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arXiv:2001.01508 · Physical Review A

Decay properties of unstable Tonks-Girardeau gases from a split trap

Przemysław Kościk

Published Sep 8, 2020• 3 citations
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Abstract

We study the decay properties of Tonks-Girardeau gases escaping from a double-well potential. Initially, the gases are constrained between two infinite $\ensuremath{\delta}$ barriers with an on-center $\ensuremath{\delta}$-split potential. The strength of one of the obstacles is suddenly reduced, and the particles start to tunnel to the open space. Using the resonance expansion method, we derive the single-term approximate expression for the $N$-particle survival probability and demonstrate its effectiveness in both the exponential and nonexponential regimes. We also predict a parity effect and provide physical insights into its nature at different stages of the time evolution. We conclude that only the initial phase of the decay of the many-particle state may comply with an exponential law. The decay properties are dramatically affected by the presence of the split barrier. Our results reveal the overall decay mechanism of unstable Tonks-Girardeau gases from single and double quantum wells.

DOI
10.1103/physreva.102.033308

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We study the decay properties of Tonks-Girardeau gases escaping from a double-well potential. Initially, the gases are constrained between two infinite \ensuremathδ\ensuremath{\delta}\ensuremathδ barriers with an on-center \ensuremathδ\ensuremath{\delta}\ensuremathδ-split potential. The strength of one of the obstacles is suddenly reduced, and the particles start to tunnel to the open space. Using the resonance expansion method, we derive the single-term approximate expression for the NNN-particle survival probability and demonstrate its effectiveness in both the exponential and nonexponential regimes. We also predict a parity effect and provide physical insights into its nature at different stages of the time evolution. We conclude that only the initial phase of the decay of the many-particle state may comply with an exponential law. The decay properties are dramatically affected by the presence of the split barrier. Our results reveal the overall decay mechanism of unstable Tonks-Girardeau gases from single and double quantum wells.
We study theoretically the few-body dynamics of atoms which leak out of a trap by tunneling through a thin barrier. We consider the two cases of bosons with strongly repulsive contact interactions and spinless fermions with strongly attractive contact interactions (Bose and Fermi Tonk-Girardeau gases, respectively). The tunneling is studied as a function of the number of particles NNN and the barrier opacity. The fermionic case reproduces a nonexponential decay of a single particle, but with a signal enhanced by a factor of NNN. In the bosonic case, we find a different regime of nonexponential decay due to the contribution of different resonances of the trap. The relevant physical realization is that of atoms confined to an optical box with an end-cap laser barrier, and the prospects for future experiments are discussed.
We determine the exact many-body properties of a bosonic Tonks-Girardeau gas confined in a harmonic potential with a tunable $\ensuremath{\delta}$-function barrier at the trap center. This is done by calculating the reduced single-particle density matrix, the pair-distribution function, and the momentum distribution of the gas as a function of barrier strength and particle number. With increasing barrier height we find that the ground-state occupation in a diagonal basis diverges from the N\sqrt{N}N​ behavior that is expected for the case of a simple harmonic trap. In fact, the scaling of the occupation number depends on whether one has an even or odd number of particles. Since this quantity is a measure of the coherence of our sample we show how the odd-even effect manifests itself in both the momentum distribution of the Bose gas and interference fringe visibility during free temporal evolution.
The most unstable quantum states and elementary particles possess more than a single decay channel. At the same time, it is well known that typically the decay law is not simply exponential. Therefore, it is natural to ask how to spot the nonexponential decay when (at least) two decay channels are opened. In this work, we study the tunneling phenomenon of an initially localized particle in two spatially opposite directions through two different barriers, mimicking two decay channels. In this framework, through specific quantum mechanical examples which can be accurately solved, we study the general properties of a two-channel decay that apply for various unstable quantum states (including unstable particles). Apart from small deviations at early times, the survival probability and the partial tunneling probability along the chosen direction are very well described by the exponential-decay model. In contrast, the ratios of the decay probabilities and probability currents are evidently not a simple constant (as they would be in the exponential limit), but display time-persisting oscillations. Hence, these ratios are optimal witnesses of deviations from the exponential-decay law.
Abstract In this article, we study an exponential decay for the gas of bosons with strong repulsive delta interactions from a double-well potential. We consider an exactly solvable model comprising an infinite wall and two Dirac delta barriers. We explore its features both within the exact method and with the resonance expansion approach. The study reveals the effect of the splitting barrier on the decay rate in dependence on the number of particles. Among other things, we find that the effect of the splitting barrier on the decay rate is most pronounced in systems with odd particle numbers. During exponential decay, the spatial correlations in an internal region are well captured by the “radiating state”.
We describe the properties of a pair of ultracold bosonic atoms in a one-dimensional harmonic trapping potential with a tunable zero-ranged barrier at the trap center. The full characterization of the ground state is done by calculating the reduced single-particle density, the momentum distribution, and the two-particle entanglement. We derive several analytical expressions in the limit of infinite repulsion (Tonks-Girardeau limit) and extend the treatment to finite interparticle interactions by numerical solution. As pair interactions in double wells form a fundamental building block for many-body systems in periodic potentials, our results have implications for a wide range of problems.
We examine an analytical expression for the survival probability for the time evolution of quantum decay to discuss a regime where quantum decay is nonexponential at all times. We find that the interference between the exponential and nonexponential terms of the survival amplitude modifies the usual exponential decay regime in systems where the ratio of the resonance energy to the decay width is less than 0.3. We suggest that such a regime could be observed in semiconductor double-barrier resonant quantum structures with appropriate parameters.