Exceptional points (EPs) have seen substantial advances in both experiment and theory. However, in quantum systems, higher-order EPs remain of great interest and possess numerous intriguing properties yet to be fully explored. Here we describe a parity-time symmetry-protected three-level non-Hermitian system with dissipative spin-orbit-coupled 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 the $^{173}\mathrm{Yb}$ fermion. We highlight the enhanced sensitivity to the external perturbation of the EP3 with cubic-root energy dispersion. Additionally, we investigate the second-order EP (EP2) with square-root energy dispersion in a three-level quantum system in the absence of parity symmetry, which proves that the enhanced sensitivity closely relates to the symmetries of the non-Hermitian system. Furthermore, we analyze the encircling behavior of the EP3 in terms of the slowly evolving limit and the nonadiabatic dynamics beyond the slowly evolving limit and discover some results different from those of the EP2.
Exceptional points (EPs) have seen substantial advances in both experiment and theory. However, in quantum systems, higher-order EPs remain of great interest and possess numerous intriguing properties yet to be fully explored. Here we describe a parity-time symmetry-protected three-level non-Hermitian system with dissipative spin-orbit-coupled 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 the 173Yb fermion. We highlight the enhanced sensitivity to the external perturbation of the EP3 with cubic-root energy dispersion. Additionally, we investigate the second-order EP (EP2) with square-root energy dispersion in a three-level quantum system in the absence of parity symmetry, which proves that the enhanced sensitivity closely relates to the symmetries of the non-Hermitian system. Furthermore, we analyze the encircling behavior of the EP3 in terms of the slowly evolving limit and the nonadiabatic dynamics beyond the slowly evolving limit and discover some results different from those of the EP2.
Non-Hermitian systems exhibit a variety of unique features rooted in the presence of exceptional points (EPs). The distinct topological structure in the proximity of an EP gives rise to counterintuitive behaviors absent in Hermitian systems, which emerge after encircling the EP either quasistatically or dynamically. However, experimental exploration of EP encirclement in quantum systems, particularly those involving high-order EPs, remains challenging due to the difficulty of coherently controlling more degrees of freedom. In this work, we experimentally investigate the eigenvalue braiding and state transfer arising from the encirclement of EP in a three-dimensional non-Hermitian quantum system using superconducting circuits. We characterize the second- and third-order EPs through the coalescence of eigenvalues. Then we reveal the topological structure near the EP3 by quasistatically encircling it along various paths with three independent parameters, which yields the eigenvalue braiding described by the braid group B 3 . Additionally, we observe chiral state transfer between three eigenstates under a fast driving scheme when no EPs are enclosed, while time-symmetric behavior occurs when at least one EP is encircled. Our findings offer insights into understanding non-Hermitian topological structures and the manipulation of quantum states through dynamic operations.
We study interacting ultracold atoms in a three-dimensional (3D) harmonic trap with spin-selective dissipations, which can be effectively described by non-Hermitian parity-time (PT) symmetric Hamiltonians. By exactly solving the non-Hermitian two-body problem of spin-1/2 (spin-1) bosons in a 3D harmonic trap, we find that the system can exhibit third-order (fifth-order) exceptional points (EPs) with ultrasensitive cube-root (fifth-root) spectral response due to interaction anisotropies in spin channels. We also present the general principle for the creation of high-order EPs and their spectral sensitivities with arbitrary particle number N and arbitrary spin s. Generally, with spin-independent interactions, the EP order of bosons can be as high as 2Ns+1, and the spectral response around EP can be as sensitive as $\ensuremath{\sim}{\ensuremath{\epsilon}}^{1/(2ks+1)}$ under a k-body interaction anisotropy. Moreover, we propose to detect the ultrasensitive spectral response through the probability dynamics of certain state. These results suggest a convenient route towards more powerful sensor devices in spinor cold atomic systems.
As one of the essential features in non-Hermitian systems coupled with environment, the exceptional point has attracted much attention in many physical fields. The phenomena that eigenvalues and eigenvectors of the system simultaneously coalesce at the exceptional point are also one of the important properties to distinguish from Hermitian systems. In non-Hermitian systems with parity-time reversal symmetry, the eigenvalues can be continuously adjusted in parameter space from all real spectra to pairs of complex-conjugate values by crossing the phase transition from the parity-time reversal symmetry preserving phase to the broken phase. The phase transition point is called an exceptional point of the system, which occurs in company with the spontaneous symmetry broken and many novel physical phenomena, such as sensitivity-enhanced measurement and loss induced transparency or lasing. Here, we focus on a two-qubit quantum system with parity-time reversal symmetry and construct an experimental scheme, prove and verify the features at its third-order exceptional point, including high-order energy response induced by perturbation and the coalescence of eigenvectors. We first theoretically study a two-qubit non-Hermitian system with parity-time reversal symmetry, calculate the properties of eigenvalues and eigenvectors, and prove the existence of a third-order exceptional point. Then, in order to study the energy response of the system induced by perturbation, we introduce an Ising-type interaction as perturbation and quantitatively demonstrate the response of eigenvalues. In logarithmic coordinates, three of the eigenvalues are indeed in the cubic root relationship with perturbation strength, while the fourth one is a linear function. Moreover, we study the eigenvectors around exceptional point and show the coalescence phenomenon as the perturbation strength becomes smaller. The characterization of the response of eigenvalues at high-order exceptional points is a quite diffcult task as it is in gneneral diffcult to directly measure eigenenergies in a quantum system composed of a few qubits. In practice, the time evolution of occupation on a particular state is used to indirectly fit the eigenvalues. In order to make the fitting of experimental data more reliable, we want to determine an accurate enough expressions for the eigenvalues and eigenstates. To this aim, we employ a perturbation treatment and show good agreement with the numerical results of states occupation obtained by direct evolution. Moreover, we find that after the system evolves for a long enough time, it will end up to one of the eigenstates, which gives us a way to demonstrate eigenvector coalescence by measuring the density matrix via tomography and parity-time reversal transformation. To show our scheme is experimentally applicable, we propose an implementation using trapped 171Yb+ ions. We can map the parity-time reversal symmetric Hamiltonian to a purely dissipative two-ion system:use microwave to achieve spin state inversion, shine a 370 nm laser to realize dissipation of spin-up state, and apply Raman operation for Mølmer-Sørensen gates to implement Ising interaction. By adjusting the corresponding microwave and laser intensity, the spin coupling strength, the dissipation rate and the perturbation strength can be well controlled. We can record the probability distribution of the four product states of the two ions and measure the density matrix by detecting the fluorescence of each ion on different Pauli basis.
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 (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.
Exceptional points (EPs) can induce strongly amplified responses to weak perturbations, but enhanced spectral sensitivity in conventional non-Hermitian systems does not necessarily translate into improved quantum-limited sensing because of the associated gain and loss noise. Here, we investigate a tunable EP sensing platform based on the intrinsic non-Hermitian Bogoliubov dynamics of a spin-orbit-angular-momentum-coupled Bose-Einstein condensate. Starting from a fully Hermitian microscopic Hamiltonian, we derive a Bogoliubov dynamical matrix that exhibits parity-time (PT) symmetry, with EPs tunable through the Raman coupling and interaction parameters. We identify multiple EPs and map their trajectories and associated stability landscapes, revealing strong quantum Fisher information enhancement when the EPs are approached from the PT-symmetric stable regime. We further find that the gap-opening rate around a second-order EP provides a useful relative indicator for comparing the sensing performance of EPs, while higher-order EPs are not necessarily accessible from the stable regime. Moreover, two second-order EPs can be tuned to overlap, allowing their sensing contributions to add and yielding a linear enhancement of the total quantum Fisher information. Finally, we show that a spin-density measurement can approach the quantum Fisher information limit, providing an experimentally accessible route to tunable EP-enhanced quantum sensing in Bose-Einstein condensates.
Non-Hermitian systems have attracted significant interest because of their intriguing properties, including exceptional points (EPs), where eigenvalues and the corresponding eigenstates coalesce. In particular, quantum systems with EPs exhibit an enhanced sensitivity to external perturbations, which increases with the order of the EP. Therefore, higher-order EPs hold significant potential for advanced sensing applications, but they are challenging to achieve due to stringent symmetry requirements. In this work, we study the dynamics of a generalized lossy waveguide beam splitter with asymmetric coupling by introducing non-reciprocity as a tunable parameter to achieve higher-order EPs even without dissipation. Moreover, we analyze the evolution of NOON-states under activated non-reciprocity, highlighting its impact on quantum systems. Our results open new pathways for realizing higher-order EPs in non-reciprocal open quantum systems.