[Paper Review] Chiral control of quantum states in non-Hermitian spin-orbit-coupled fermions

Zejian Ren, Dong Liu+5 more|arXiv (Cornell University)|Jun 9, 2021

Quantum Mechanics and Non-Hermitian Physics7 citations

TL;DR

This study demonstrates chiral control of quantum states in ultracold fermions with engineered spin-orbit coupling and tunable dissipation, realizing a parity-time (PT) symmetry-breaking transition at an exceptional point (EP). By dynamically encircling the EP in parameter space, the experiment observes direction-dependent spin transfer—providing direct evidence of non-adiabatic, chiral quantum state evolution in a many-body fermionic system, a hallmark of non-Hermitian topological physics.

ABSTRACT

Spin-orbit coupling is an essential mechanism underlying quantum phenomena such as the spin Hall effect and topological insulators. 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. 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. 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.

Motivation & Objective

• To investigate the interplay between spin-orbit coupling and non-Hermitian dissipation in a quantum many-body system.
• To observe the parity-time (PT) symmetry-breaking transition in a synthetic non-Hermitian Hamiltonian realized with ultracold fermions.
• To demonstrate chiral quantum state transfer by encircling the exceptional point in parameter space.
• To explore the topological nature of non-Hermitian quantum phases in a fully quantum regime with fermionic statistics.

Proposed method

• Engineered spin-orbit coupling in ultracold 40K fermions using Raman lasers with two hyperfine states.
• Implemented state-selective atom loss via a detuned laser beam to create tunable, spin-dependent dissipation (γ↓).
• Controlled the system's evolution by dynamically tuning the loss rate and transverse momentum (qx) to encircle the exceptional point in parameter space.
• Performed time-of-flight imaging and spin-resolved measurements after adiabatic or non-adiabatic encircling to detect chiral state transfer.
• Used numerical simulations of the non-Hermitian effective Hamiltonian to model state conversion efficiency and validate experimental observations.
• Applied optical Stern-Gerlach pulses to measure final spin polarization after encircling, enabling quantification of chiral transfer.

Experimental results

Research questions

• RQ1 How does non-Hermitian dissipation affect the energy spectrum and topological properties of spin-orbit-coupled fermions?
• RQ2 Can a parity-time (PT) symmetry-breaking transition be experimentally realized in a many-body ultracold fermionic system?
• RQ3 What is the role of non-adiabatic dynamics near the exceptional point in determining quantum state evolution?
• RQ4 How does the chiral response of the quantum state depend on the direction and speed of encircling the exceptional point?
• RQ5 Can topologically robust chiral spin transfer be observed in a fermionic system with engineered non-Hermiticity?

Key findings

• The system exhibits a parity-time (PT) symmetry-breaking transition at a critical loss rate γ↓ = 10 Er, where the energy gap closes at the exceptional point (EP).
• When the EP is encircled in a counterclockwise direction over 10.1 ms, the initial |↓⟩ state is predominantly transferred to |↑⟩ with a conversion efficiency C ≫ 0, indicating chiral state evolution.
• For clockwise encircling, the spin transfer efficiency drops to C = 0, confirming the chiral nature of the non-adiabatic response.
• The chiral behavior vanishes when the EP is far from the encircling loop (e.g., at γ↓^max = 2 Er), confirming the dependence on proximity to the EP.
• Numerical simulations show that slower encircling (longer T) enhances non-adiabatic transitions and lowers the threshold for chiral transfer, consistent with experimental observations.
• The system's dynamics are well described by a 2×2 non-Hermitian effective Hamiltonian, with quantum jump effects negligible due to rapid relaxation of hole excitations on the Fermi energy timescale.