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+---
+title: "Quantum control theory for Bose-Einstein condensates"
+promoter: Karel Van Acoleyen, Alain Sarlette
+supervisor: Clara Tanghe
+contact: Clara Tanghe
+topic: "Bose-Einstein condensate as a quantum simulator"
+year: "2024"
+---
+
+#### Context
+
+A central problem in quantum sciences and technology - whether it is in the context of quantum computing, quantum sensing or quantum experiments (quantum simulation) - is the preparation of a desired target quantum state using the limited available resources (time, experimental control). The new research field of **quantum control merges concepts of classical control theory with the intricacies of quantum physics** to find optimal preparation protocols. While quantum systems cover essentially all dynamics in the universe, this thesis will focus on **developing quantum control strategies inspired by** a particular application: **ultra-cold quantum many body states** (see e.g. [1-2]) **that we are creating in our Bose-Einstein condensate (BEC) lab**.
+
+In summary, a BEC consists of >10.000 bosonic atoms (Rb87 in our case) that are cooled to temperatures T<1 microKelvin. At these temperatures a new phase of matter emerges, the so called Bose-Einstein condensate, with all the atoms condensed into one collective quantum state. The unique feature of cold atom experiments such as ours is the high level of control: carefully tuned electromagnets and lasers provide many ‘knobs’ for manipulating the BEC and thereby realizing new experiments that can explore different aspects of the quantum realm. We have launched our experimental effort in 2022 and are now ready to start the first original experiments, in which quantum control will play a crucial role.
+
+[1] Optimal control of complex atomic quantum systems, S. van Frank et al, [arXiv:1511.02247](https://arxiv.org/abs/1511.02247)
+
+[2] Shortcuts to adiabaticity: concepts, methods, and applications, D. Guéry-Odelin et al, [arXiv:1904.08448](https://arxiv.org/abs/1904.08448)
+
+#### Goal
+
+The goal of the thesis is to study, develp and apply control theory in the quantum context, in particular in the context of BEC physics. A specific quantum control task that we have in mind involves the coherent splitting of the BEC in two separate clouds (A and B), with a particular relative complex phase between the clouds. This relative phase can be interpreted as a piece of quantum data that is hidden in the correlation between A and B (see [3]), which can only be read out by looking at the interference patterns that emerge in time of flight images. The aim then is to design the optimal driving protocols that allow for maximal control on this relative phase. On the one hand this will entail simulations of the famous Gross-Pitaevskii equation (with existing numerical packages and/or within a to be determined approximation), that can describe the evolution of the BEC state under different driving conditions. On the other hand, the plan is also to test optimized driving protocols that come out of this numerical work in the actual experiment.
+
+
+
+
+
+As such this thesis consists of **a blend of theory and numerical work in the context of quantum physics and quantum information, in combination with the unique opportunity to collaborate on a cutting-edge cold atom experiment**. Depending on the interest and skill of the student the topic can be oriented more towards theory, more towards numerics or more towards the actual experiment.
+
+
+[3] Quantum nonlocality in the presence of superselection rules and data hiding protocols, F. Verstraete, J.I. Cirac, [arXiv:0302039](https://arxiv.org/abs/quant-ph/0302039)
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diff --git a/_thesistopics/2024/CTanghe2.md b/_thesistopics/2024/CTanghe2.md
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+---
+title: "Engineering synthetic dimensions in cold atom systems"
+promoter: Karel Van Acoleyen
+supervisor: Akshay Shankar, Clara Tanghe
+contact: Akshay Shankar
+topic: "Bose-Einstein condensate as a quantum simulator"
+year: "2024"
+---
+
+#### Context
+
+The physics of interacting many-body systems has been of great interest to researchers for decades, as they host a variety of wildly exotic phenomena emerging from the rich interplay of quantum effects. However, a large class of these systems remain theoretically and numerically intractable due to an exponential growth of the system description. The concept of **quantum simulation** is a particularly elegant formulation designed to tackle this, originally proposed by Feynman [1]. It is based on the idea of engineering the Hamiltonian of an experimentally controllable quantum system, such that its dynamics can be used as a proxy to understand the physics of seemingly unrelated models that are encoded within it. Such a construction is, in fact, so flexible that it not only provides insight into condensed matter systems, but also into systems of relevance to cosmology and high-energy physics. In recent years, the spectacular advances in experimental techniques facilitating a high degree of control and manipulation of atoms has led to the emergence of cold‐atom experiments as a versatile platform for realizing such quantum simulators.
+
+One such experiment is hosted within our own **Bose-Einstein condensate** (BEC) lab, wherein, thousands of Rb87 atoms are cooled down to the order of micro-Kelvins such that a new phase of matter emerges (i.e., a BEC) that is fundamentally quantum in nature. Such a phase arises from the sudden condensation of all the atoms into a collective state, resulting in a macroscopic quantum object that can be manipulated with laser spots and magnetic fields. This experimental effort was originally initiated in 2022 and we are now ready to start with the first original experiments. A particularly powerful feature of the setup is its flexible projection system that allows us to 'paint' arbitrary potentials onto the BEC, paving the way to encode Hamiltonians into the system. One possible route to achieve this is by applying a periodically driven external potential on the system, such that the time-averaged dynamics are governed by the encoded Hamiltonian, an approach that is broadly known as **Floquet engineering** [2].
+
+While there exist several techniques for engineering new Hamiltonians, a particularly interesting one involves the manufacturing of **synthetic dimensions** [3]. The basic idea is to introduce a coupling between internal degrees of the system and re‐interpret their behavior as dynamics along an effective spatial dimension. This allows us to then simulate the physics of lattice models using our continuous BEC system. A simple way to realize such a construction is by leveraging the formalism of periodically driven systems as mentioned above, and early attempts at this have been corroborated by experiments as well [4]. As a result, this line of research shows considerable promise in realizing exotic quantum dynamics and is an exciting avenue to pursue, motivated by the access to our very own cold-atom experiment.
+
+[1] Simulating Physics with Computers, Richard P. Feynman, [doi:10.1007/BF02650179](https://vql.cs.msu.ru/Feynman.pdf)
+
+[2] Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields, N. Goldman, J. Dalibard, [arXiv:1404.4373](https://arxiv.org/abs/1404.4373)
+
+[3] Hannah M. Price, Tomoki Ozawa, Nathan Goldman, Synthetic dimensions for cold atoms from shaking a harmonic trap, [arXiv:1605.09310](https://arxiv.org/abs/1605.09310)
+
+[4] Bloch oscillations along a synthetic dimension of atomic trap states, C. Oliver, et. al., [arXiv:2112.1064](https://arxiv.org/abs/2112.1064)
+
+#### Goal
+
+Initial attempts at manufacturing synthetic dimensions involve rather simple approaches such as the periodic driving of a linear-gradient potential on a non-interacting BEC system [4]. The effects of including interactions as well as the capabilities of more carefully constructed driving schemes remains unexplored.
+
+The goal of this thesis is to understand and develop one such novel periodic driving scheme to engineer a non-trivial lattice Hamiltonian, with a focus on realizing it in our BEC setup. This will involve experimenting with various driving schemes and identifying relevant observables and their experimental signatures that can be detected in our setup. To begin with, the student will familiarize themselves with the formalism of Floquet dynamics of periodically driven systems. This will enable them to formulate theoretically-motivated driving potentials and study their dynamics through numerical simulations of the Gross-Pitaevskii equation using existing software libraries. An ambitious student may also attempt to augment their schemes to mitigate certain unwanted effects, such as the micro-motion [2] resulting from Floquet driving.
+
+As such this thesis consists of **a blend of theory and numerical work in the context of quantum physics, in combination with the unique opportunity to collaborate on a cutting-edge cold atom experiment**. Depending on the interest and skill of the student the topic can be oriented more towards theory, more towards numerics or more towards the actual experiment.
+
+
+ 
+
+
diff --git a/_thesistopics/2024/CTanghe3.md b/_thesistopics/2024/CTanghe3.md
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+---
+title: "Holographic light shaping for quantum simulation"
+promoter: Karel Van Acoleyen
+supervisor: Clara Tanghe
+contact: Clara Tanghe
+topic: "Bose-Einstein condensate as a quantum simulator"
+year: "2024"
+---
+
+#### Context
+
+“Nature isn't classical, dammit, and if you want to make a simulation of nature, you'd better make it quantum mechanical, and by golly it's a wonderful problem, because it doesn't look so easy.” The new blooming field of **quantum simulation** [1] is turning these memorable words of Feynman, uttered more than 40 years ago, into reality. It is based on the idea of engineering the Hamiltonian of an experimentally controllable quantum system, such that its dynamics can be used as a proxy to understand the physics of seemingly unrelated models that are encoded within it. Such a construction is, in fact, so flexible that it not only provides insight into condensed matter systems, but also into systems of relevance to cosmology and high-energy physics.
+
+In recent years, the spectacular advances in experimental techniques facilitating a high degree of control and manipulation of atoms has led to the emergence of cold‐atom experiments as a versatile platform for realizing such quantum simulators. One such experiment is hosted within our own **Bose-Einstein condensate** (BEC) lab, wherein, thousands of Rb87 atoms are cooled down to the order of micro-Kelvins such that a new phase of matter emerges (i.e., a BEC) that is fundamentally quantum in nature. Such a phase arises from the sudden condensation of all the atoms into a collective state, resulting in a macroscopic quantum object that can be manipulated with laser spots and magnetic fields. This experimental effort was originally initiated in 2022 and we are now ready to start with the first original experiments.
+
+The crucial part of the set-up that gives us the finest control both in space and in time is the laser projection system that allows us to shape the light-field that interacts with the atoms. This system is based on Acousto Optical Deflectors (AOD), see for example Ref [2] where they consider attractive light fields.
+
+The AODs contain a crystal whose refractive index can be altered via perturbing it with a sound wave. This creates effectively a diffraction grating for a light beam that passes through this crystal. By programming a simple sinusoidal waveform into the crystal, the diffraction angle of the light can be adjusted. Using different frequencies in the sine wave, this diffracts the light beam in different deflection angles. However, recently a new promising approach emerged for programming optimal diffraction gratings into the AODs, based on the holographic framework. This approach comprises of a more advanced description of the complete light field in terms of changes in amplitude and phase, see Ref [3].
+
+
+ 
+ 
+
+
+[1] Simulating Physics with Computers, Richard P. Feynman, [doi:10.1007/BF02650179](https://vql.cs.msu.ru/Feynman.pdf)
+
+[2] Precise shaping of laser light by an acousto-optic deflector, D. Trypogeorgos, et al., [arXiv:1307.6734](https://arxiv.org/abs/1307.6734)
+
+[3] Artifact-free holographic light shaping through moving acousto-optic holograms, D. Treptow, et al., [doi:10.1038/s41598-021-00332-4](https://doi.org/10.1038/s41598-021-00332-4)
+
+#### Goal
+
+The goal of this thesis is to study and engineer the holographic method unto our AODs with the aim to create specific target potentials, thereby further developing our system towards a full-fledged quantum simulator. As such, the student has the opportunity to **develop and apply numerical methods and quantum optics theory on a cutting-edge quantum experiment**.
+
+The student will start by familiarizing themselves with the workings of an AOD and with the theory of the holographic method on these components. Studying which algorithms, e.g. the Gerchberg-Saxton algorithm, can be adapted to the usage in our system to optimize the information of the target potential into the encodings of the AODs. Then the student will implement the holographic method on the system and compare with the naïve deflection angle method. This encompasses writing code to program the sound wave into the AODs, and taking and analyzing the resulting data of the projected potential. Depending on the interest of the student, machine learning tools such as neural networks, can be applied to improve the light shaping in an automated fashion.
+
+
+
+
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