Nonexponential tunneling decay of a single ultracold atom

Abstract

By using an exact analytical approach to the time evolution of decay we investigate the tunneling decay of ultracold single atoms, to discuss the conditions for deviations of the exponential decay law. We find that $R$, given by the ratio of the energy of the decaying fragment ${\mathcal{E}}_r$ to its corresponding width ${\Gamma }_r$, is the relevant quantity in this study. When $R$ is less than $0.3$ the decay of the atom goes to a good approximation for the first few lifetimes as $\exp (-{\Gamma }_{r}t/2\hslash )t^{-3/2}$. We also find that for values of $R\sim 1$, the nonexponential behavior occurs in a post-exponential regime that goes as $t^{-3}$ after around a dozen of lifetimes. The above conditions depend on suitable designed potential parameters and suggest that for values $R\lesssim 1$, the experimental verification of nonexponential decay might be possible.

arXiv comment9 pages, 7 figures

References in corpus (26)

• Many-Body Physics with Ultracold Gases
• Quasinormal modes of black holes and black branes
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Deterministic Preparation of a Tunable Few-Fermion System
• Observation of the Quantum Zeno and Anti-Zeno effects in an unstable system
• Fermionization of two distinguishable fermions
• Quantum Zeno effect by general measurements
• Pairing in few-fermion systems with attractive interactions
• Quantum transients
• Long-time behavior of many-particle quantum decay
• How does an interacting many-body system tunnel through a potential barrier to open space?
• Decay by tunneling of Bosonic and Fermionic Tonks-Girardeau Gases
• Tunneling theory of two interacting atoms in a trap
• Nonexponential decay of an unstable quantum system: Small-$Q$-value s-wave decay
• Fidelity of fermionic atom-number states subjected to tunneling decay
• Full time nonexponential decay in double-barrier quantum structures
• Time evolution of decay of two identical quantum particles
• Resonance expansions in quantum mechanics
• Negative Probabilities, Fine's Theorem and Linear Positivity
• Tunneling dynamics of two interacting one-dimensional particles
• Pair tunneling of two atoms out of a trap
• Hermitian and non-Hermitian formulations of the time evolution of quantum decay
• Tunneling Theory for Tunable Open Quantum Systems of Ultracold Atoms in One-Dimensional Traps
• Analytical study of quadratic and non-quadratic short-time behavior of quantum decay
• Transient effects and reconstruction of the energy spectra in the time evolution of transmitted Gaussian wave packets
• Decay modes of two repulsively interacting bosons

Cited by in corpus (11)

• Macroscopic Quantum Tunneling Escape of Bose-Einstein Condensates
• Numerical calculation of the decay widths, the decay constants, and the decay energy spectra of the resonances of the delta-shell potential
• Capturing non-exponential dynamics in the presence of two decay channels
• Quantum decay law: Critical times and the Equivalence of approaches
• Formal Aspects of Quantum Decay
• Multichannel decay law
• Heisenberg uncertainty relations for the non-Hermitian resonance state solutions to the Schrödinger equation
• Decay properties of unstable Tonks-Girardeau gases from a split trap
• Underlying non-Hermitian character of the Born rule in open quantum systems
• Effect of the resonance spectra in the propagation of two decaying entangled particles
• Analysis of quantum decay law: Is quantum tunneling really exponential?