Probing Sensitivity Near a Quantum Exceptional Point Using Waveguide Quantum Electrodynamics
Aziza Almanakly, Réouven Assouly, Harry Hanlim Kang, Michael Gingras, Bethany M. Niedzielski, Hannah Stickler, Mollie E. Schwartz, Kyle Serniak, Max Hays, Jeffrey A. Grover, William D. Oliver
Non-Hermitian Hamiltonians with complex eigenenergies are useful tools for describing the dynamics of open quantum systems. In particular, parity and time (PT) symmetric Hamiltonians have generated interest due to the emergence of exceptional-point degeneracies, where both eigenenergies and eigenvectors coalesce as the energy spectrum transitions from real to complex valued. Because of the abrupt spectral response near exceptional points, such systems have been proposed as candidates for precision quantum sensing. In this Letter, we emulate a passive PT dimer using a two-mode, non-Hermitian system of superconducting qubits comprising one high-coherence qubit coupled to an intentionally lossy qubit via a tunable coupler. The loss is introduced by strongly coupling the qubit to a continuum of photonic modes in an open waveguide environment. Using both pulsed and continuous-wave measurements, we characterize the system dynamics near the exceptional point. We observe a behavior broadly consistent with an ideal passive PT dimer with some corrections due to the tunable coupler element. We extract the complex eigenenergies associated with the two modes and calculate the sensitivity as a function of the coupling strength. Confirming theoretical predictions, we observe no sensitivity enhancement near the quantum exceptional point. This Letter elucidates the limitations of exceptional-point systems as candidates for quantum-enhanced sensing. We establish waveguide quantum electrodynamics as a versatile platform for exploring non-Hermitian quantum dynamics in superconducting circuits.
Non-Hermitian Hamiltonians with complex eigenenergies are useful tools for describing the dynamics of open quantum systems. In particular, parity and time (PT) symmetric Hamiltonians have generated interest due to the emergence of exceptional-point degeneracies, where both eigenenergies and eigenvectors coalesce as the energy spectrum transitions from real to complex valued. Because of the abrupt spectral response near exceptional points, such systems have been proposed as candidates for precision quantum sensing. In this Letter, we emulate a passive PT dimer using a two-mode, non-Hermitian system of superconducting qubits comprising one high-coherence qubit coupled to an intentionally lossy qubit via a tunable coupler. The loss is introduced by strongly coupling the qubit to a continuum of photonic modes in an open waveguide environment. Using both pulsed and continuous-wave measurements, we characterize the system dynamics near the exceptional point. We observe a behavior broadly consistent with an ideal passive PT dimer with some corrections due to the tunable coupler element. We extract the complex eigenenergies associated with the two modes and calculate the sensitivity as a function of the coupling strength. Confirming theoretical predictions, we observe no sensitivity enhancement near the quantum exceptional point. This Letter elucidates the limitations of exceptional-point systems as candidates for quantum-enhanced sensing. We establish waveguide quantum electrodynamics as a versatile platform for exploring non-Hermitian quantum dynamics in superconducting circuits.
Non-Hermitian systems exhibit phenomena absent from Hermitian systems, including exceptional points (EPs), at which two or more eigenvectors coalesce. Conventional implementations rely on gain and loss, which strongly limit quantum coherence. Here, following a proposal by Wang and Clerk (PRA 2019), we realize a closed four-mode quantum system that emulates the dynamics of a PT dimer - two coupled resonators with balanced gain and loss - without engineered dissipation. The four modes are implemented as harmonics of a superconducting coplanar-waveguide resonator, with parametric couplings engineered using a current-pumped SNAIL. We use this device as a sensor for small variations in the PT dimer coupling strength. From signal-to-noise-ratio measurements, we observe enhanced sensitivity near the EP in a non-quantum-limited regime.
ABSTRACT Exceptional points (EPs), singularities in non‐Hermitian systems where eigenvalues and eigenstates coalesce, exhibit unique spectral responses and enhanced sensitivity. However, in quantum‐interference settings such as two‐photon measurements, the interference transition generally does not occur at the EPs, limiting their applications for quantum sensing. To address this issue, we develop an anti‐parity‐time‐symmetric model based on indirectly coupled waveguides and introduce a cascaded‐waveguide configuration that produces an effective rotation of the system's eigenbasis. This modification shifts the two‐photon bunching‐antibunching transition to coincide with the EP. Near the EP, a small refractive‐index perturbation leads to a sharp change in visibility, which becomes more pronounced by increasing waveguide length. This passive, gain‐free design may minimize noise and offer a feasible route toward EP‐enhanced quantum phase sensing on integrated platforms.
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.
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.
Abstract Parity‐time (PT) symmetric systems with gain‐loss balanced structures can have entirely real eigenenergy spectra despite their non‐Hermitian nature, leading to peculiar discoveries such as single‐mode lasers, wireless power transfer, and non‐reciprocal light propagation. Recently, the study of PT‐symmetry has extended to the quantum realm, inspiring a search for PT‐symmetric quantum effects as well as their unique applications. Here, quantum entanglement and sensing with a PT‐symmetric system of two qubits are studied with Ising‐type interaction. It is shown that exceptional points (EPs) can induce exceptional entanglement phenomena such as collapse‐revival and steady‐state entanglement on the two sides of EPs. The entanglement in the PT‐symmetric system is also found to be generated more quickly than that in the Hermitian counterpart. In addition, a scheme for realizing EP‐enhanced quantum sensing is proposed by calculating the quantum Fisher information to estimate the parameters of the system. The work provides new insights into EP‐engineered quantum effects and can benefit a wide range of applications based on non‐Hermitian quantum devices.
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.