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arXiv:2211.11619 · Physical Review Research

Probing the nonexponential decay regime in open quantum systems

S. M. Wang, Witold Nazarewicz, Alexander Volya, Y. G.

Published Jun 23, 2023• 28 citations
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Abstract

The most important law of radioactivity is that of the exponential decay. In the realm of quantum mechanics, however, this decay law is neither rigorous nor fundamental. The deviations from the exponential decay have been observed experimentally at the early stage of a decay process, but there is little evidence for nonexponential behavior at long times. Yet such long-term nonexponentiality is expected theoretically to probe the nonresonant background components of the initial wave function which preserve the structural interference and the memory of how the state was created. In this paper, we propose new observables that can be used for experimental investigations of the post-exponential decay regime, including the decay of threshold resonances, particle correlations in three-body decays, and interference between near-lying resonances. While the specific examples presented in this work pertain to atomic nuclei, the properties of nonexponential decay are generic, i.e., they apply to other many-body open quantum systems, such as hadrons, atoms, molecules, and nanostructures.

DOI
10.1103/physrevresearch.5.023183

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The most important law of radioactivity is that of the exponential decay. In the realm of quantum mechanics, however, this decay law is neither rigorous nor fundamental. The deviations from the exponential decay have been observed experimentally at the early stage of a decay process, but there is little evidence for nonexponential behavior at long times. Yet such long-term nonexponentiality is expected theoretically to probe the nonresonant background components of the initial wave function which preserve the structural interference and the memory of how the state was created. In this paper, we propose new observables that can be used for experimental investigations of the post-exponential decay regime, including the decay of threshold resonances, particle correlations in three-body decays, and interference between near-lying resonances. While the specific examples presented in this work pertain to atomic nuclei, the properties of nonexponential decay are generic, i.e., they apply to other many-body open quantum systems, such as hadrons, atoms, molecules, and nanostructures.
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 NNN, the exponent becomes quadratic in NNN 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.
Precision tests of decay law of radioactive nuclei have not so far found any deviation from the exponential decay law at early time, as predicted by quantum mechanics. In this paper, we show that the quantum decoherence time (i.e. the timescale of nonexponential decay) of the quasifission or fission process should be of the order of attosecond considering the atom of the fissioning nucleus as a quantum detector. Hence, the observed decay timescale of the quasifission or fission process of even highly excited (EX greater than 50 MeV) transuranium and uraniumlike complexes should be rather long (of the order of attosecond) in spite of their very fast exponential decay timescale (of the order of zeptosecond) as measured by the nuclear techniques. Recent controversy regarding the observation of very long (of the order of attosecond ) and very short (of the order of zeptosecond ) quasifission or fission timescales for similar systems at similar excitation energies as obtained by direct techniques (crystal blocking, X ray fission fragment) and nuclear techniques could be interpreted as evidence for nonexponential decays in nuclear systems
Abstract 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.
In a quantum many-body system, such as atoms, molecules, and atomic nuclei, interparticle interactions generate a complex quantum level scheme that can be analyzed progressively: from the simplest picture of independent quasiparticles moving in a self-consistent mean field to more complete descriptions that include residual interactions and the opening of decay channels above some excitation thresholds. Residual interactions lead to two seemingly contrasting phenomena: the emergence of collective modes (such as rotational and vibrational excitations) associated with specific symmetries, and internal thermalization, which gives rise to features of quantum chaos and causes these collective modes to damp. The picture becomes more intricate once decay channels become energetically accessible, allowing the system to decay irreversibly by means such as particle emission and thus transition to an open quantum regime. In this work, we investigate the competition between internal many-body dynamics and explicit, irreversible decay. These processes can occur on comparable timescales, leading to an initial stage of rapid dynamics followed by equilibration. We show that the decay of the faster components drives the system into an exponentially decaying regime, characterized by a noisy decay current. For this study, we adopt a general, albeit simplified, model of a collective mode embedded in a chaotic background and coupled to open decay channels. The interplay of timescales revealed in this framework appears to reflect universal features of open quantum systems.