Decoherence-Induced Exceptional Points in a Dissipative Superconducting Qubit

Photonic Chiral State Transfer near the Liouvillian Exceptional Point

As branch-point singularities of non-Hermitian matrices, the exceptional points (EPs) exhibit unique spectral topology and criticality, with intriguing dynamic consequences in non-Hermitian settings. In quantum open systems, EPs also emerge in the Liouvillian spectrum, but their dynamic impact often pertains to the transient dynamics and is challenging to demonstrate. Here, using the flexible control afforded by single-photon interferometry, we study the chiral state transfer when the Liouvillian EP is parametrically encircled. Reconstructing the density-matrix evolution by experimentally simulating the quantum Langevin equation, we show that the chirality of the dynamics is only present within an intermediate encircling timescale and dictated by the landscape of the Liouvillian spectrum near the EP. However, the chirality disappears at long times as the system always relaxes to the steady state. We then demonstrate the power-law decay of the chirality in regard to the encircling time with a parameter-dependent exponent. Our experiment confirms the transient nature of chiral state transfer near a Liouvillian EP in quantum open systems, while our scheme paves the way for simulating general open-system dynamics using single photons.

Engineering Nonequilibrium Steady States through Floquet Liouvillians

We experimentally study the transient dynamics of a dissipative superconducting qubit under periodic drive toward its nonequilibrium steady states. The corresponding stroboscopic evolution, given by the qubit states at times equal to integer multiples of the drive period, is determined by a (generically non-Hermitian) Floquet Liouvillian. The drive period controls both the transients across its non-Hermitian degeneracies and the resulting nonequilibrium steady states. These steady states can exhibit higher purity compared to those achieved with a constant drive. We further study the dependence of the steady states on the direction of parameter variation and relate these findings to the recent studies of dynamically encircling exceptional points. Our Letter provides a new approach to control non-Hermiticity in dissipative quantum systems and presents a new paradigm in quantum state preparation and stabilization.

Observation of quantum strong Mpemba effect

An ancient and counterintuitive phenomenon known as the Mpemba effect (water can cool faster when initially heated up) showcases the critical role of initial conditions in relaxation processes. How to realize and utilize this effect for speeding up relaxation is an important but challenging task in purely quantum system till now. Here, we experimentally study the strong Mpemba effect in a single trapped ion system in which an exponentially accelerated relaxation in time is observed by preparing an optimal quantum initial state with no excitation of the slowest decaying mode. Also, we demonstrate that the condition of realizing such effect coincides with the Liouvillian exceptional point, featuring the coalescence of both the eigenvalues and the eigenmodes of the systems. Our work provides an efficient strategy to engineer the dynamics of open quantum system, and suggests a link unexplored yet between the Mpemba effect and the non-Hermitian physics.

Chiral Bell-State Transfer via Dissipative Liouvillian Dynamics

Chiral state transfer along closed loops in the vicinity of an exceptional point is one of the many counterintuitive observations in non-Hermitian physics. The application of this property beyond proof-of-principle in quantum physics, is an open question. In this work, we demonstrate chiral state conversion between singlet and triplet Bell states through fully quantum Liouvillian dynamics. Crucially, we demonstrate that this property can be used for the chiral production of Bell states from separable states with a high fidelity and for a large range of parameters. Additionally, we show that the removal of quantum jumps from the dynamics through postselection can result in near-perfect Bell states from initially separable states. Our work presents the first application of chiral state transfer in quantum information processing and demonstrates a novel way to control entangled states by means of dissipation engineering.

Chiral quantum heating and cooling with an optically controlled ion

Quantum heat engines and refrigerators are open quantum systems, whose dynamics can be well understood using a non-Hermitian formalism. A prominent feature of non-Hermiticity is the existence of exceptional points (EPs), which has no counterpart in closed quantum systems. It has been shown in classical systems that dynamical encirclement in the vicinity of an EP, whether the loop includes the EP or not, could lead to chiral mode conversion. Here, we show that this is valid also for quantum systems when dynamical encircling is performed in the vicinity of their Liouvillian EPs (LEPs), which include the effects of quantum jumps and associated noise-an important quantum feature not present in previous works. We demonstrate, using a Paul-trapped ultracold ion, the first chiral quantum heating and refrigeration by dynamically encircling a closed loop in the vicinity of an LEP. We witness the cycling direction to be associated with the chirality and heat release (absorption) of the quantum heat engine (quantum refrigerator). Our experiments have revealed that not only the adiabaticity breakdown but also the Landau-Zener-Stückelberg process play an essential role during dynamic encircling, resulting in chiral thermodynamic cycles. Our observations contribute to further understanding of chiral and topological features in non-Hermitian systems and pave a way to exploring the relation between chirality and quantum thermodynamics.

Entanglement signatures for quantum synchronization with single-ion phonon laser

The entanglement properties of quantum synchronization, based on a single-ion phonon laser subjected to an external drive, have been studied. It is found that the maximum value of steady-state entanglement between the ion's internal and external states occurs near the noiseless boundary from synchronization to unsynchronization, accompanied by noticeable oscillatory behaviors during the corresponding time evolution of entanglement. In addition, the later time dynamics of entanglement also indicates the occurrence of frequency entrainment, as evidenced by the strong consistency between the bending of the observed frequency and the emergence of Liouvillian exceptional points (LEPs) in the first two eigenvalues of the Liouvillian eigenspectrum. Moreover, the emergence of LEPs, which is intimately associated with frequency entrainment, should be widely observed in quantum synchronization and can be explored in LEPs-based applications.

Transfer learning from Hermitian to non-Hermitian quantum many-body physics

Identifying phase boundaries of interacting systems is one of the key steps to understanding quantum many-body models. The development of various numerical and analytical methods has allowed exploring the phase diagrams of many Hermitian interacting systems. However, numerical challenges and scarcity of analytical solutions hinder obtaining phase boundaries in non-Hermitian many-body models. Recent machine learning methods have emerged as a potential strategy to learn phase boundaries from various observables without having access to the full many-body wavefunction. Here, we show that a machine learning methodology trained solely on Hermitian correlation functions allows identifying phase boundaries of non-Hermitian interacting models. These results demonstrate that Hermitian machine learning algorithms can be redeployed to non-Hermitian models without requiring further training to reveal non-Hermitian phase diagrams. Our findings establish transfer learning as a versatile strategy to leverage Hermitian physics to machine learning non-Hermitian phenomena.

Multistage entanglement swapping using superconducting qubits in the absence and presence of dissipative environment without Bell state measurement

In recent decades the entangled state generation is of great importance in the quantum information processing and technologies. In this paper, producing the distributed entangled state of superconducting (SC) qubits is considered using an entanglement swapping protocol in three successive stages. The SC qubit pairs [Formula: see text] with [Formula: see text], where each pair of the qubits has been placed on a separate chip, are initially prepared in maximally entangled states. The external magnetic fields on capacitively coupled pairs [Formula: see text] and [Formula: see text] are implemented for modulating the frequency of qubits. Then, the SC qubits [Formula: see text] and [Formula: see text] are converted into entangled states via operating proper measurements instead of Bell state measurement (which is generally a hard task). Finally, the distributed entangled state of target SC qubits [Formula: see text] can be obtained by applying external magnetic fields on qubits [Formula: see text] and via operating suitable measurements. This process is studied in the absence and presence of thermal decoherence effects. The concurrence, as a measure of entanglement between two target qubits, success probability of the distributed entangled states and the corresponding fidelities are evaluated, by which we find that the state of target SC qubits [Formula: see text] is converted to Bell state with maximum entanglement at some moments of time. Under appropriate conditions the maximum of success probability of the obtained states in each stage approaches 1. However, the maxima of concurrence and success probability gradually decrease due to the thermal noise as time goes on. Moreover, compelling amounts of fidelity, success probability and entanglement can be obtained for the achieved entangled states.

Parametrically driving a quantum oscillator into exceptionality

The mathematical objects employed in physical theories do not always behave well. Einstein's theory of space and time allows for spacetime singularities and Van Hove singularities arise in condensed matter physics, while intensity, phase and polarization singularities pervade wave physics. Within dissipative systems governed by matrices, singularities occur at the exceptional points in parameter space whereby some eigenvalues and eigenvectors coalesce simultaneously. However, the nature of exceptional points arising in quantum systems described within an open quantum systems approach has been much less studied. Here we consider a quantum oscillator driven parametrically and subject to loss. This squeezed system exhibits an exceptional point in the dynamical equations describing its first and second moments, which acts as a borderland between two phases with distinctive physical consequences. In particular, we discuss how the populations, correlations, squeezed quadratures and optical spectra crucially depend on being above or below the exceptional point. We also remark upon the presence of a dissipative phase transition at a critical point, which is associated with the closing of the Liouvillian gap. Our results invite the experimental probing of quantum resonators under two-photon driving, and perhaps a reappraisal of exceptional and critical points within dissipative quantum systems more generally.

Observation of Exceptional Points in Thermal Atomic Ensembles

Exceptional points (EPs) in non-Hermitian systems have recently attracted wide interest and spawned intriguing prospects for enhanced sensing. However, EPs have not yet been realized in thermal atomic ensembles, which is one of the most important platforms for quantum sensing. Here we experimentally observe EPs in multilevel thermal atomic ensembles and realize enhanced sensing of the magnetic field for 1 order of magnitude. We take advantage of the rich energy levels of atoms and construct effective decays for selected energy levels by employing laser coupling with the excited state, yielding unbalanced decay rates for different energy levels, which finally results in the existence of EPs. Furthermore, we propose the optical polarization rotation measurement scheme to detect the splitting of the resonance peaks, which makes use of both the absorption and dispersion properties and shows an advantage with enhanced splitting compared with the conventional transmission measurement scheme. Additionally, in our system both the effective coupling strength and decay rates are flexibly adjustable, and thus the position of the EPs are tunable, which expands the measurement range. Our Letter not only provides a new controllable platform for studying EPs and non-Hermitian physics, but also provide new ideas for the design of EP-enhanced sensors and opens up realistic opportunities for practical applications in the high-precision sensing of magnetic field and other physical quantities.

Universal Subdiffusive Behavior at Band Edges from Transfer Matrix Exceptional Points

We discover a deep connection between parity-time symmetric optical systems and quantum transport in one-dimensional fermionic chains in a two-terminal open system setting. The spectrum of one dimensional tight-binding chain with periodic on-site potential can be obtained by casting the problem in terms of 2×2 transfer matrices. We find that these non-Hermitian matrices have a symmetry exactly analogous to the parity-time symmetry of balanced-gain-loss optical systems, and hence show analogous transitions across exceptional points. We show that the exceptional points of the transfer matrix of a unit cell correspond to the band edges of the spectrum. When connected to two zero temperature baths at two ends, this consequently leads to subdiffusive scaling of conductance with system size, with an exponent 2, if the chemical potential of the baths are equal to the band edges. We further demonstrate the existence of a dissipative quantum phase transition as the chemical potential is tuned across any band edge. Remarkably, this feature is analogous to transition across a mobility edge in quasiperiodic systems. This behavior is universal, irrespective of the details of the periodic potential and the number of bands of the underlying lattice. It, however, has no analog in absence of the baths.

Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch

Nontrivial spectral properties of non-Hermitian systems can lead to intriguing effects with no counterparts in Hermitian systems. For instance, in a two-mode photonic system, by dynamically winding around an exceptional point (EP) a controlled asymmetric-symmetric mode switching can be realized. That is, the system can either end up in one of its eigenstates, regardless of the initial eigenmode, or it can switch between the two states on demand, by simply controlling the winding direction. However, for multimode systems with higher-order EPs or multiple low-order EPs, the situation can be more involved, and the ability to control asymmetric-symmetric mode switching can be impeded, due to the breakdown of adiabaticity. Here we demonstrate that this difficulty can be overcome by winding around exceptional curves by additionally crossing diabolic points. We consider a four-mode [Formula: see text]-symmetric bosonic system as a platform for experimental realization of such a multimode switch. Our work provides alternative routes for light manipulations in non-Hermitian photonic setups.

The effect of thermal photons on exceptional points in coupled resonators

We analyse two quantum systems with hidden parity-time ([Formula: see text]) symmetry: one is an optical device, whereas another is a superconducting microwave-frequency device. To investigate their symmetry, we introduce a damping frame (DF), in which loss and gain terms for a given Hamiltonian are balanced. We show that the non-Hermitian Hamiltonians of both systems can be tuned to reach an exceptional point (EP), i.e., the point in parameter space at which a transition from broken to unbroken hidden [Formula: see text] symmetry takes place. We calculate a degeneracy of a Liouvillian superoperator, which is called the Liouvillian exceptional point (LEP), and show that, in the optical domain, LEP is equivalent to EP obtained from the non-Hermitian Hamiltonian (HEP). We also report breaking the equivalence between LEP and HEP by a non-zero number of thermal photons for the microwave-frequency system.

Enhancement of Quantum Heat Engine by Encircling a Liouvillian Exceptional Point

Quantum heat engines are expected to outperform the classical counterparts due to quantum coherences involved. Here we experimentally execute a single-ion quantum heat engine and demonstrate, for the first time, the dynamics and the enhanced performance of the heat engine originating from the Liouvillian exceptional points (LEPs). In addition to the topological effects related to LEPs, we focus on thermodynamic effects, which can be understood by the Landau-Zener-Stückelberg process under decoherence. We witness a positive net work from the quantum heat engine if the heat engine cycle dynamically encircles a LEP. Further investigation reveals that a larger net work is done when the system is operated closer to the LEP. We attribute the enhanced performance of the quantum heat engine to the Landau-Zener-Stückelberg process, enabled by the eigenenergy landscape in the vicinity of the LEP, and the exceptional point-induced topological transition. Therefore, our results open new possibilities toward LEP-enabled control of quantum heat engines and of thermodynamic processes in open quantum systems.

Anomalous spontaneous emission dynamics at chiral exceptional points

An open quantum system operated at the spectral singularities where dimensionality reduces, known as exceptional points (EPs), demonstrates distinguishing behavior from the Hermitian counterpart. Here, we present an analytical description of local density of states (LDOS) for microcavity featuring chiral EPs, and unveil the anomalous spontaneous emission dynamics from a quantum emitter (QE) due to the non-Lorentzian response of EPs. Specifically, we reveal that a squared Lorentzian term of LDOS contributed by chiral EPs can destructively interfere with the linear Lorentzian profile, resulting in the null Purcell enhancement to a QE with special transition frequency, which we call EP induced transparency. While for the case of constructive interference, the squared Lorentzian term can narrow the linewidth of Rabi splitting even below that of bare components, and thus significantly suppresses the decay of Rabi oscillation. Interestingly, we further find that an open microcavity with chiral EPs supports atom-photon bound states for population trapping and decay suppression in long-time dynamics. As applications, we demonstrate the advantages of microcavity operated at chiral EPs in achieving high-fidelity entanglement generation and high-efficiency single-photon generation. Our work unveils the exotic cavity quantum electrodynamics unique to chiral EPs, which opens the door for controlling light-matter interaction at the quantum level through non-Hermiticity, and holds great potential in building high-performance quantum-optics devices.

Dynamical control of quantum heat engines using exceptional points

A quantum thermal machine is an open quantum system coupled to hot and cold thermal baths. Thus, its dynamics can be well understood using the concepts and tools from non-Hermitian quantum systems. A hallmark of non-Hermiticity is the existence of exceptional points where the eigenvalues of a non-Hermitian Hamiltonian or a Liouvillian superoperator and their associated eigenvectors coalesce. Here, we report the experimental realization of a single-ion heat engine and demonstrate the effect of Liouvillian exceptional points on the dynamics and the performance of a quantum heat engine. Our experiments have revealed that operating the engine in the exact- and broken-phases, separated by a Liouvillian exceptional point, respectively during the isochoric heating and cooling strokes of an Otto cycle produces more work and output power and achieves higher efficiency than executing the Otto cycle completely in the exact phase where the system has an oscillatory dynamics and higher coherence. This result opens interesting possibilities for the control of quantum heat engines and will be of interest to other research areas that are concerned with the role of coherence and exceptional points in quantum processes and in work extraction by thermal machines.