My research interests range from exploring the foundations of quantum physics and developing novel applications for next generation quantum technologies to investigating nonlinear optical effects. The recurring theme of most of my research can be described as exploring complex transverse structures of the photons, testing their special features to address fundamental questions, and using their benefits for classical and quantum information schemes. Lastly, I still have an ongoing (at the moment more passive) interest in atom physics and quantum optics with ions, which dates back to my days as a Master student.

## Entangled photons with complex transverse structures

The transverse spatial degree of freedom of single photons offers various interesting features, which can be used to perform fundamental test of physics and enhance quantum information schemes. The most popular feature being its orbital angular momentum (OAM), which is related to a helical phase front, hence the names twisted photons (see figure on the right). In addition, if photons are superimposed with two different transverse phase structures each having an orthogonal polarization (or spin angular momentum), the transverse profile shows an arbitrary complex polarization pattern. These general transverse spatial states are usually referred to as structured photons.

Over the last years, I was involved in different experiments developing novel ways to generate [1,2], manipulate [3] and measure [4,5] structured photons and investigate their properties in quantum entanglement experiments [6]. Novel technologies such as triggerable single photon sensitive cameras have made it possible to image the effect of entanglement, even in real time (see youtube video on the left for more information). More importantly, complex spatial modes of photons, i.e. twisted and structured photons, can be used in interesting classical and quantum information schemes as well as fundamental test, as they can be used to enlarge the information content, they can serve as a realization of a high-dimensional quantum state and the physical property of OAM can be arbitrary large, in principle.

The field of structured light just turned 25 years old, hence it is still young enough to offer plenty things to discover and already mature enough to bring established features close to real-world applications [7].

## Foundations of quantum physics with twisted photons

One particularly interesting utilization of twisted photons is their implementation in fundamental tests of quantum physics. By taking advantage of the theoretically unbounded, quantized OAM of photons it is possible to test quantum mechanical predictions in the laboratory and push known limits from smaller to larger scales.

In one set of experiments [8,9], we were able to generate entangled photons with an OAM quantum number of more than 10,000, thereby the enormous complexity photonic structures may have (see image on the right) and that a claim of a quantum-to-classcial transition for large quantum numbers might be too simple.

In another experiment, we demonstrated that using the well-known down conversion process of a non-linear material it is possible to generate a more than (100×100)-dimensionally entangled quantum states [10]. Not only can such complex states be useful for quantum information schemes, as the size of the underlying Hilbert-Space is nearly as big as 14 entangled qubits, but they are also of fundamental interest of how much information can be shared between two parties of an entangled system.

We were also able to increase the number of involved particles and their dimensionality at the same time [11]. The achieved quantum states was a tripartite (3,3,2)-dimensionally entangled state (graphically depicted in the picture on the left). Interestingly, the complicated experimental setup was found by a autonomous computer program ‘MELVIN’ [12]. Increasing the number of particles along with the dimensionality enables the realization and investigation of novel asymmetric quantum states to explore and possibly apply in next generation quantum technologies.

Lastly, we investigated another fundamental feature of quantum physic, the no-cloning theorem, which forbids perfect copies and, thus, essentially enables (together with the Heisenberg uncertainty principle) the absolute security of quantum cryptography. Nevertheless, we were able to built an universal quantum cloning machine for OAM states, which copies any high-dimensional quantum state as good as the co-cloning theorem permits. We were able to show, that even with such a machine, hacking a secure quantum link is not possible and even easier to detect in a high-dimensional system [13].

## Long-distance classical and quantum information using structured light

Another vivid and promising research branch of structured light, which is already close to real-world applications is to use the different orthogonal modes, either as additional classical channels to increase data transmission rates or as means to distribute high-dimensional quantum states for next generation quantum communication schemes, e.g. quantum key distribution. In different recent experiments, we tested in both classical and quantum communication schemes the influence of strong turbulence disturbance on the quality of the structure and introduced errors, respectively.

By using specific superposition, consisting of two modes with the same OAM but opposite handedness, that have a distinctive intensity structure, we were able to send and detect up to 16 different modes, thus transmitting up to 4-bits of information in a single shot over a 3 km long frees-space intra-city link (see Youtube movie below for more information) [14]. Recently, we were able to extend the distance up to 143 km and send a short message between to Canary islands using a similar scheme and encoding the information in the lights structure [15]. The results demonstrated that the use of OAM can be beneficial in terms of classical communication, even under very strong turbulence conditions.

After these first successful tests with laser light, we took the next step to the quantum regime and distributed two-dimensionally entangled OAM photons via the 3 km long intra-city link in Vienna [16]. We were able to show that the entanglement of photons carrying up to 2 OAM quanta is not destroyed by the detrimental effect of strong atmospheric turbulence. In more recent experiments, we achieved the next crucial step towards more practical applications, namely the demonstration of a high-dimensional quantum key distribution over a 300 m long intra-city link in Ottawa (see image on the right) [17]. The results show that by using ququarts, i.e. four-dimensional quantum states, the distributed key-rates can be enhanced (theoretically 2 times more, in our case 1.5 times more due to errors introduced by turbulence) or in other words, high-dimensionally encoded quantum states allow the encoding of more information per single carrier.

All these results demonstrate that it is possible to perform first proof-of-principle experiments without using adaptive optics. However, they indicate that going to longer distances and high-dimensions, such turbulence compensation is inevitable.

## Twisted bright squeezed vacuum

As part of my Banting post-doctoral fellowship, I am currently also working on bright squeezed vacuum, i.e. high gain parametric down conversion and its connection to twisted light. We were recently able to show that spatial OAM spectrum of two strongly pumped nonlinear crystals can be controlled such that only a few low order OAM modes are generates, by changing the distance between the crystals [18]. The results might enable us to investigate the quantum properties of what is often referred to macroscopic quantum light.

## Nonlinear optics with structured light

More recently, I got also interested the effect of the strong non-linear response of certain media on the structures of light, e.g. caustic pattern. Caustics can be seen as nature’s way to focus energy without using a lens. They are also connected to rogue or freak waves, which have extremely large amplitudes, appear more often than a normal distribution would predict and have been considered to be fairy tales of sailors until they have been scientifically recorded in 1995. Interestingly, the mechanism behind the formation of rogue waves is still under debate. In our experiment, we were able to show that while in a linear media only large phase fluctuations generate caustics and rogue wave events, already small phase fluctuations lead to strong caustics and an increase in rogue wave events when light travels through a nonlinear medium, i.e. Rubidium vapour [19].

Because oceans are also described by a third order nonlinearity, our results may not only hold for optical systems but also be helpful in understanding of oceanic rogue waves and the forecast of the effects of tsunami waves.

## Deterministic ultra-cold ion beam

Finally, I am still interested in the research of ion beams in connection to quantum optics and atom physics. This interest originates in the research I have been doing during my Master thesis. At that time, I worked on an ultra-cold deterministic ion beam based on an ion trap [20]. We developed customized ion optics in order to focus the beam down to a few micrometer [21] (even nanometer in simulation [22]). After many years of hard work, I am very impressed by the recent demonstration of my former colleagues in which they realized the predicted nanometer resolution [Jacob. et al. PRL 117 (4) 043001 (2016)].

- Fickler et al. Quantum entanglement of complex photon polarization patterns in vector beams Physical Review A 89, 060301(R) (2014).
- Larocque et al. Arbitrary optical wavefront shaping via spin-to-orbit coupling Journal of Optics 18, 124002 (2016).
- Schlederer et al. Cyclic transformation of orbital angular momentum modes New Journal of Physics 18, 043019 (2016).
- Fickler et al. Custom-tailored spatial mode sorting by controlled random scattering Physical Review B 95, 161108(R) (2017).
- Fickler et al. Real-time imaging of quantum entanglement Scientific Reports 3, 1914 (2013).
- Fickler Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information Nature Communications 5, 4502 (2014).
- Rubinsztein-Dunlop et al. Roadmap on structured light Journal of Optics 19, 013001 (2017).
- Fickler et al. Quantum entanglement of high angular momenta Science 338, 640-643 (2012).
- Fickler et al. Quantum entanglement of angular momentum states with quantum numbers up to 10,010 PNAS 113, 13642–13647 (2016).
- Krenn et al. Generation and confirmation of a (100× 100)-dimensional entangled quantum system PNAS 111, 6243-6247 (2014).
- Malik et al. Multi-photon entanglement in high dimensions Nature Photonics 10, 248-252 (2016).
- Krenn et al. Automated Search for new Quantum Experiments Physical Review Letters 116, 090405 (2016).
- Bouchard et al. High-dimensional quantum cloning and applications to quantum hacking Science Advances 3, e1601915 (2017).
- Krenn et al. Communication with spatially modulated light through turbulent air across Vienna New Journal of Physics 16, 113028 (2014).
- Krenn et al. Twisted light transmission over 143 km PNAS 113, 13648–13653 (2016).
- Krenn et al. Twisted photon entanglement through turbulent air across Vienna PNAS 112, 14197-14201 (2015).
- Sit et al. High-Dimensional Intra-City Quantum Cryptography with Structured Photons, Optica 4, 1006 (2017)
- Beltran et al. Orbital angular momentum modes of high-gain parametric down-conversion Journal of Optics 19, 044005 (2017).
- Safari et al. Generation of Caustics and Spatial Rogue Waves from Nonlinear Instability https://arxiv.org/abs/1706.01589
- Schnitzler et al. Deterministic ultracold ion source targeting the Heisenberg limit Physical Review Letters 102 (7), 70501 (2009).
- Schnitzler et al. Focusing a deterministic single-ion beam New Journal of Physics 12 (6), 065023 (2010).
- Fickler et al. Optimised focusing ion optics for an ultracold deterministic single ion source targeting nm resolution Journal of Modern Optics 56 (18-19), 2061-2075 (2009).