The quantum mechanical decay of two or more overlapped resonances in a common continuum is largely influenced by Fano interference, leading to important phenomena such as the existence of bound states in the continuum, fractional decay and quiescent dynamics for single particle decay, and signature of particle statistics in the many-body quantum decay. An overlooked yet essential requirement to observe Fano interference is time reversal symmetry of the bath. Here we consider multilevel quantum decay in a bath sustaining unidirectional (chiral) propagating states, such as in quantum Hall or in Floquet topological insulators, and show that the chiral nature of scattering states fully suppresses Fano interference among overlapping resonances. As a result, there are not bound states in the continuum, quantum decay is complete, and there is not any signature of particle statistics in the decay process. Nonetheless, some interesting features are disclosed in the multilevel decay dynamics in a topological bath, such as the appearance of high-order exceptional points, long quiescent dynamics followed by a fast decay, and the possibility to observe damped non-Hermitian Bloch oscillations.
We study the decay of a prepared state $E_0$ into a continuum {E_k} in the case of non-Ohmic models. This means that the coupling is $|V_{k,0}| \propto |E_k-E_0|^{s-1}$ with $s \ne 1$. We find that irrespective of model details there is a universal generalized Wigner time $t_0$ that characterizes the evolution of the survival probability $P_0(t)$. The generic decay behavior which is implied by rate equation phenomenology is a slowing down stretched exponential, reflecting the gradual resolution of the bandprofile. But depending on non-universal features of the model a power-law decay might tak…
Phonon trapping has an immense impact in many areas of science and technology, from the antennas of interferometric gravitational wave detectors to chip-scale quantum micro- and nano-mechanical oscillators. It usually relies on the mechanical suspension--an approach, while isolating selected vibrational modes, leads to serious drawbacks for interrogation of the trapped phonons, including limited heat capacity and excess noises via measurements. To circumvent these constraints, we realize a new paradigm of phonon trapping using mechanical bound states in the continuum (BICs) with topological fe…
We derive and investigate an expression for the dynamically modified decay of states coupled to an arbitrary continuum. This expression is universally valid for weak temporal perturbations. The resulting insights can serve as useful recipes for optimized control of decay and decoherence.
A simple quantum mechanical model consisting of a discrete level resonantly coupled to a continuum of finite width, where the coupling can be varied from perturbative to strong (Fano-Anderson model), is considered. The particle is initially localized at the discrete level, and the time dependence of the amplitude to find the particle at the discrete level is calculated without resorting to perturbation theory. The deviations from the exponential decay law, predicted by the Fermi's Golden Rule, are discussed. We also study analytic structure of the Green's function (GF) for the model. We analyz…
We study the decay of a prepared state into non-flat continuum. We find that the survival probability $P(t)$ might exhibit either stretched-exponential or power-law decay, depending on non-universal features of the model. Still there is a universal characteristic time $t_0$ that does not depend on the functional form. It is only for a flat continuum that we get a robust exponential decay that is insensitive to the nature of the intra-continuum couplings. The analysis highlights the co-existence of perturbative and non-perturbative features in the local density of states, and the non-linear dep…
The decay of a bound state weakly-coupled to a non-Hermitian tight-binding unstable continuum, i.e. a continuum of states comprising energies with positive imaginary part, is theoretically investigated. As compared to quantum decay in an Hermitian continuum, in the non-Hermitian case a richer scenario can be found as a result of non-unitary dynamics. Different behaviors are observed depending on the kind of instability of the continuum. These include complete or fractional decay in convectively-unstable continua, the absence of quantum decay for a bound state with energy embedded in the contin…
We propose a scheme for slowing down decay into a continuum. We make use of a sequence of ultrashort $2π$-pulses applied on an auxiliary transition of the system so that there is a destructive interference between the two transition amplitudes - one before the application of the pulse and the other after the application of the pulse. We give explicit results for a structured continuum. Our scheme can also inhibit unwanted transitions.
The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a two-dimensional cloud of atoms dressed to Rydberg states, where excitations propagate by dipolar exchange interaction, while the Rydberg blockade phenomenon naturally gives rise to a characteristic length scale, suppressing the hopping on short distances. Then, the system becomes independent of the atoms' spatial arrangement and can be described by a contin…
The discrete Hamiltonian of Su, Schrieffer and Heeger (SSH) is a well-known one-dimensional translation-invariant model in condensed matter physics. The model consists of two atoms per unit cell and describes in-cell and out-of-cell electron-hopping between two sub-lattices. It is among the simplest models exhibiting a non-trivial topological phase; to the SSH Hamiltonian one can associate a winding number, the Zak phase, which depends on the ratio of hopping coefficients and takes on the values $0$ and $1$ labeling the two distinct phases. We display two homotopically equivalent continuum Ham…
Bound states in the continuum (BSCs) were reported in a linear vibronic coupling model with a conical intersection (CI) [Cederbaum et al. Phys. Rev. Lett. 90, 013001 (2003)]. It was also found that these states are destroyed within the Born-Oppenheimer approximation (BOA). We investigate whether a nontrivial topological or geometric phase (GP) associated with the CI is responsible for BSCs. To address this question we explore modifications of the original two-dimensional two-state linear vibronic coupling model supporting BSCs. These modifications either add GP effects after the BOA or remove …
We extend the input-output formalism to study the behavior of uncoupled discrete modes (bosonic cavity modes and fermionic qubits) when they decay to the same Markovian continuum. When the continuum interacts with only a single mode, this decay is irreversible. However, when multiple modes decay to the same Markovian continuum they develop correlations and decay collectively. In the input-output formalism these correlations manifest in additional terms in the quantum Langevin equation. For two modes this collective decay can dramatically extend the lifetimes of both modes (Dicke subradiance) a…
It is known that quantum systems yield non-exponential (power law) decay on long time scales, associated with continuum threshold effects contributing to the survival probability for a prepared initial state. For an open quantum system consisting of a discrete state coupled to continuum, we study the case in which a discrete bound state of the full Hamiltonian approaches the energy continuum as the system parameters are varied. We find in this case that at least two regions exist yielding qualitatively different power law decay behaviors; we term these the long time `near zone' and long time `…
We study the dynamics of a simple model for quantum decay, where a single state is coupled to a set of discrete states, the pseudo continuum, each coupled to a real continuum of states. We find that for constant matrix elements between the single state and the pseudo continuum the decay occurs via one state in a certain region of the parameters, involving the Dicke and quantum Zeno effects. When the matrix elements are random several cases are identified. For a pseudo continuum with small bandwidth there are weakly damped oscillations in the probability to be in the initial single state. For i…
In a previous paper [B. Deb and G. S. Agarwal, Phys. Rev. A 90, 063417 (2014)], it was theoretically shown that, magneto-optical manipulation of low energy scattering resonances and atom-molecule transitions could lead to the formation of a bound state in continuum (BIC), provided there is no spontaneous emission. We find that even an exceedingly small spontaneous decay from exited molecular states can spoil the BIC. In this paper, we show how to circumvent the detrimental effect of spontaneous emission by making use of vacuum-induced coherence (VIC) which results in the cancellation or suppre…
Coupling a discrete state to a quasi-continuum: A model quantum mechanical system that interpolates between Rabi oscillations and decay-revival dynamics
Free University of Berlin（柏林自由大学）；Boğaziçi University（博阿齐奇大学）
We numerically study the single-flavor Schwinger model with a topological $θ$-term, which is practically inaccessible by standard lattice Monte Carlo simulations due to the sign problem. By using numerical methods based on tensor networks, especially the one-dimensional matrix product states, we explore the non-trivial $θ$-dependence of several lattice and continuum quantities in the Hamiltonian formulation. In particular, we compute the ground-state energy, the electric field, the chiral fermion condensate, and the topological vacuum susceptibility for positive, zero, and even negative fermio…
Stabilizer codes are a powerful method for implementing fault-tolerant quantum memory and in the case of topological codes, they form useful models for topological phases of matter. In this paper, we discuss the theory of stabilizer codes as a discrete version of a linear gauge structure, a concept we introduce here. A linear gauge structure captures all the familiar ingredients of $U(1)$ gauge theory including a generalization of charge conservation, Maxwell equations and topological terms. Using this connection, we prove some important results for stabilizer codes which can be used to charac…
