Quantum measurements severely disrupt the dynamic evolution of a quantum system by collapsing the probabilistic wavefunction. This principle can be leveraged to control quantum states by effectively freezing the system's dynamics or enhancing transitions between states. These are known as the quantum Zeno effect (ZE) and anti-Zeno effect (AZE), respectively. However, it remains elusive how quantum measurements affect topological states, which are famous for their robustness against disorder and perturbations. Here, we theoretically and experimentally show that the dynamic evolution of topological boundary states (TBSs) can be controlled by quantum-like measurement (QLM). Our work is based on spatially modulated topological acoustic waveguide systems with varying parameters that adiabatically pump the TBS across the bulk to the opposite boundary. Therein, the QLM is emulated using a perturbation to the Hamiltonian known as the Zeno subspace. With the help of quantum metrics, we identify the general conditions for ZE and AZE, and experimentally demonstrate their effects in freezing and accelerating the tunneling of the TBS. Furthermore, we discover a tunneling mechanism by varying the strength of the QLM. These results highlight QLM as a versatile tool for manipulating topological states and wave propagation.
Quantum measurements severely disrupt the dynamic evolution of a quantum system by collapsing the probabilistic wavefunction. This principle can be leveraged to control quantum states by effectively freezing the system's dynamics or enhancing transitions between states. These are known as the quantum Zeno effect (ZE) and anti-Zeno effect (AZE), respectively. However, it remains elusive how quantum measurements affect topological states, which are famous for their robustness against disorder and perturbations. Here, we theoretically and experimentally show that the dynamic evolution of topological boundary states (TBSs) can be controlled by quantum-like measurement (QLM). Our work is based on spatially modulated topological acoustic waveguide systems with varying parameters that adiabatically pump the TBS across the bulk to the opposite boundary. Therein, the QLM is emulated using a perturbation to the Hamiltonian known as the Zeno subspace. With the help of quantum metrics, we identify the general conditions for ZE and AZE, and experimentally demonstrate their effects in freezing and accelerating the tunneling of the TBS. Furthermore, we discover a tunneling mechanism by varying the strength of the QLM. These results highlight QLM as a versatile tool for manipulating topological states and wave propagation.
Measurements fundamentally alter the evolution of a quantum system by disturbing its state, which can either freeze its dynamics (quantum Zeno effect, ZE) or accelerate transitions (anti-Zeno effect, AZE). While these effects are well established for ordinary quantum states, their impact on topological states-renowned for their robustness against disorder-has remained unexplored. Here we explore this interplay in a classical wave analog of quantum dynamics, demonstrating both theoretically and experimentally that topological boundary states can be controlled by quantumlike measurements implemented in spatially modulated acoustic waveguides. By introducing controlled perturbations, we emulate repeated measurements and reveal how they freeze or accelerate boundary-state tunneling. Using a geometric framework based on the quantum metric, we identify the general conditions for ZE and AZE, and further uncover a new tunneling mechanism enabled by varying measurement strength. These results establish quantumlike measurement as a versatile tool for manipulating topological states and wave propagation, with broad relevance to photonic, elastic, and quantum systems.
The quantum-Zeno and anti-Zeno effects (QZE/AZE) are known for a long time, in a quantum system with coupled levels, the measurement of a particular level population can lead to either acceleration (i.e. AZE) or retardation (i.e. QZE) of its population transfer to other levels. Here we consider how one can control the population flow from a coupled quantum state by measurement at a particular time, and what system parameters are responsible for that. We propose a framework for analysis of quantum Zeno dynamics based on time-dependent density matrix perturbation theory. This framework allows us to clearly separate state populations from their coherences and to predict appearance of either QZE or AZE. We illustrate our analysis on two model systems: 1) two coupled levels and 2) a level coupled to a continuum. In both cases dynamics of quantum coherences play a crucial role, and perturbative considerations allow us to predict the effect of projective measurements. In addition, we have extended our consideration to a closely related coherent control scenario, a unitary transformation flipping a sign of a state in a coherent superposition describing the system wavefunction.
In quantum systems, a counterintuitive phenomenon known as quantum Zeno dynamics is usually exploited to tailor and protect the coherent evolution of quantum states by the back action of quantum measurements and strong couplings. Here, with the quantum-classical analogy, we report that the acoustic Zeno dynamics can be reproduced in acoustic waveguide arrays by setting segmented waveguides. We experimentally demonstrate that the segmented waveguide acts as an acoustic barrier to tailor the whole Hilbert space into different subspaces by separating the communication between waveguides. By arranging the acoustic Zeno barriers, we can control the sound transport in waveguide arrays into the target output ports, such as the Zeno dynamics, analog-quantum walk, and analog-quantum logic gates. In this context, we highlight that the Zeno barrier can be a versatile tool to arbitrarily control and guide the sound transport in waveguide arrays, which can provide an alternative choice for acoustic metamaterials and metasurfaces without cumbersome and complicated structure design. The acoustic Zeno barrier may provide a versatile approach to manipulate acoustic wave propagation for designing advanced on-chip integrated sound devices.
If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected "quantum Zeno subspace" is called "quantum Zeno dynamics:" for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.
Abstract. If frequent measurements ascertain whether a quantum system is still in its initial state, transitions to other states are hindered and the quantum Zeno effect takes place. However, in its broader formulation, the quantum Zeno effect does not necessarily freeze everything. On the contrary, for frequent projections onto a multidimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. The continuing time evolution within the projected “quantum Zeno subspace ” is called “quantum Zeno dynamics: ” for instance, if the measurements ascertain whether a quantum particle is in a given spatial region, the evolution is unitary and the generator of the Zeno dynamics is the Hamiltonian with hard-wall (Dirichlet) boundary conditions. We discuss the physical and mathematical aspects of this evolution, highlighting the open mathematical problems. We then analyze some alternative strategies to obtain a Zeno dynamics and show that they are physically equivalent.
Frequent observations to a quantum system modify its coherent evolution through the Zeno effect and Zeno dynamics. Generally, the measurement process destroys the evolution environment of the monitored system, making repeated observations remain a challenge. Here, using the quantum analogy experiments, we realize and engineer the Zeno effect and Zeno dynamics in optical waveguide arrays, where the optical modes correspond to distinct quantum states, and the temporal evolution is mapped into the spatial propagation. We propose a new, extensible experimental strategy for realizing an optical analog of stroboscopic measurements, which are performed by the build-in, on-demand segmented waveguide portions. The weak-to-strong stroboscopic measurements are realized, where the monitored system undergoes a transition from free evolution to optical Zeno freezing. Setting the measurements in the strong regime, the optical Zeno effect and optical Zeno dynamics are successfully generated, and their relationship is demonstrated in optics. We then propose a novel quantum Zeno slicing approach, which allows us to dynamically engineer the Hilbert space of the monitored system. This generic approach is verified by generating a series of Zeno subspaces with different measurement projectors, based on the quantum-optical analogy. The complexity of light dynamics is largely increased, providing full control of the propagation via steering Zeno dynamics. Our results pave the way for manipulation of quantum states by harnessing Zeno dynamics in integrated photonics.