Quantum Simulation of Non-Hermitian Quantum Dynamics in Spin-Orbit Coupled Fermionic Gas

While spin-orbit coupling (SOC), an essential mechanism underlying quantum phenomena from the spin Hall effect to topological insulators, has been widely studied in well-isolated Hermitian systems, much less is known when the dissipation plays a major role in spin-orbit-coupled quantum systems. Here, we realize dissipative spin-orbit-coupled bands filled with ultracold fermions, and observe a parity-time ( $\mathcal{PT}$ ) symmetry-breaking transition as a result of the competition between SOC and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables the energy gap, opened by SOC, to be engineered and closed at the critical dissipation value, the so-called exceptional point (EP). The realized EP of the non-Hermitian band structure exhibits chiral response when the quantum state changes near the EP. This topological feature enables us to tune SOC and dissipation dynamically in the parameter space, and observe the state evolution is direction-dependent near the EP, revealing topologically robust spin transfer between different quantum states when the quantum state encircles the EP. This topological control of quantum states for non-Hermitian fermions provides new methods of quantum control, and also sets the stage for exploring non-Hermitian topological states with SOC.While spin-orbit coupling (SOC), an essential mechanism underlying quantum phenomena from the spin Hall effect to topological insulators, has been widely studied in well-isolated Hermitian systems, much less is known when the dissipation plays a major role in spin-orbit-coupled quantum systems. Here, we realize dissipative spin-orbit-coupled bands filled with ultracold fermions, and observe a parity-time ($\mathcal{PT}$) symmetry-breaking transition as a result of the competition between SOC and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables the energy gap, opened by SOC, to be engineered and closed at the critical dissipation value, the so-called exceptional point (EP). The realized EP of the non-Hermitian band structure exhibits chiral response when the quantum state changes near the EP. This topological feature enables us to tune SOC and dissipation dynamically in the parameter space, and observe the state evolution is direction-dependent near the EP, revealing topologically robust spin transfer between different quantum states when the quantum state encircles the EP. This topological control of quantum states for non-Hermitian fermions provides new methods of quantum control, and also sets the stage for exploring non-Hermitian topological states with SOC.

Jun 9, 20211 citation

Quantum-classical correspondence of non-Hermitian spin-orbit coupled bosonic junction

Xin Yan, Hongzheng Wu, Changwei Fan +5 more

Abstract We investigate the classical-quantum correspondence of non-Hermitian Spin-orbit (SO)-coupled bosonic junctions, where an effective decay term is introduced in one of the two wells. Starting from the normalized two-point functions, we analytically demonstrate that the mean-field system has a classical Hamiltonian structure, and we successfully derive a non-Hermitian discrete nonlinear Schrödinger (Gross–Pitaevskii) equation. We discover that near the symmetry-breaking phase transition point, the correspondence between classical (mean-field) and quantum dynamics is more likely to break down. Our numerical simulations of the full quantum model, limited to a finite number of particles due to computational constraints, reveal that when the effective spin–orbit coupling (SOC) strength takes half-integer values, atomic self-trapping in a non-lossy well consistently occurs regardless of the system parameters, and the corresponding quantum dynamics exhibit remarkable insensitivity to the number of particles in this scenario. Additionally, we reveal that in both the mean-field and many-particle models, the SOC effects can greatly promote the synchronous periodic oscillations between the spin-up and spin-down components, and this synchronous dynamic is closely related to symmetry.Abstract We investigate the classical-quantum correspondence of non-Hermitian Spin-orbit (SO)-coupled bosonic junctions, where an effective decay term is introduced in one of the two wells. Starting from the normalized two-point functions, we analytically demonstrate that the mean-field system has a classical Hamiltonian structure, and we successfully derive a non-Hermitian discrete nonlinear Schrödinger (Gross–Pitaevskii) equation. We discover that near the symmetry-breaking phase transition point, the correspondence between classical (mean-field) and quantum dynamics is more likely to break down. Our numerical simulations of the full quantum model, limited to a finite number of particles due to computational constraints, reveal that when the effective spin–orbit coupling (SOC) strength takes half-integer values, atomic self-trapping in a non-lossy well consistently occurs regardless of the system parameters, and the corresponding quantum dynamics exhibit remarkable insensitivity to the number of particles in this scenario. Additionally, we reveal that in both the mean-field and many-particle models, the SOC effects can greatly promote the synchronous periodic oscillations between the spin-up and spin-down components, and this synchronous dynamic is closely related to symmetry.

arXiv:2410.13176Physica ScriptaApr 2, 20252 citations

\mathcal{PT}

) symmetry-breaking transition as a result of the competition between SOC and dissipation. Tunable dissipation, introduced by state-selective atom loss, enables the energy gap, opened by SOC, to be engineered and closed at the critical dissipation value, the so-called exceptional point (EP). The realized EP of the non-Hermitian band structure exhibits chiral response when the quantum state changes near the EP. This topological feature enables us to tune SOC and dissipation dynamically in the parameter space, and observe the state evolution is direction-dependent near the EP, revealing topologically robust spin transfer between different quantum states when the quantum state encircles the EP. This topological control of quantum states for non-Hermitian fermions provides new methods of quantum control, and also sets the stage for exploring non-Hermitian topological states with SOC.