Survival Probability in Quantum Conveyance: Effects of Adiabatic Tunneling and Acceleration Discontinuity

TL;DR

This work addresses the problem of quantifying the survival probability of a particle conveyed by a moving trapping potential under nonadiabatic dynamics. It develops a two-component framework that separates nonadiabatic losses into switch disturbances at the start and end of the protocol and adiabatic tunneling during acceleration, combining them into the compact formula p_{ m SW-AT}(t) = p_{ m SW} p_{ m AT}(t), where p_{ m AT}(t) = \\exp(-\\int_0^t \\Gamma(a(t')) dt') and p_{ m SW} encodes discontinuities in the acceleration protocol. The main contributions include explicit expressions for the switch-disturbance factors, a generalization to higher-order derivative discontinuities with coefficients B_n, and a robust asymptotic scaling 1 - p(\\tau) \\propto L^2 \\tau^{-2n-4} for large conveyance times. The results are validated across multiple acceleration protocols (cos, sin, shifted sin, and higher-order) and show that survival probabilities can be estimated for arbitrary protocols without performing full dynamical simulations, significantly aiding design and analysis of quantum transport in traps. The approach has broad implications for quantum control in 3D systems and could extend to Bose-Einstein condensate transport and other low-dissipation quantum platforms.

Abstract

In the real-time manipulation of quantum states, it is necessary to dynamically control the parameters of the system's Hamiltonian. We have studied the survival probability during the conveyance of a particle by a trapping potential, where the particle may escape from the potential well due to quantum mechanical processes. We investigate how nonadiabatic disturbances arise and identify two main ingredients. One of them is a shock-type disturbance at switching points. To transfer a particle from one place to another, it is necessary to switch on the acceleration and switch it off at the endpoint; this effect is referred to as switch disturbance. We analyze this effect and derive an analytical formula from the perspective of adiabatic theory and find that the factor due to this effect does not depend on the details of the transfer protocols. The other ingredient is adiabatic tunneling during conveyance. During conveyance, the particle is accelerated and decelerated, which induces nonadiabatic processes leading to so-called adiabatic tunneling. Taking these two types of effects into account, we show that the escape mechanisms can be described by a compact formula composed of factors representing these effects. In this paper, we quantitatively examine the survival probabilities in conveyance processes by analyzing the decay of survival probability originating from these effects. We find that the decay behavior under various acceleration protocols is almost perfectly reproduced by a combination of switch disturbance and an integral form of adiabatic tunneling. The rate of adiabatic tunneling is also obtained from an analysis assuming constant acceleration, independent of specific conveyance protocols. Therefore, once the relevant factors are determined, the survival probability for any acceleration protocol can be estimated without performing dynamical simulations for each individual case.

Figures (10)

• Figure 1: The survival probability $p(t)$ (open circles) for constant acceleration $a=0.145$, and an exponential fitting (solid line). Values of parameters are $m=w=z=1$ setting $\hbar=1$. The fitted curve is given by $p(t) = A \exp (-\Gamma t)$ with $A=0.899$ and $\Gamma = 0.0136$.
• Figure 2: Dependence of the decay rate $\Gamma(a)$ on a constant acceleration $a$.
• Figure 3: Comparison of the numerically obtained $p(t)$ (open circle) and $p_{\rm AT}(t)$ (lines) for the cases of $\tau=500$. (a) the cos-protocol with $L=5000$ (black) and $L=8000$ (blue), and (b) sin-protocol with $L=8000$ (black) and $L=11000$ (blue).
• Figure 4: Dependence of $1-\sqrt{p_{\rm SW}}$ on $a$ (open circles) and a fitting $1-\sqrt{p_{\rm SW}} = 2.55 a^2$ (line).
• Figure 5: Comparison of numerically obtained survival probabilities (open circles) for $\tau=500$. (a) cos-protocol compared with Eq.(\ref{['eq:p-adia-corrected']}) (lines) for $L=5000$ (black) and $L=8000$ (blue). (b) sin-protocol compared with Eq. (\ref{['eq:p-sin-corrected']}) (lines) for $L=5000$ (black) and $L=8000$ (blue).