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Spin–orbit coupling is an essential mechanism underlying quantum phenomena such as the spin Hall effect and topological insulators 1 . It has been widely studied in well-isolated Hermitian systems, but much less is known about the role dissipation plays in spin–orbit-coupled systems 2 . Here we implement dissipative spin–orbit-coupled bands filled with ultracold fermions, and observe parity-time symmetry breaking as a result of the competition between the spin–orbit coupling and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables us to tune the energy gap and close it at the critical dissipation value, the so-called exceptional point 3 . In the vicinity of the critical point, the state evolution exhibits a chiral response, which enables us to tune the spin–orbit coupling and dissipation dynamically, revealing topologically robust chiral spin transfer when the quantum state encircles the exceptional point. This demonstrates that we can explore non-Hermitian topological states with spin–orbit coupling. Spin–orbit coupling is an important feature of isolated quantum systems, but less is known about how it responds to dissipation. An experiment in a cold atomic gas now shows how these two effects enable topologically robust spin transfer.

The concept of non-Hermiticity has expanded the understanding of band topology, leading to the emergence of counter-intuitive phenomena. An example is the non-Hermitian skin effect (NHSE) 1 , 2 , 3 , 4 , 5 , 6 – 7 , which involves the concentration of eigenstates at the boundary. However, despite the potential insights that can be gained from high-dimensional non-Hermitian quantum systems in areas such as curved space 8 , 9 – 10 , high-order topological phases 11 , 12 and black holes 13 , 14 , the realization of this effect in high dimensions remains unexplored. Here we create a two-dimensional (2D) non-Hermitian topological band for ultracold fermions in spin–orbit-coupled optical lattices with tunable dissipation, which exhibits the NHSE. We first experimentally demonstrate pronounced nonzero spectral winding numbers in the complex energy plane with nonzero dissipation, which establishes the existence of 2D skin effect. Furthermore, we observe the real-space dynamical signature of NHSE in real space by monitoring the centre of mass motion of atoms. Finally, we also demonstrate that a pair of exceptional points are created in the momentum space, connected by an open-ended bulk Fermi arc, in contrast to closed loops found in Hermitian systems. The associated exceptional points emerge and shift with increasing dissipation, leading to the formation of the Fermi arc. Our work sets the stage for further investigation into simulating non-Hermitian physics in high dimensions and paves the way for understanding the interplay of quantum statistics with NHSE. A two-dimensional non-Hermitian topological band is created in an ultracold system of fermions, which exhibits the non-Hermitian skin effect.

The power of machine learning (ML) provides the possibility of analyzing experimental measurements with a high sensitivity. However, it still remains challenging to probe the subtle effects directly related to physical observables and to understand physics behind from ordinary experimental data using ML. Here, we introduce a heuristic machinery by using machine learning analysis. We use our machinery to guide the thermodynamic studies in the density profile of ultracold fermions interacting within SU( N ) spin symmetry prepared in a quantum simulator. Although such spin symmetry should manifest itself in a many-body wavefunction, it is elusive how the momentum distribution of fermions, the most ordinary measurement, reveals the effect of spin symmetry. Using a fully trained convolutional neural network (NN) with a remarkably high accuracy of ~94% for detection of the spin multiplicity, we investigate how the accuracy depends on various less-pronounced effects with filtered experimental images. Guided by our machinery, we directly measure a thermodynamic compressibility from density fluctuations within the single image. Our machine learning framework shows a potential to validate theoretical descriptions of SU( N ) Fermi liquids, and to identify less-pronounced effects even for highly complex quantum matter with minimal prior understanding. The detection of the effects of spin symmetry in momentum distribution of an SU(N)-symmetric Fermi gas has remained challenging. Here, the authors use supervised machine learning to connect the spin multiplicity to thermodynamic quantities associated with different parts of the momentum distribution.

One of the most interesting directions in quantum simulations with ultracold atoms is the expansion of our capability to investigate exotic topological matter. Using sophisticated atom-light couplings in an atomic system, scientists have demonstrated several iconic lattice models that exhibit non-trivial band topology in a controlled manner.With atom-light couplings in atomic systems, scientists have demonstrated several iconic lattice models that exhibit non-trivial band topology in controlled manners, which expands our capability to investigate exotic topological matter.

The ultracold atom system serves as an exceptional and highly controllable platform for investigating topological matter induced by spin-orbit coupling. The realization of spin orbit coupling in both continuum and higher dimensional optical lattices has already been achieved in ultracold atom systems. Recent advancements in the field have expanded the horizons of ultracold atom research by incorporating dissipation, leading to the exploration of non-Hermitian physics.The first part of this thesis focuses on the realization of a two-dimensional non-Hermitian topological band for ultracold fermions in spin-orbit-coupled optical lattices with tunable dissipation. Through experimental examinations of the spectral topology in the complex eigenenergy plane, we provide evidence for the existence of the skin effect—a distinct feature characterized by pronounced nonzero spectral winding when dissipation is introduced to the system. In this system, we also demonstrate the creation of exceptional points (EPs) in momentum space, forming a pair connected by an open-ended bulk Fermi arc, which stands in contrast to the closed loops observed in Hermitian systems. Remarkably, these EPs dynamically shift as the level of dissipation increases, ultimately resulting in the formation of the Fermi arc. Our work not only sets the stage for further investigations into simulating non-Hermitian physics in higher dimensions but also paves the way for a deeper understanding of the interplay between quantum statistics and the non-Hermitian skin effect.The second part of this thesis introduces two applications of machine learning techniques in quantum gas experiments. In the first application, we propose a heuristic approach that utilizes machine learning analysis to classify SU(N)Fermi gases based on their time-of-flight density distributions. This framework showcases the ability of neural networks to effectively combine features from high momentum signals and density fluctuations, enabling the accurate discrimination of different SU(N)fermions. In the second application, we present successful identification of topological phase transitions achieved through the utilization of a deep convolutional neural network trained with experimental data obtained from a symmetry-protected topological system of spin orbit-coupled fermions.The work presented in this thesis opens a new avenue to explore the rich physics with ultracold atoms systems. The results of researches in this thesis not only sets the stage for further investigation into simulating non-Hermitian physics in high dimensions but also demonstrate the potential of machine learning techniques in enhancing the analysis of quantum gas experiments. The findings of this thesis will contribute to the development of future studies in the field of ultracold atom research and quantum simulation.

The concept of non-Hermiticity has expanded the understanding of band topology leading to the emergence of counter-intuitive phenomena. One example is the non-Hermitian skin effect (NHSE), which involves the concentration of eigenstates at the boundary. However, despite the potential insights that can be gained from high-dimensional non-Hermitian quantum systems in areas like curved space, high-order topological phases, and black holes, the realization of this effect in high dimensions remains unexplored. Here, we create a two-dimensional (2D) non-Hermitian topological band for ultracold fermions in spin-orbit-coupled optical lattices with tunable dissipation, which exhibits the NHSE. We first experimentally demonstrate pronounced nonzero spectral winding numbers in the complex energy plane with non-zero dissipation, which establishes the existence of 2D skin effect. Further, we observe the real-space dynamical signature of NHSE in real space by monitoring the center of mass motion of atoms. Finally, we also demonstrate that a pair of exceptional points (EPs) are created in the momentum space, connected by an open-ended bulk Fermi arc, in contrast to closed loops found in Hermitian systems. The associated EPs emerge and shift with increasing dissipation, leading to the formation of the Fermi arc. Our work sets the stage for further investigation into simulating non-Hermitian physics in high dimensions and paves the way for understanding the interplay of quantum statistics with NHSE.

We propose a flexible Raman lattice system for alkaline-earth-like atoms to theoretically investigate localization behaviors in a quasi-periodic lattice with controllable non-Hermiticity. Our analysis demonstrates that critical phases and mobility edges can arise by adjusting spin-dependence of the incommensurate potentials in the Hermitian regime. With non-Hermiticity introduced by spin-selective atom loss, our calculations reveal that critical localization behaviour in this system can be suppressed by dissipation. Our work provides insights into interplay between quasi-periodicity and non-Hermitian physics, offering a new perspective on localization phenomena.

Although classifying topological quantum phases have attracted great interests, the absence of local order parameter generically makes it challenging to detect a topological phase transition from experimental data. Recent advances in machine learning algorithms enable physicists to analyze experimental data with unprecedented high sensitivities, and identify quantum phases even in the presence of unavoidable noises. Here, we report a successful identification of topological phase transitions using a deep convolutional neural network trained with low signal-to-noise-ratio (SNR) experimental data obtained in a symmetry-protected topological system of spin-orbit-coupled fermions. We apply the trained network to unseen data to map out a whole phase diagram, which predicts the positions of the two topological phase transitions that are consistent with the results obtained by using the conventional method on higher SNR data. By visualizing the filters and post-convolutional results of the convolutional layer, we further find that the CNN uses the same information to make the classification in the system as the conventional analysis, namely spin imbalance, but with an advantage concerning SNR. Our work highlights the potential of machine learning techniques to be used in various quantum systems.

We introduce a flexible Raman lattice system for alakaline-earth like atoms to investigate localization behaviors in a quasi-periodic lattice with controllable non-Hermiticity. We demonstrate that critical phases and mobility edges can arise by adjusting spin-dependence of the incommensurate potentials in the Hermitian regime. With non-Hermiticity introduced by spin-selective atom loss, we find the localization behaviour in this system can be suppressed by dissipation. Our work provides insights into interplay between quasi-periodicity and non-Hermitian physics, offering a new perspective on localization phenomena.

Exceptional points (EPs) has seen substantial advances in both experiment and theory. However, in quantum systems, higher-order exceptional points remain of great interest and possess numerous intriguing properties yet to be fully explored. Here, we describe a PT symmetry-protected three-level non-Hermitian system with the dissipative spin-orbit-coupled (SOC) fermions in which a third-order exceptional point (EP3) emerges when both the eigenvalues and eigenstates of the system collapse into one. The band structure and its spin dynamics are explored for \\(^173\\)Yb fermions. We highlight the enhanced sensitivity to the external perturbation of EP3 with cubic-root energy dispersion. Additionally, we investigate the second-order exceptional point (EP2) with square-root energy dispersion in a three-level quantum system with the absence of parity symmetry, which proves that the enhanced sensitivity closely relates to the symmetries of the NH system. Furthermore, we analyze the encircling behavior of EP3 in terms of the adiabatic limit and the nonadiabatic dynamics and discover some different results from that of EP2.