion relation of a free particle with a mass of $m_\text{ph}$. The grey shaded areas mark the limits of our measurement setup in momentum space due to the numerical aperture of the imaging objective. e Integrated position space spectrum (along $x$) of the cavity fluorescence for a box potential below ($N=55\pm2$), around ($N=144\pm3$) and above ($N=469\pm7$) the critical particle number$N_\text{c}$. The red dashed line shows an thermal distribution $\exp{(-h\Delta\nu/k_\text{B} T)}$ and the orange points show the expected relative photon density based on the mode degeneracy and the Bose-Einstein distribution for $T=300K$.
• Figure 2: a Sketch of the cavity setup for a double well potential. With a mechanical mirror distance $D_0$, a height of the polymer structure $h_\text{S}$ and a center-to-center distance between the pillars of $d$. b Dependence of the couplings strength over center-to-center distance $d$ of the two pillars. The solid orange line shows the numerically predicted strength, where $r=0.6µm$, $h_s=0.6µm$ and $q=10$. c Position space spectrum of the cavity fluorescence for a cavity with two coupled pillars for different center-to-center distances $d$. With increasing distance the mode splitting $\Delta\nu$ ($=2J$) decreases. On the top microscope images of the corresponding polymer structures are shown.
• Figure 3: a Sketch of the mirror surface structure imprinted on one of the cavity mirrors for a topological non-trivial SSH-array. The coupling of sites inside $J_\text{i}$ and between $J_\text{o}$ the unit cells is controlled via their distance. b Predicted position space spectrum for the topological trivial (left) and topological non-trivial (right) structure. In both cases exist a optical band gap (marked with black arrows) but only in the topological non-trivial case exist states in the center of the band gab which are localized at the ends of the array (marked with red arrows). c Microscope images of the polymer structures. d Position space spectrum of the cavity fluorescence for an SSH array. The experimentally observed spectra shows the predicted features, as the bandgap (marked with black arrows) and edge states (marked with red arrows).
• Figure 4: Dip-in configuration (left column) and immersion configuration (right column) in comparison. a Sketch of the used direct laser writing configurations. In the dip-in configuration, reflection from the dielectric coating causes self-interference of the laser focus, which causes written structures to have discrete steps in height. For the immersion configuration, a large part of the mirror substrate must first be removed. On the other hand, there is no self-interference of the focus and structures with a smooth curved surface can be written. b Microscope image and Atomic force microscope measurement of the surface of an isotropic paraboloid written in the two configurations, respectively. c Sections through the AFM data along the $x$ axis (blue dashed) and the $y$ axis (light blue dotted) compared to a parabola with the curvature programmed for the 3D print (orange straight). The parallel gray lines in the bottom left plot have a distance of 230nm.
• Figure 5: Schematic sketch of the photon BEC setup. The pump beam is structured using a spatial light modulator (SLM) before entering the cavity via an objective. The light emitted by the cavity is collected via a second objective on the other side of the cavity. A lens is used to image the cavity in the focal plane of the lens, where an aperture can be used to block light modes that are not confined by the potential. From there on, the light can be directed to various imaging setups to get the position space image, the position space spectra or the momentum space spectra.