Dynamical phase transitions in open quantum systems govern how nonequilibrium states relax toward a stationary state. We study these transitions experimentally using a discrete-time photonic quantum walk on a three-node graph. A tunable synthetic gauge flux and calibrated dephasing allow us to control time-reversal symmetry and the detailed balance properties of the effective Markovian dynamics. With detailed balance, we observe a first-order dynamical phase transition marked by a crossing of real Liouvillian eigenvalues. When detailed balance is broken, we observe a second-order dynamical phase transition at an exceptional point where eigenvalues and eigenvectors coalesce. By progressively reducing the dephasing strength, we track the crossover toward the quantum-coherent regime and determine that the transitions persist down to a finite threshold. Our results establish a controllable platform for the experimental investigation of a class of relaxation dynamical phase transitions governed by detailed balance and exceptional points, linking Liouvillian spectral topology to relaxation criticality.
Dynamical phase transitions in open quantum systems govern how nonequilibrium states relax toward a stationary state. We study these transitions experimentally using a discrete-time photonic quantum walk on a three-node graph. A tunable synthetic gauge flux and calibrated dephasing allow us to control time-reversal symmetry and the detailed balance properties of the effective Markovian dynamics. With detailed balance, we observe a first-order dynamical phase transition marked by a crossing of real Liouvillian eigenvalues. When detailed balance is broken, we observe a second-order dynamical phase transition at an exceptional point where eigenvalues and eigenvectors coalesce. By progressively reducing the dephasing strength, we track the crossover toward the quantum-coherent regime and determine that the transitions persist down to a finite threshold. Our results establish a controllable platform for the experimental investigation of a class of relaxation dynamical phase transitions governed by detailed balance and exceptional points, linking Liouvillian spectral topology to relaxation criticality.
Dynamical phase transitions in open quantum systems govern how non-equilibrium states relax toward a stationary state. We study these transitions experimentally using a discrete-time photonic quantum walk on a three-node graph. A tunable synthetic gauge flux and calibrated dephasing allow us to control time-reversal symmetry and the detailed balance properties of the effective Markovian dynamics. With detailed balance, we observe a first-order dynamical phase transition marked by a crossing of real Liouvillian eigenvalues. When detailed balance is broken, we observe a second-order dynamical phase transition at an exceptional point where eigenvalues and eigenvectors coalesce. By progressively reducing the dephasing strength, we track the crossover toward the quantum-coherent regime and determine that the transitions persist down to a finite threshold. Our results link Liouvillian spectral topology to relaxation criticality and demonstrate a controllable platform for engineered dissipative dynamics.
Abstract Dynamical phase transitions in the relaxation behavior of stochastic quantum walks are investigated, focusing on systems where coherent unitary evolution is periodically interrupted by dephasing. This interplay leads to a classicalization of the dynamics, effectively described by non‐equilibrium Markovian processes that can violate detailed balance. As a result, such systems exhibit a richer and more complex spectral structure than their equilibrium counterparts. Extending recent insights from classical Markov dynamics [G. Teza et al. , Phys. Rev. Lett. 130 , 207103 (2023)], it is demonstrated that these quantum‐classical hybrid systems can host not only first‐order dynamical phase transitions – characterized by eigenvalue crossings – but also second‐order transitions marked by the coalescence of eigenvalues and eigenvectors at exceptional points. Two paradigmatic models are analyzed: a quantum walk on a ring under gauge fields and a walk on a finite line with internal degrees of freedom, both exhibiting distinct mechanisms for breaking detailed balance. These findings reveal a novel class of critical behavior in open quantum systems, where decoherence‐induced classicalization enables access to non‐Hermitian spectral phenomena. Beyond their fundamental interest, these results offer promising implications for quantum technologies, including quantum simulation, error mitigation, and the engineering of controllable non‐equilibrium quantum states.
Open quantum systems generally do not perfectly preserve phase coherence: coupling to uncontrolled environments requires a density-matrix description based on the Liouvillian framework beyond pure-state wave evolution. Realizing and probing such dynamics in a programmable platform is therefore essential for connecting coherent physics to realistic dissipative settings. Here we implement a tunable open-system quantum walk in a photonic mesh lattice, where controlled phase noise produces adjustable dephasing and non-reciprocal gain-loss imbalance provides an independently tunable non-Hermitian drive. This allows us to continuously interpolate between coherent quantum walks and incoherent classical walks, and to observe how directional transport evolves in the Liouvillian regime. Using non-Hermitian skin dynamics as a probe, we measure the center-of-mass drift over both the coherence and non-Hermiticity parameters, revealing a crossover from coherence-enhanced to decoherence-enhanced transport in quantitative agreement with quantum-channel simulations. We further program spatial and temporal interfaces to demonstrate interface accumulation and a long-time drift governed by the instantaneous channel. Our results establish a controllable photonic platform for simulating open quantum dynamics and show that decoherence can actively reshape non-Hermitian transport.
One of the most remarkable features that distinguish open systems from closed ones is the presence of exceptional points (EPs), where two or more eigenvectors of a non-Hermitian operator coalesce, accompanying the convergence of the corresponding eigenvalues. So far, EPs have been demonstrated on a number of platforms, ranging from classical optical systems to fully quantum-mechanical spin-boson models. In these demonstrations, the reservoir that induced the non-Hermiticity was treated as a Markovian one, without considering its memory effect. We here present the first experimental demonstration of non-Markovian quantum EPs, engineered by coupling a Josephson-junction-based qubit to a leaky electromagnetic resonator, which acts as a non-Markovian reservoir. We map out the spectrum of the extended Liouvillian superoperator by observing the quantum state evolution of the qubit and the pseudomode, in which the memory of the reservoir is encoded. We identify a twofold second-order EP and a third-order EP in the Liouvillian spectrum, which cannot be realized with a Markovian reservoir. Our results pave the way for experimental exploration of exotic phenomena associated with non-Markovian quantum EPs.
Signaled by nonanalyticities in the time evolution of physical observables, dynamic quantum phase transitions (DQPTs) emerge in quench dynamics of topological systems and possess an interesting geometric origin captured by dynamic topological order parameters (DTOPs). In this Letter, we report the experimental study of DQPTs using discrete-time quantum walks of single photons. We simulate quench dynamics between distinct Floquet topological phases using quantum-walk dynamics and experimentally characterize DQPTs and the underlying DTOPs through interference-based measurements. The versatile photonic quantum-walk platform further allows us to experimentally investigate DQPTs for mixed states and in parity-time-symmetric nonunitary dynamics for the first time. Our experiment directly confirms the relation between DQPTs and DTOPs in quench dynamics of topological systems and opens up the avenue of simulating emergent topological phenomena using discrete-time quantum-walk dynamics.
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.