Prof. Pavlos Lagoudakis

Background:
Vortices are a primary topological objects which have a vital role in many branches of fundamental physics, including high-energy physics, superfluidity, superconductors, and optics. Quantized vortices are described by the complex wavefunction which has as a point in two-dimensional space of vanishing density about which the phase winds by 2πm – where m is an integer. A vortex is said to be of higher multiplicity, or topological charge, when m is greater than 1 – the so called Giant Vortices. Vorticies, giant or not, have been notoriously difficult to detect and create in polariton condensates due to stochastic and unpinned nature. For ones with higher multiplicity they go further and break apart into many individual vortices due to the fragile nature of the structures.

Recently our group has performed the creation of giant vortices in odd-numbered polygons of polariton condensates. Using non-resonant excitation and geometrically frustrated coupling between condensates to form a stable and discrete vortex state of high topological charge. The current can be observed throughout the polygon and the central vortex can be observed in the heptagon to increase in size as the coupling between condensates is modificed, see Figure 1.

Figure 1: Heptagon of polariton condensates with in-phase coupling, ±2π/7, ±4π/7 and ±6π/7 coupling between nearest neighbours.

Additionally, we have demonstrated spontaneous formation of a nonlinear vortex cluster state in a microcavity exciton-polariton condensate. We optically pump with a ring-shaped, non-resonant laser which results in a trapped condensate at the centre. The condensate experiences intricate high-order mode competition with robust condensate density beatings showing the periodic appearance of orderly arranged vortices, as shown in Figure 2. This work moves towards the design of complex structured light sources in the strong light-matter coupling regime.

Figure 2: Schematic of ring-shaped excitation scheme and the resulting trapped condensate with time-periodic orderly vortices.

The projets is currently investigating the time- and spatial dynamics of vortices in polariton condensates and works towards coupling neighboring vortices for analog polariton simulators.

Learning Outcome:
You will learn advanced optics and spectroscopy, different features interferometric techniques and off-axis digital holography phase extraction. You will interact with an international group, present your work in weekly meetings and seminars.

Highlighted Publications:
[1] “Geometric frustration in polygons of polariton condensates creating vortices of varying topological charge”, Cookson, T., et al., Nature Communications 12, 2120 (2021)
[2] “Spontaneous formation of time-periodic vortex cluster in nonlinear fluids of light”,  Sitnik, K., et al., Physical Review Letters 128, 237402 (2022)

Background:
Various optimisation problems with many degrees of freedom are difficult to near-impossible to solve with classical computers, as their complexity grows exponentially with the number of variables. It is, for example, impossible to algorithmically determine how to colorize countries on a world map while keeping neighbouring countries in different colours. Artificial lattices of coherently coupled macroscopic states are at the heart of applications ranging from solving hard combinatorial optimization problems to simulating complex many-body physical systems. Tightly pumped polariton condensates expand ballistically and are able to coherently couple, (as shown in Figure 1 for a dyad and a chain). Our work exploits this to create coherently coupled polariton lattices in simple to bespoke geometries. Well-defined initial conditions are first imprinted to the lattices while carefully controlling the coupling strength between the condensates. By ‘simply’ letting the system relax to a steady state, it is then possible to reverse engineer an optimal configuration for problem being solved.

Figure 1: (Left hand side) A dyad at different distances demonstrating the coupling in the near-field (a,d), total far-field (b,e) and far-field from condensate centres (c,f). (Right hand side) A polariton condensate chain of 11 condensates with coherent coupling.

Back in 2017 we demonstrated the potential of polariton graphs as an efficient analogue simulator for the XY model and by imprinting polariton condensate lattices of bespoke geometries we show that we can engineer various coupling strengths between the lattice sites [1]. Recently, we expanded this by engineering large polariton condensate lattices (shown in Figure 2) with active control on the spatial arrangement and condensate density to unravel the dependence of spatial correlations between polariton condensates on the lattice geometry [2].

An alternative approach we use is inverse optical pumping, where we engineer the polariton landscape to create condensates to occur away from the optical pump spots. We have used this to create matter-wave scatterer lattices, where high energy matter waves undergo transmission and reflection through narrow width barriers giving potential insight into quantum fluids [3]. Furthermore, we have realized a liquid light machine for the NP-hard max-3-cut problem based on a network of synchronized exciton-polariton condensates by overcoming the binary limitation from the Ising machine using the phases’ continuous degree  of freedom [4].

Figure 2: Extended polariton condensate lattice in square (left) and triangular (right) geometries with spatial and density stabilisation.

This project is currently moving towards extended lattices of thousands of condensates with controllable coupling, externally coupling of condensates within large lattices, and quasi-periodic lattices.

Learning Outcome:
You will learn advanced optics and spectroscopy, polariton condensate coupling within lattices and, formation of holograms on a spatial light modulator. You will also become familiar with techniques of data acquisition automation (including equipment interfacing and programming) and advanced data analysis. You will interact with an international group, present your work in weekly meetings and seminars.

Highlighted Publications:
[1] “Realizing the classical XY Hamiltonian in polariton simulators”, Berloff, N., et al., Nature Materials 16, 1120–1126 (2017)
[2] “Engineering spatial coherence in lattices of polariton condensates”, Töpfer, J. D., et al., Optica 8 106-113 (2021)
[3] “Quantum fluids of light in all-optical scatterer lattices”, Alyatkin, S., et al., Nature Communications 12, 5571 (2021)
[4] “Solving the max-3-cut problem with coherent networks”, Harrison, S. L., et al., Physical Review Applied 17, 024063 (Feb 2022)

Background:
Since 2014, polariton condensates have been shown to be possible at room temperature with no need for cryogenic cooling or vacuum assistance, thus creating the way for the development of “practical” polaritonic devices. Whilst polaritonics as a platform, was then ticking a lot of the boxes required for optical computing applications (stable condensates at room temperature, low cost of fabrication of samples, scalability, etc.), the challenge remained to find a way to design the basic blocks of computing, such as transistors, logic gates, switches, while demonstrating a clear superiority over classical computing.

Our lab demonstrated in 2019 not only the all-optical room-temperature polaritonics transistor, but also two of the fundamental logic gates required for logic circuitry – the AND and OR gate. This pioneering work was featured then on the cover of Nature Photonics (Figure 1, left). The technology was fundamentally based on a dual beam approach: one beam (a “pump”) was used to excite a population of excitons and bring the polaritons close to the condensation threshold, and a much weaker beam (a “probe”) was carefully tuned to trigger stimulated emission into an appropriate state. By using multiple beams in this configuration and advanced external feedback, we proved that all-optical logic was possible at room temperature using polariton condensates.

Figure 1: (Left) Organic polariton logic gates in ambient conditions (cover), (Center) Polariton condensation from pump-seed excitation where the pump excites a hot-exciton gas and seed provides stimulated emission from the ground state. (Right) Switching on of the condensate (right) for 26 aJ (a), 4 aJ (b), and 1 aJ (c), over 5000 individual condensate realizations.

While the probe beam in the previous configuration was weak, it still contained millions of photons, thus drastically limiting the power consumption advantage over conventional computing. We recently circumvented this issue by decreasing the probe beam to a single photon and demonstrating single-photon switching of a condensate at room temperature. Again in the pump-probe configuration (figure 1, center), we were able to ascertain that even a single-photon (probe beam at ~1 aJ) is able to cause a mass occupation in the groundstate and “switch-on” the condensate (right side of figure 1, right). This is only possible due to the record non-linearity of our systems, where a single photon can trigger the condensation of many thousands of polaritons in the state of interest.

The project is currently moving towards full polariton circuitry and the realization of the universal logic gate (NAND or NOR gate). Leveraging the inherent switching speed of our system, we also aim to demonstrate all-optical logic gates with operating speeds of up to 1Thz.

Learning Outcome:
You will learn advanced optics and spectroscopy, femtosecond laser pulse synchronization, and automation of optical set up using LabView. You will interact with an international group, present your work in weekly meetings and seminars.

Highlighted Publications:
[1] “A room-temperature organic polariton transistor”, Zasedatelev, A.V., et al., Nature Photonics 13, 378–383 (2019)
[2] “Single-photon nonlinearity at room temperature”, Zasedatelev, A.V., et al., Nature 597, 493–497 (2021)

Background:
Polariton condensation has been a heavily investigated topic since it was first demonstrated in 2006 – the effect had long been searched for, having been predicted 10 years before. The subsequent work eventually moved into organic semiconductors in 2014, as the desire to build polaritonic based devices required ambient working conditions. Excitation of polariton condensates in ambient conditions has been however plagued by issues with photo-bleaching and burning of the material. This has limited most studies to single pulse excitation in the femto- or pico- second regime. As such the search continues to find stable materials for ambient temperature polaritonic studies. Back in 2017, we demonstrated polariton condensation in a different class of organic semiconductors: molecular dyes diluted in a polymer matrix. The material was shown to undergo polariton condensation at room temperature. However applications, such as polariton routers, and many-body condensed matter phenomena are hindered buy the ultra-short polariton lifetimes in these materials.

In recent years, we have taken this further by demonstrating nano-second polariton condensation at room temperature in a microcavity of the same molecular dye. The long-lasting condensate exceeds the polariton lifetime by several orders of magnitude and pushes the system one step closer towards the steady-state regime, allowing for studies in superfluidity and condensate interactions at room temperature.

Left: Back cover of Advance Optical Materials presenting results on organic condensation, Right: Real-space (upper) and dispersion (lower) of a polariton condensate excited with a nano-second pulsed laser below (left) and above (right) condensation threshold.

Future plans of the project include investigation of novel materials capable of supporting continuous-wave excitation, in collaboration with international collaborators (IBM, University of Sheffield, etc.), thus bringing ambient polaritonics devices one step closer to reality.

Learning Outcome:
You will learn advanced optics and spectroscopy at room temperature under nano-second excitation, different features of interferometric techniques and off-axis digital holography phase extraction. You will also become familiar with techniques of data acquisition automation (including equipment interfacing and programming) and advanced data analysis. You will interact with an international group and collaborators, present your work in weekly meetings and seminars.

Highlighted Publications:
1. “A yellow polariton condensate in a dye filled Microcavity”, Cookson, T., et al., Advanced Optical Materials 1700203 (2017)
2. “Room temperature broadband polariton lasing from a dye-filled microcavity”, Sannikov, D.,  Advanced Optical Materials 7, 17 (2019)
3. “Nano-second exciton-polariton lasing in organic microcavities”, Putinsev, A., et al., Applied Physics Letters 117, 123302 (2020)