Parity-time symmetry and coherent perfect absorption in a cooperative atom response

Parity-Time ( P T $\mathcal{P}\mathcal{T}$ ) symmetry has become an important concept in the design of synthetic optical materials, with exotic functionalities such as unidirectional transport and nonreciprocal reflection. At exceptional points, this symmetry is spontaneously broken, and solutions transition from those with conserved intensity to exponential growth or decay. Here, we analyze a quantum-photonic surface formed by a single layer of atoms in an array with light mediating strong cooperative many-body interactions. We show how delocalized collective excitation eigenmodes can exhibit an effective P T $\mathcal{P}\mathcal{T}$ symmetry and nonexponential decay. This effective symmetry is achieved in a passive system without gain by balancing the scattering of a bright mode with the loss from a subradiant dark mode. These modes coalesce at exceptional points, evidenced by the emergence of coherent perfect absorption where coherent incoming light is perfectly absorbed and scattered only incoherently. We also show how P T $\mathcal{P}\mathcal{T}$ symmetry can be generated in total reflection and by balancing scattering and loss between different polarizations of collective modes.

Probing Nonexponential Decay in Floquet–Bloch Bands

Exponential decay laws describe systems ranging from unstable nuclei to fluorescent molecules, in which the probability of jumping to a lower-energy state in any given time interval is static and history-independent. These decays, involving only a metastable state and fluctuations of the quantum vacuum, are the most fundamental nonequilibrium process and provide a microscopic model for the origins of irreversibility. Despite the fact that the apparently universal exponential decay law has been precisely tested in a variety of physical systems, it is a surprising truth that quantum mechanics requires that spontaneous decay processes have nonexponential time dependence at both very short and very long times. Cold-atom experiments have proven to be powerful probes of fundamental decay processes; in this article, we propose the use of Bose condensates in Floquet–Bloch bands as a probe of long-time nonexponential decay in single isolated emitters. We identify a range of parameters that should enable observation of long-time deviations and experimentally demonstrate a key element of the scheme: tunable decay between quasi-energy bands in a driven optical lattice.

Toward a QFT treatment of nonexponential decay

We study the properties of the survival probability of an unstable quantum state described by a Lee Hamiltonian. This theoretical approach resembles closely Quantum Field Theory (QFT): one can introduce in a rather simple framework the concept of propagator and Feynman rules, Within this context, we re-derive (in a detailed and didactical way) the well-known result according to which the amplitude of the survival probability is the Fourier transform of the energy distribution (or spectral function) of the unstable state (in turn, the energy distribution is proportional to the imaginary part of the propagator of the unstable state). Typically, the survival probability amplitude is the starting point of many studies of non-exponential decays. This work represents a further step toward the evaluation of the survival probability amplitude in genuine relativistic QFT. However, although many similarities exist, QFT presents some differences w.r.t. the Lee Hamiltonian which should be studied in the future.

Local Quasi-equilibrium Description of Multiscale Systems

Systems whose dynamics result from the existence of a wide variety of time and length scales frequently exhibit slow relaxation behavior, manifested through the aging compartment of the correlations and the nonexponential decay of the response function. Experiments performed in systems such as amorphous polymers and supercooled liquids and glasses seem to indicate that these systems undergo, in general, non-Markovian and nonstationary dynamics. Hence, in this contribution, we present a dynamical description of slow relaxation systems based on a generalization of Onsager’s theory to nonequilibrium aging states. By assuming the existence of a local quasi-equilibrium state characterized by a nonstationary probability distribution the entropy of the system is expressed in terms of the conditional probability density by means of the Gibbs entropy postulate. Thus, by taking into account probability conservation and the rules of nonequilibrium thermodynamics, the generalized Fokker–Planck equation is derived.

Nonexponential decay of the surface-NMR signal and implications for water content estimation

Noninvasive surface nuclear magnetic resonance (SNMR) measurements can yield direct and quantitative estimates of water content in the near surface. A fundamental assumption that is always made in the analysis of SNMR data is that the measured signal exhibits an exponential decay. Although the assumption of exponential decay is frequently valid, it can be shown that in the presence of an inhomogeneous magnetic field, the decay may be nonexponential in form. Simulated SNMR data were used to explore how the decay shape will vary with certain environmental and measurement conditions and to assess how nonexponential decay will affect SNMR-based estimates of water content. Results derived from analytical and pore-scale modeling demonstrated that the shape of the decay depends strongly on both pore geometry and the statistics of the regional or pore-scale magnetic field. In particular, the decay is most likely to be nonexponential when pores are large and when a strongly inhomogeneous magnetic field is present. For conditions in which the SNMR signal cannot be accurately modeled as exponential, standard processing approaches were found to result in significant errors in estimated water content—specifically, water content tends to be overestimated. Analysis of data misfits suggests that, in practice, it will be difficult to directly identify errors associated with nonexponential decay based only on the measured signal. Therefore, a description of the conditions leading to nonexponential decay and the implications for water content estimates is useful to support improved interpretation of SNMR measurements.