A metastable quantum state coupled to a continuum undergoes an exponential decay in the Weisskopf-Wigner (Markovian) approximation. However, quantum theory strictly predicts deviations from an exponential decay law both at small and long time scales. In multilevel systems, even in the Markovian approximation strong deviations from an exponential decay can be observed in the intermediate time scale owing to interference of overlapping resonances. Such interference effects are simply described by an effective non-Hermitian Hamiltonian and are known to explain, for example, the existence of dark states and fractional decay. Here we show that the wide variety of anomalous behaviors observed in multilevel quantum decay are rooted in the non-normal nature of the effective non-Hermitian Hamiltonian, revealing strong similarities between anomalous quantum mechanical decay and non-normal dynamics found in hydrodynamic flows. Major signatures of non-normal dynamics include delayed decay, accelerated decay, and exponential-power-law decay at an exceptional point. Such signatures are exemplified by suggesting simple tight-binding lattice realizations of multilevel quantum decay, which could be emulated in integrated photonic experiments. Finally, it is shown that for noninteracting particles with fermionic statistics the usual exponential decay law is restored, i.e., all anomalous decay effects arising from single-particle non-normal dynamics are washed out.
A metastable quantum state coupled to a continuum undergoes an exponential decay in the Weisskopf-Wigner (Markovian) approximation. However, quantum theory strictly predicts deviations from an exponential decay law both at small and long time scales. In multilevel systems, even in the Markovian approximation strong deviations from an exponential decay can be observed in the intermediate time scale owing to interference of overlapping resonances. Such interference effects are simply described by an effective non-Hermitian Hamiltonian and are known to explain, for example, the existence of dark states and fractional decay. Here we show that the wide variety of anomalous behaviors observed in multilevel quantum decay are rooted in the non-normal nature of the effective non-Hermitian Hamiltonian, revealing strong similarities between anomalous quantum mechanical decay and non-normal dynamics found in hydrodynamic flows. Major signatures of non-normal dynamics include delayed decay, accelerated decay, and exponential-power-law decay at an exceptional point. Such signatures are exemplified by suggesting simple tight-binding lattice realizations of multilevel quantum decay, which could be emulated in integrated photonic experiments. Finally, it is shown that for noninteracting particles with fermionic statistics the usual exponential decay law is restored, i.e., all anomalous decay effects arising from single-particle non-normal dynamics are washed out.
Controlling the decay dynamics of an unstable state coupled to a continuum is a longstanding problem of major interest in different areas of quantum and classical physics. Suppression of quan- tum mechanical decay and slow-down of the escape dynamics in macroscopic quantum and optical tunneling via dynamical decoupling methods have been proposed and experimentally demonstrated in different physical systems over the last two decades. So far most of dynamical decoupling schemes have been focused to Hermitian dynamics. In this work we consider the decay of an unstable state coupled to a continuum via a time-dependent non-Hermitian coupling with finite (albeit arbitrarily long) duration, and show rather generally that for a wide class of coupling temporal shapes, in which the real and imaginary parts of the coupling are related each other by a Hilbert transform, the metastable state returns to its initial condition after the interaction with the continuum. Re- markably, the absence of decay holds even beyond the weak-coupling (Markovian) limit and for arbitrarily slow (adiabatic) interactions. The method is illustrated by considering a paradigmatic example of decay dynamics of a metastable state coupled to a tight-binding continuum described by a Fano-Anderson model and realized by a semi-infinite tight-binding lattice. Non-Hermitian coupling can be implemented by fast modulation of the complex site energy of the edge site in the lattice.
Spontaneous emission of a quantum emitter, such as an excited atom, is a fundamental process in quantum electrodynamics (QED), typically associated with exponential decay to the ground state accompanied by irreversible photon emission. This simple Markovian picture, however, is profoundly modified in the presence of time-delayed feedback, structured continua, or cooperative emission, as occurs when an emitter radiates in front of a mirror, when several emitters radiate collectively, or in the case of a giant atom. In such regimes, strong non-Markovian dynamics arise from photon reabsorption and interference effects, leading to pronounced deviations from exponential decay. Here we demonstrate the emergence of exceptional points (EPs) in these highly non-Markovian waveguide-QED environments, i.e., non-Markovian EPs. These EPs appear directly in the relaxation dynamics as sharp transitions to oscillatory behavior, manifested by the appearance of real zeros in the excited-state amplitude. We analyze in detail the spontaneous emission of giant atoms with two or more coupling points, highlighting the mechanisms leading to non-Markovian EPs, and show that similar phenomena arise in other waveguide-QED settings, such as the collective spontaneous emission of spatially separated point-like emitters. Our results reveal waveguide-QED systems as experimentally accessible platforms for realizing and exploring non-Markovian EP physics.
While exponential decay is ubiquitous in nature, deviations at both short and long times are dictated by quantum mechanics. Nonexponential decay is known to arise due to the possibility of reconstructing the initial state from the decaying products. We discuss the quantum decay dynamics by tunneling of a many-particle system, characterizing the long-time nonexponential behavior of the nonescape and survival probabilities. The effects of contact interactions and quantum statistics are described. It is found that, whereas for noninteracting bosons the long-time decay follows a power law with an exponent linear in the number of particles N, the exponent becomes quadratic in N in the fermionic case. The same results apply to strongly interacting many-body systems related by the generalized Bose-Fermi duality. The faster fermionic decay can be traced back to the effective hard-core interactions between particles, which are as well the decaying products, and exhibit spatial antibunching which hinders the reconstruction of the initial unstable state. The results are illustrated with a paradigmatic model of quantum decay from a trap allowing leaks by tunneling, whose dynamics is described exactly by means of an expansion in resonant states.
The quantum Mpemba effect refers to the counterintuitive phenomenon in which a system initially farther from equilibrium relaxes faster than one prepared closer to it. Several mechanisms have been identified in open quantum systems to explain this behavior, including the strong Mpemba effect, non-Markovian memory, and initial system-reservoir entanglement. Here, we unveil a distinct mechanism rooted in the non-normal nature of the Liouvillian superoperator in Markovian dynamics. When the Liouvillian's eigenmodes are non-orthogonal, transient interference between decaying modes can induce anomalous early-time behavior-such as delayed thermalization or transient freezing-even though asymptotic decay rates remain unchanged. This differs fundamentally from strong Mpemba effects, which hinge on suppressed overlap with slow-decaying modes. We demonstrate this mechanism using a waveguide quantum electrodynamics model, where quantum emitters interact with the photonic modes of a one-dimensional waveguide. The directional and radiative nature of these couplings naturally introduces non-normality into the system's dynamics. As a result, certain initial states-despite being closer to equilibrium-can exhibit slower relaxation at short times. This work reveals a previously unexplored and universal source of Mpemba-like behavior in memoryless quantum systems, expanding the theoretical framework for anomalous relaxation and opening new avenues for control in engineered quantum platforms.
Both non-Hermitian systems and the behavior of emitters coupled to structured baths have been studied intensely in recent years. Here, we study the interplay of these paradigmatic settings. In a series of examples, we show that a single quantum emitter coupled to a non-Hermitian bath displays a number of unconventional behaviors, many without Hermitian counterpart. We first consider a unidirectional hopping lattice whose complex dispersion forms a loop. We identify peculiar bound states inside the loop as a manifestation of the non-Hermitian skin effect. In the same setting, emitted photons may display spatial amplification markedly distinct from free propagation, which can be understood with the help of the generalized Brillouin zone. We then consider a nearest-neighbor lattice with alternating loss. We find that the long-time emitter decay always follows a power law, which is usually invisible for Hermitian baths. Our Letter points toward a rich landscape of anomalous quantum emitter dynamics induced by non-Hermitian baths.
It is well known, both theoretically and experimentally, that the survival probability for an unstable quantum state, formed at t = 0 , is not a simple exponential function, even if the latter is a good approximation for intermediate times. Typically, unstable quantum states/particles can decay in more than a single decay channel. In this work, the general expression for the probability that an unstable state decays into a certain i -th channel between the initial time t = 0 and an arbitrary t > 0 is provided, both for nonrelativistic quantum states and for relativistic particles . These partial decay probabilities are also not exponential and their ratio turns out to be not a simple constant, as it would be in the exponential limit. Quite remarkably, these deviations may last relatively long, thus making them potentially interesting in applications. Thus, multichannel decays represent a promising and yet unexplored framework to search for deviations from the exponential decay law in quantum mechanical systems, such as quantum tunneling, and in the context of particle decays .