Non-Hermitian systems satisfying parity-time (PT) symmetry have aroused considerable interest owing to their exotic features. Anti-PT symmetry is an important counterpart of the PT symmetry, and has been studied in various classical systems. Although a Hamiltonian with anti-PT symmetry only differs from its PT-symmetric counterpart in a global ±i phase, the information and energy exchange between systems and environment are different under them. It is also suggested theoretically that anti-PT symmetry is a useful concept in the context of quantum information storage with qubits coupled to a bosonic bath. So far, the observation of anti-PT symmetry in individual quantum systems remains elusive. Here, we implement an anti-PT-symmetric Hamiltonian of a single qubit in a single trapped ion by a designed microwave and optical control-pulse sequence. We characterize the anti-PTphase transition by mapping out the eigenvalues at different ratios between coupling strengths and dissipation rates. The full information of the quantum state is also obtained by quantum state tomography. Our work allows quantum simulation of genuine open-system feature of an anti-PT-symmetric system, which paves the way for utilizing non-Hermitian properties for quantum information processing.
In recent years, non-Hermitian parity-time (
PT)-symmetric quantum systems have gained significant attention due to their unique physical properties, with experimental realizations demonstrated across diverse platforms. Two popular approaches have been used to implement
PT-symmetric dynamics: one removes quantum jumps from dissipative natural atoms (e.g., cold atoms, trapped ions) or artificial atoms (e.g., superconducting qubits) through postselection whose experimental fidelity is severely limited by unavoidable population backflow effects; the other embeds the desired non-Hermitian Hamiltonian into a larger Hermitian system, which achieves higher fidelity but typically enables simulating
PT-symmetric dynamics only within restricted parameter regimes. This paper proposes and experimentally demonstrates a trapped-ion-based scheme for digital simulation of
PT-symmetric quantum systems with high fidelity across the full parameter space. By leveraging high-fidelity logic gates and postselection on a four-level single ion to synthesize the target
PT-symmetric dynamics, this approach enables accurate characterization of
PT-symmetric properties, especially the exotic features in the vicinity of the exceptional point (EP). Distinct dynamical properties in the
PT-symmetric unbroken phase (PTS),
PT-symmetric broken phase (PTB), and at the EP are experimentally demonstrated with the data agreeing well with theoretical predictions. This high-fidelity simulation scheme also enables precise measurement of quantum Fisher information (QFI) near the EP, essential for evaluating non-Hermitian quantum sensing performance. It is shown that, after accounting for the low postselection probability, QFI divergence near the EP vanishes, providing no more information than their Hermitian counterparts, which echoes with recent theoretical findings. Our scheme establishes a paradigm for full-parameter-space precise simulation of non-Hermitian effects in quantum systems, and is applicable to various other platforms.
In this paper we study exceptional-point (EP) effects and quantum sensing in a parity-time (PT)-symmetric two-qubit system with the Ising-type interaction. We explore EP properties of the system by analyzing degeneracy of energy eigenvalues or entanglement of eigenstates. We investigate entanglement dynamics of the two qubits in detail. In particular, we demonstrate that the system can create the steady-state entanglement in the PT-broken phase and collapse-revival phenomenon of entanglement in the PT-symmetric phase during the long-time evolution. We show that entanglement can be generated more quickly than the corresponding Hermitian system. Finally, we prove that the sensitivity of eigenstate quantum sensing for the parameters exhibits the remarkable enharncement at EPs, and propose a quantum-coherence measurement to witness the existence of EPs.
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.
Non-Hermitian systems with parity-time reversal (
PT) or anti-
PT symmetry have attracted a wide range of interest owing to their unique characteristics and counterintuitive phenomena. One of the most extraordinary features is the presence of an exceptional point, across which a phase transition with spontaneously broken
PT symmetry takes place. We implement a Floquet Hamiltonian of a single qubit with anti-
PT symmetry by periodically driving a dissipative quantum system of a single trapped ion. With stroboscopic emission and quantum state tomography, we obtain the time evolution of density matrix for an arbitrary initial state, and directly demonstrate information retrieval, eigenstate coalescence, and topological energy spectra as unique features of non-Hermitian systems.
Hermiticity in quantum mechanics ensures the reality of energies, while parity-time symmetry offers an alternative route. Interestingly, in a three-level system, parity-time symmetry-breaking can lead to third-order exceptional points with distinctive topological properties. Experimentally implementing this in open quantum systems requires two well-controlled loss channels, resulting in dynamics that challenges a pure non-Hermitian description. Here we address the challenge by employing two approaches to eliminate the effects of quantum jump terms, ensuring pure non-Hermitian dynamics in a dissipative trapped ion. Based on this, we experimentally observe a parity-time symmetry-breaking-induced third-order exceptional point through non-Hermitian absorption spectroscopy. Quantum state tomography further demonstrates the coalescence of three eigenstates into a single eigenstate at the exceptional point. Finally, we identify an intrinsic third-order Liouvillian exceptional point via quench dynamics. Our experiments can be extended to observe other non-Hermitian phenomena involving multiple dissipative levels and potentially find applications in quantum information technology. Parity-time symmetry breaking and related non-Hermitian phenomena, such as high-order exceptional points, have attracted significant interest across various experimental platforms. Here the authors demonstrate a third-order exceptional point induced by parity-time symmetry breaking in a dissipative trapped ion.