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.
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.
The exceptional point has presented considerably interesting and counterintuitive phenomena associated with nonreciprocity, precision measurement, and topological dynamics. The Liouvillian exceptional point (LEP), involving the interplay of energy loss and decoherence inherently relevant to quantum jumps, has recently drawn much attention due to capability to fully capture quantum system dynamics and naturally facilitate non-Hermitian quantum investigations. It was also predicted that quantum jumps could give rise to third-order LEPs in two-level quantum systems for its high dimensional Liouvillian superoperator, which, however, has never been experimentally confirmed until now. Here we report the first observation of the third-order LEPs emerging from quantum jumps in an ultracold two-level trapped-ion system. Moreover, by combining decay with dephasing processes, we present the first experimental exploration of LEPs involving combinatorial effect of decay and dephasing. In particular, due to non-commutativity between the Lindblad superoperators governing LEPs for decay and dephasing, we witness the movement of LEPs driven by the competition between decay and dephasing occurring in an open quantum system. This unique feature of non-Hermitian quantum systems paves a new avenue for modifying nonreciprocity, enhancing precision measurement, and manipulating topological dynamics by tuning the LEPs.
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.
Topological phenomena are fundamentally underlain by the geometric phase of eigenstates. Time-varying Hamiltonians furthermore allow for a dynamical topological invariant associated with continuous flows. We study chiral and nonreciprocal dynamics by encircling the exceptional points (EPs) of non-Hermitian Hamiltonians in a trapped ion system. We find that these dynamics are topologically robust against external perturbations even in the presence of dissipation-induced nonadiabatic transitions. Furthermore, our results indicate that these behaviors are protected by dynamical vorticity—an emerging topological invariant associated with the energy dispersion of non-Hermitian band structures in a parallel transported eigenbasis. Through the quantum state tomography, the symmetry breaking and other key features of topological dynamics are directly verified. These results mark a significant step towards exploring topological properties of open quantum systems. The complex energy surface of a non-Hermitian system is not single-valued, and windings around its so-called exceptional branching points lead to the chiral and non-reciprocal transfer of eigenstates. Here, the authors experimentally demonstrate such topological state transfers in trapped ion systems, which are being established as promising platforms for quantum simulation.
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.
Exceptional points (EPs) of a non-Hermitian Hamiltonian with parity-time-reversal (PT) symmetry have the potential to drastically enhance the capabilities of metrology and sensing through their power-law growing sensitivity to external perturbation. With the ability of generating and tuning dissipation in a single trapped ion system, we observe rich dynamics and detailed quantum phase transitions from the PT-symmetric phase to the symmetry-breaking phase. In this single qubit full quantum system, we develop a method to precisely determine the location of EP without any fitting parameter, and extract the eigenvalues in a unified way through all parameter regions. We can also obtain the full density matrix by quantum state tomography. Finally, we suggest from theoretical analysis that the periodically driving PT-symmetric non-Hermitian system can be used to measure the magnitude, frequency, and phase of time-dependent perturbation with EP enhancement.
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.