Collective Phenomena in Quantum Many-Body Physics: From Quantum Matter to Light

The effect of incommensurate/quasiperiodic modulations in crystals can dramatically change the nature of the quantum wavefunction. Upon increasing the strength of quasiperiodicity, electronic wave-functions can become localized/confined to a specific spatial region, in contrast with pristine crystals, where they extend throughout the system in the form of plane waves. The simplest model that captures the transition between extended and localized phases at a critical strength of quasiperiodic modulation is the celebrated Aubry-André model. This is a one-dimensional model of non-interacting tight-binding fermions in a cosine potential that is incommensurate with the lattice, which has a remarkable duality between localized and delocalized states. In a series of works, we showed that this duality, previously thought to be fine-tuned, is actually generic for many families of models but "hides" near the localization/delocalization transition [1,2]. Recently, we extended our study to localization transitions in one-dimensional systems of interacting spinless fermions. Interestingly, we showed that interactions of this type are irrelevant around the transition [3]. Furthermore, we found in this case the same scenario of hidden dualities that underlies non-interacting localization transitions. We achieved these results using a combination of numerical methods, finite-size scaling of correlation functions (Chalker scaling [4]), and renormalization group arguments. In this project, we study the role of electronic (i.e. spinful) interactions at the delocalization transition. Our goal is to determine if this type of interactions become relevant at the transition, as observed in disorder-driven transitions at higher dimensions [5], or if it remains irrelevant, as in the spinless case. We will also study whether hidden dualities emerge around this transition, and try to generalize our renormalization group method to this crucial case. The outcome of this work will allow us to understand if quasiperiodicity-driven localization transitions can always be well described by a non-interacting theory or if interactions may change the nature of this quantum phase transition. [1] Miguel Gonçalves, Bruno Amorim, Eduardo V. Castro, Pedro Ribeiro, SciPost Phys. 13, 046 (2022) [2] Miguel Gonçalves, B. Amorim, Eduardo V. Castro, and Pedro Ribeiro, Phys. Rev. B 108, L100201 (2023) [3] Miguel Gonçalves, Jedediah H. Pixley, Bruno Amorim, Eduardo V. Castro, Pedro Ribeiro, arXiv:2304.09197 (2023) [4] J. T. Chalker and G. J. Daniell, Phys. Rev. Lett. 61, 593 (1988) [5] D. Belitz and T. R. Kirkpatrick, Rev. Mod. Phys. 66, 261 (1994)

A quasi two-dimensional superfluid confined into a rotating trap is characterised by the presence of quantized vortices. According to the Point Vortex model, each vortex is effectively described as a massless point-like particle around which the superfluid flows with quantized circulation. However, it has been observed that vortex cores may host massive particles, for example when the superfluid is a binary mixture of atomic Bose-Einstein condensates. For such massive vortices an Effective Point-like Dynamical Model has been derived from a Time Dependent Variational Approximation scheme. The aim of this research was to investigate the main effects of core mass on the static and dynamic properties of vortex patterns formed according to the trap rotation. The study was carried out semianalytically and based on the global minimization of system's free energy, as well as on solving the system's dynamical equations. As regards the non-trivial oscillations of a vortex crystal, it has been observed a linear superposition of the Tkachenko modes, characteristic of massless vortices, and cyclotron-like modes associated to a non-zero core mass.

Exciton-polariton condensates have recently been explored theoretically and experi- mentally as ultrafast nonlinear optical elements for both digital and analog computing [1]. This growing interest comes from their all-optical tunability and measuring their response in situ, as well as the possibility of building distinct lattice configurations using structured excitation light (e.g. spatial light modulators) [2]. In this scenario, we explore the possibility of employing a lattice of polariton condensates as a neural network (NN). Distinct from previous works that mostly focus on reservoir computing [3] and binarized networks [4], here we propose a deep-learning device whose interactions between polariton condensates from distinct lattice sites are trainable by all-optical means [5]. We start our preliminary analysis by describing the condensate NN using the discretized driven-dissipative Gross-Pitaevskii equation (dGPE) [5]. Considering the limit of fast active reservoir relaxation and equal condensation density in all lattice sites, the dGPE particularly corresponds to the paradigmatic Kuramoto model of phase-coupled oscillators, which allows obtaining a variational energy function that depends on both the condensate phase and interaction between nearest neighbor condensates. Due to this variational feature, we propose applying equilibrium propagation [6] for training the NN of polariton condensates. We expect that through proper training of the synaptic weights, i.e., the interaction between nearest neighbor condensates, the number of required neurons (condensates) will dramatically decrease, making a practical device design much more feasible. We further expect that our optical-based training strategies will enhance the overall energy efficiency of the proposed polariton NN architecture while maintaining high accuracy. [1] A. Opala and M. Matuszewski, Opt. Mater. Express 13, 2674-2689 (2023). [2] J. D. Töpfer, I. Chatzopoulos, H. Sigurðsson, et al., Optica 8, 106–113 (2021). [3] D. Ballarini, A. Gianfrate, R., A. Opala, et al., Nano Letters 20 (5), 3506-3512 (2020). [4] R. Mirek, A. Opala, P. Comaron, et al., Nano Letters 21 (9), 3715-3720 (2021). [5] S. Alyatkin, J.D. Töpfer, A. Askitopoulos, et al., Phys. Rev. Lett. 124, 207402 (2020). [6] B. Scellier Y. and Bengio, Front. Comput. Neurosci. 11, 24 (2017).

When bosonic atoms are trapped in a potential well and cooled down to very low temperatures, their de Broglie wavelength becomes of the order of their mean interaction distance. The system undergoes a phase transition for which a fraction of atoms are trapped in the ground state. The condensed phase can be extened to the whole system by lowering the temperature even more. The trapped atoms all belong to a global wave function. Nowadays, it is possible to study the behavior of condensates trapped in electromagnetic potential wells. Furthermore, it is possible to design interference experiments for matter waves.

In this poster I aim to describe my work on developing magic wavelength traps for ultracold strontium atoms to enhance quantum metrology and quantum information processing. We have constructed the optical setups for a 2D magneto-optical trap (MOT) and a 3D blue MOT for cooling strontium atoms. Currently, we are optimizing the atomic beam in the 2D MOT. My main focus is now on building an optics breadboard for an 813 nm laser to create a 1D lattice, enabling precise control over clock transitions. This work will potentially investigate applications in optical tweezers, Rydberg interactions, and qubits.

The variational method is widely used to describe the ground state of a quantum system. The better the variational trial wave function, the lower its energy. However, there is usually little information on how close it is to the actual ground state. This can be helped by providing a lower bound on energy by using the idea of Anderson [1]. One writes the Hamiltonian as a sum of sub-Hamiltonians on finite clusters to get a lower bound. The sum of the ground state energies of the sub-Hamiltonians is lower than the actual ground state energy of the system. By allowing free parameters in the sub-Hamiltonians, one can maximize the energy of their ground state and get a good estimate for the lower bound. In this work, I considered the one-dimensional chains \begin{equation} \mathcal{H}=\sum_{i} \mathcal{H}_{N}(i) , \end{equation} with the sub-Hamiltonian defined on an $N$-length chain segment as \begin{equation} \mathcal{H}_{N}(i)=\sum_{j=1}^{N-1}\mathcal{J}_{j,j+1} h_{i+j,i+j+1}. \end{equation} In the segment (finite cluster), $h_{j,j+1}$ acts on the sites $j$ and $j+1$ with $\mathcal{J}_{j,j+1}$ interaction strength $\mathcal{J}_{j,j+1}$. The $h_{j,j+1}$ describes fermions hopping between nearest neighbors or spins interacting by Heisenberg interaction. For spinless free fermions and the spin-1/2 Heisenberg chain on moderately large $N$ (say $N=10$), we found that the maximal ground state energy realizes when the bond strength becomes uniform over the whole lattice and the $\mathcal{J}_{j,j+1}$ parameters follow \begin{equation} \mathcal{J}_{j,j+1} \propto \sin^2{\left(\frac{\pi j}{N}\right)}. \end{equation} These models, known as the sine-square deformation, are used to suppress finite-size effects and boundary oscillations (like Friedel oscillation) caused by open edges [2,3]. Our work establishes a connection between the sine-square deformation and the method to get optimal lower bounds for the ground state energy. [1] P. W. Anderson, \textit{Phys. Rev.} \textbf{83}, 1260 (1951). [2] A. Gendiar, R. Krcmar, and T. Nishino, \textit{Prog. Theor. Phys.} \textbf{122}, 953 (2009). [3] Hosho Katsura, \textit{J. Phys. A: Math. Theor.} \textbf{45}, 115003, (2012).

Our research is focused on producing a new species of fermionic molecules, $^6\mathrm{Li}^{87}\mathrm{Rb}$ (LiRb), which possess a pronounced dipole moment. This study explores the potential transition from a dipolar Bardeen-Cooper-Schrieffer (BCS) superfluid composed of diatomic molecules to a Bose-Einstein condensate (BEC) of tetraatomic molecules near a field-linked resonance. The anticipated critical temperature for observing these unique quantum phases is estimated to be about 14% of the Fermi temperature. This value is notably three times lower than the lowest temperature achieved with previously created molecular Fermi gases, such as in NaK molecules. LiRb molecules exhibit a substantial molecular-frame dipole moment of 4.1 Debye, which significantly exceeds the dipole moments observed in other known fermionic ground-state molecules, being seven times greater than that of KRb and 1.5 times that of NaK. Moreover, the advanced cooling techniques that have been developed for Li and Rb atoms, combined with favorable inter-species collision properties, enable the production of a large Fermi gas of LiRb molecules at exceptionally low temperatures. This advancement is pivotal for exploring dipolar superfluidity and the BEC of polyatomic molecules. We are constructing a highly compact and miniaturized vacuum system designed for the rapid experimental cycle times of ultracold LiRb molecules, which is one of the highlights of this experiment. This new system significantly simplifies the experimental process for producing quantum degenerate gases of polar molecules. By reducing the complexity of the experimental setup, researchers can concentrate more effectively on exploring novel physical phenomena in molecular Fermi gases.

Robert Matysiak$^{1,2}$, Markus Peil$^{3}$, Joonas Hilska$^{3}$, Teemu Hakkarainen$^{3,4}$, Anna Musiał$^{1}$ and Michał Gawełczyk$^{2}$ 1 Department of Experimental Physics, Wrocław University of Science and Technology, Poland 2 Institute of Theoretical Physics, Wrocław University of Science and Technology, Poland 3 Optoelectronics Research Centre, Physics Unit, Tampere University, Finland 4Tampere Institute for Advanced Study, Tampere University, Finland The classical cryptography is based on the complexity of mathematics behind it (e.g. factorisation of big biprime numbers), while the quantum one is based on the fundamental laws of quantum mechanics (e.g. no-cloning theorem). The widely known BB84 protocol requires non-classical sources of single photons (SPS) for achieving functional and secure transmission of quantum information. Additionally, the emission wavelength of such SPS has to match the third telecommunication window to take advantage of the low-loss transmission via existing fiber-based infrastructure. Usage of epitaxial semiconductor quantum dots (QDs) seems to be the most promising option. Indeed, over the last two decades, droplet-epitaxy etched almost strain-free GaAs/AlGaAs QDs have been shown to provide unmatched optical quality e.g., QD ensemble homogeneity, purity and indistinguishability of single-photons, photon pair entanglement fidelity). Unfortunately, emitted photons of arsenide QDs are not at telecom wavelengths. We propose to use an alternative material platform, namely type I GaSb QDs on AlGaSb surface. Thus combining QDs growth proven advantageous for QD optical quality at shorter wavelengths and maturity of GaSb platform in terms of methodology for device integration on the Si platform. There are strong indications that such QDs may serve as high-quality SPS working at the third transmission window This contribution focuses on the theoretical aspects of the project. To obtain the theoretical predictions of the QDs’ optical properties, we follow a multistep theoretical work beginning with the use a custom state-of-the-art software employing a multi-band theoretical \textbf{k}$\cdot$\textbf{p} framework. In the calculation, we take into account the impact of strain and piezoelectric effects included up to second order in strain tensor elements, spin-orbit coupling and arbitrary external fields. In that manner, we compute the electron and hole quantum states. using many-body calculations like configuration interactions. On top of that, properties of complexes of two or more carriers need to be calculated. To find these many-particle states, we use the configuration interaction method. This calculation yields the states of so-called excitons (interaction electron-hole pair) and higher complexes well as their binding energies. We also calculate a quantum states of excitons, biexcitons, trions and their binding energies. As we want to use the QD as an emitter coupled to either free of confined electromagnetic field, we use the formalism of quantum optics to describe the emission process and gain insight into the optical properties. Based on large-scale simulations over wide multidimensional parameter space, we are able to estimate the optimal QD parameters providing the best possible optical properties of GaSb QDs. This constitutes important feedback for guiding the growth of QDs with enhanced properties and data for comparison with results of optical experiments. It also provides important insight into description of electronic structure and fundamental optical properties for this novel type of QDs. This work was financed by FiGAnti project funded within the QuantERA II Programme that has received funding from the European Union’s Horizon 2020 research and innovation programme under Grant Agreement No 101017733 and National Science Centre, Poland- project 2023/05/Y/ST3/00125.

Recent developments in simulating open quantum systems utilize highly effective Matrix Product Operator (MPO) representations to capture the temporal correlations of strongly coupled non-Markovian environments. We present how a novel approach based on infinite MPO evolution [1] can be used for efficient computation of a driven dynamics and both linear and non-linear response. This method also allows us to directly calculate the Floquet propagator, enabling the extraction of the asymptotic Floquet state without resorting to real-time evolution. We apply our results to a driven spin-boson model. [1] Valentin Link, Hong-Hao Tu, and Walter T. Strunz, Open Quantum System Dynamics from Infinite Tensor Network Contraction, Phys. Rev. Lett. 132, 200403 (2024)

Excitations not only determine the low-temperature properties of a system, such as specific heat or susceptibility but also provide indications about the nature of the ground state. Such excitations in magnetic systems are called magnons. Magnons can interact, and this interaction can lead to a bound state. In contrast to single-magnon excitations, the exact behavior of two-magnon bound states is less well understood. A repulsive interaction between magnons leads to an antiferromagnetic state when the magnons condense. Conversely, if the interaction between the magnons is attractive, condensation of the two-magnon bound states can occur, leading to a nematic phase that does not break time reversal invariance. This problem has been addressed in a recent article on first- and second-neighbour coupling in a square lattice [1]. This work investigates two-magnon excitations in the Heisenberg model with first-, second-, and third-neighbor interactions in a triangular lattice. I first constructed the model's phase diagram using the Luttinger-Tisza method and the dispersion relation of magnons in the ferromagnetic state. After deriving the Schrödinger equation describing the interaction of two magnons, we solved it using a self-consistent approach by decomposing the interaction term into a sum of products of partial waves. For the case when the total momentum of the two-magnon bound state is at the high-symmetry $\Gamma$ or $K$ point in the Brillouin zone, the self-consistent equation decouples according to the irreducible representations of the $D_{6}$ point group. Assuming that the bound state first appears at high-symmetric points, I determined where the bound state gap vanishes at the ferromagnetic phase boundary, thus the parameter range over which a nematic phase can occur. [1] S. Jiang, et al., Phys. Rev. Lett. 130, 116701 (2023)

TBD

In a cold atom experiment, atoms are laser cooled to temperatures very close to absolute zero, in order to produce a localized and coherent sample of atoms suitable for experiments. Preparing an atomic sample typically involves multiple experimental steps, but the most common workhorse of such experiments is the magneto-optical trap (MOT). A magneto-optical trap generates a trapping and confining force from the interplay between magnetic fields and intersecting lasers. For strontium, the atom most commonly used to build the world's most accurate atomic clocks, there are commonly two MOT stages; a broad blue-light ${}^1 S_0 - {}^1 P_1$ MOT that brings the atomic sample into the mK level, and a narrow-line red ${}^1 S_0 - {}^3 P_1$ MOT that can cool the atom into the lower $\micro$K level. In this poster, we present an efficient light distribution system for said red MOT. We will discuss the narrow-line cooling regimes and investigations of the trapped MOT atoms. Future work will include loading atoms into tweezer arrays and build large superposition states through entangled Rydberg interactions. The experiment aims to combine the words of quantum computing and optical lattice clocks to investigate new physics, and challenge state-of-the-art quantum metrology as well as quantum information processing techniques.

Recently magnetic skyrmions received considerable attention due to their potential in spintronic devices as information carriers. Magnetic properties of skyrmions are often described by a classical Heisenberg model with tensorial couplings. We have developed a conjugate gradient method to find the local minima of the energy of a classical spin system. I was able to create precise skyrmions using this method. I determined the radius of the skyrmion as a function of the applied external magnetic field and compared my results to experiments. By analyzing the energy of an isolated skyrmion and of pair of skyrmions in the case of FePd bilayer on Ir(111) substrate$^1$ interactions can be derived as a function of the separation of the skyrmions. The knowledge of the pair interactions permits us to perform Monte Carlo simulations treating skyrmions as quasi particles. 1. Phys. Rev. B 93, 024417 (2016)

The adiabatic theorem guarantees that a transition between two states coupled by means of a weak perturbation is possible if the system is driven past an avoided crossing. Quench dynamics is notoriously complex but some asymptotic results can be obtained, in the form of the Landau-Zener formula. We have identified new classes of adiabatic transitions which cannot be described directly using this paradigm and have a more general theory which allows us to calculate asymptotic fidelities of (a)diabatic preparations of these more general kinds. We are also looking into ways to apply this to Rydberg atoms where adiabatic sweeps are possible due to the advent of chirped lasers and anticipate that new schemes based on this theory would reduce the number of adiabatic passages required in adiabatic preparation schemes. Collaborators: Dr Rejish Nath, Siddharth Seetharaman (While we do have a lot of work already done, I am not completely certain that we will have this up on Arxiv by the time of the school. In case of such an issue, I would be able to present my previous work on a new experimentally feasible scheme for quantum computing using the atom-optics kicked rotor. (https://doi.org/10.48550/arXiv.2406.13211) )

It is known that for isolated quantum many-body systems, it can be hard to describe thermalization dynamically because the time evolution is untary so generaly no information of the initial state will lose. However, we can see relaxation clearly in the subsystem of an isloated quantum system, for example few spins in an one-dimensinal XX spin chain. Recently a quantity named entanglement asymmetry is presented to describe the character of subsystem relaxation.(https://doi.org/10.1038/s41467-023-37747-8) I seek for a speed limit for general subsystem relaxation using entanglement asymmetry as a measure of distance. The speed limit shows the character that the larger the subsystem, the lower its relaxation. I have some progress of this problem, but I haven't solved it completely yet.