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arXiv:2509.19062

Analysis of switching operation in quantum conveyance

Yoshiaki Teranishi, Satoshi Morita, Seiji Miyashita

Published Sep 23, 2025• 0 citations
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Abstract

In this paper, we study the quantum dynamics of a particle conveyed by a moving potential well, with a focus on its survival probability. In physical systems, this process is inevitably subjected to external disturbances, such as environmental coupling, which reduce survival probability. Even when external noise is suppressed, however, intrinsic disturbances remain, leading to unwanted leakage from the trapping potential. Specifically, dynamic parameter variations induce nonadiabatic transitions. Various types of nonadiabatic transitions arise from the time-dependence of the potential parameters. When the potential well is smoothly accelerated, the trapped particle may escape due to inertia, a phenomenon known as adiabatic tunneling. Beyond this, the switching procedures (starting and stopping the motion) exert a significant impact that depends heavily on the abruptness of the operation. Consequently, precise dynamical control of the system Hamiltonian is essential, yet it remains a highly nontrivial task. We analytically investigate the mechanism underlying these switching effects and derive a closed-form formula to quantify them. By combining this switching contribution with the adiabatic tunneling rate, we accurately approximate the total nonadiabatic effect. Our framework reproduces survival probabilities across various acceleration protocols with high precision. Since the switching effect is derived analytically and the adiabatic tunneling rate is determined by constant-acceleration analysis, the model is independent of specific, complex protocols. Once the fundamental parameters determined from a few numerical simulations of typical cases are established, the survival probabilities for arbitrary acceleration protocols can be predicted. This provides a practical framework for real-time quantum control without the need for full dynamical simulations.

DOI
10.48550/arxiv.2509.19062

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•Sep 5, 2026•0 citations
In this paper, we study the quantum dynamics of a particle conveyed by a moving potential well, with a focus on its survival probability. In physical systems, this process is inevitably subjected to external disturbances, such as environmental coupling, which reduce survival probability. Even when external noise is suppressed, however, intrinsic disturbances remain, leading to unwanted leakage from the trapping potential. Specifically, dynamic parameter variations induce nonadiabatic transitions. Various types of nonadiabatic transitions arise from the time-dependence of the potential parameters. When the potential well is smoothly accelerated, the trapped particle may escape due to inertia, a phenomenon known as adiabatic tunneling. Beyond this, the switching procedures (starting and stopping the motion) exert a significant impact that depends heavily on the abruptness of the operation. Consequently, precise dynamical control of the system Hamiltonian is essential, yet it remains a highly nontrivial task. We analytically investigate the mechanism underlying these switching effects and derive a closed-form formula to quantify them. By combining this switching contribution with the adiabatic tunneling rate, we accurately approximate the total nonadiabatic effect. Our framework reproduces survival probabilities across various acceleration protocols with high precision. Since the switching effect is derived analytically and the adiabatic tunneling rate is determined by constant-acceleration analysis, the model is independent of specific, complex protocols. Once the fundamental parameters determined from a few numerical simulations of typical cases are established, the survival probabilities for arbitrary acceleration protocols can be predicted. This provides a practical framework for real-time quantum control without the need for full dynamical simulations.
Quantum mechanical control of the position of a particle by using a trapping potential well is an important problem for the manipulation of a quantum particle. We study the probability of successful conveyance of the particle trapped in a potential well for a given length within a given fixed time, i.e., survival probability after the motion. For the actual motion of conveyance, we need to accelerate the particle to move and then decelerate it to stop at the destination. Acceleration and deceleration cause a dropoff of a particle from the trapping potential well. The relaxation of the survival probability in a process with a constant acceleration rate is studied in detail. First, the process is studied as the relaxation of the survival probability of the trapped particle by direct numerical calculations. The survival probability obeys an exponential decay in a long time, which is analyzed from a viewpoint of eigenvalue problem. The value of survival probability is also estimated by the Wentzel-Kramers-Brillouin method with connection formulas using the Airy function and the Weber function. The value is further estimated by a method of the resonance states. We emphasize the fact that an important source of dropoff comes from a nonanalytic change of velocity at the starting point. When the rested particle begins to move, the ground state of the rest frame is redistributed to eigenstates of the moving frame, and then each eigenstate of the moving frame evolves in time. The dephasing of wave functions of the distributed populations reduces the probability of successful conveyance. In general, a smooth start gives a small initial disturbance but it requires a large acceleration during the process to reach the destination in the fixed time which causes a larger dropoff in the process. Considering these conflicting facts, we study the survival probability in concrete conveyance schemes, i.e., protocols with (1) a sudden change of velocity to a constant velocity, (2) a sudden change of acceleration rate to a constant acceleration, and (3) a smooth change of acceleration by studying the real-time change of populations of the adiabatic (instantaneous) eigenstates. We observe the time evolution of the trapped probability and the population distribution during the conveyance process. In cases that the potential well has several bound states, we propose a method to select the particle trapped at the ground state by making use of the difference of survival probabilities of bound states. Published by the American Physical Society 2024
We investigate the capture of a quantum particle in free space by a moving trapping potential. The capture is investigated for various initial conditions. We examine the dependence of the probability of capture on the shape and depth of the trapping potential, initial speed and mass of the particle, and other parameters. We take the trapping potential to move with an initial speed v 0 and to decelerate with constant acceleration a c until the well stops moving. We study the motion during the time the well is moving and after the well has stopped. We compare the probability of capture to the probability that the particle is in a stationary state (while the well is moving) and the probability the particle is in a bound state (after the well's motion has stopped). Our work could be of interest to instructors and students in upper-year undergraduate quantum mechanics courses.
The properties of the conveyance of quantum particles by a moving potential well are studied. We sweep a bell-shape potential well with constant velocity, and study how the potential well traps the particle. In particular, we study the case where we suddenly change the velocity up to a constant velocity. We investigate the number of particles conveyed as a function of the sweep velocity. The effect of the discretization of space in the numerical method is also investigated. We also study how the potential well carries the particle up from a region where the potential energy is low, to another region of high potential energy. Here, we find that the tunneling effect reduces the number of particles carried up. This process is well described by the Landau–Zener mechanism. The dynamics of the density of particles under the sweeping potential well is also studied in noninteracting Fermi particle systems, where the position of the Fermi level plays an important role.
The spontaneous switching of a quantum particle between the wells of a double-well potential is a phenomenon of general interest to physics and chemistry. It was broadly believed that the switching rate decreases steadily as a function of the size of the energy barrier. This view was challenged by a recent experiment on a driven superconducting Kerr nonlinear oscillator (often called the Kerr-cat qubit or the Kerr parametric oscillator), whose energy barrier can be continuously increased by ramping up the drive. Remarkably, as the drive amplitude increases, the switching rate exhibits a steplike decrease termed the ``staircase.'' The view challenged by the experimental staircase demands a deep review of our understanding of the role of quantum effects in double wells. In this work, we use a Lindbladian model of dissipation to derive a semianalytical formula for the switching rate, resolving a continuous transition between tunneling-dominated dynamics and dissipation-dominated dynamics. These two dynamics are observed respectively in the flat part and the steep part of each step in the staircase. Our formula exposes two distinct dissipative processes that limit tunneling: the dephasing of interwell superpositions freezes tunneling via the quantum Zeno effect, and the decay from one excited state to another limits the time during which tunneling can be attempted. This physical understanding allows us to pinpoint the critical drive amplitude that separates the flat and steep part of each step using an equation involving the rates of the two dissipative processes and the tunnel splitting. In addition, analyzing the transition matrix elements in the formula shows that in the regime of a few ($\ensuremath{\lesssim}10$) states in the well and under moderate to low temperatures, highly excited states are populated predominantly via cascaded and direct thermal heating rather than quantum heating. At very low temperatures, we find that the perturbation induced by the non-Hermitian Hamiltonian part of the Lindbladian model becomes increasingly important and facilitates a form of quantum heating that has not been identified before. We numerically map the activation mechanism as a function of drive amplitude, damping rate, and temperature. Our theory deepens the understanding of switching dynamics between metastable quantum states, highlights the importance of a general interplay between tunneling and dissipation, and identifies a novel quantum regime in activated transitions.
The adiabatic following of eigenstates of time-varying Hamiltonians can serve as a useful tool in preparing or manipulating quantum states. If the time variation is not sufficiently slow, however, nonadiabatic transitions to unwanted states occur. Recently, it has been shown that the adiabatic following can be perfectly restored if the original Hamiltonian is complemented with an additional term. Although there is an explicit formula for this compensating term, typically one may not always be able to construct it in an experiment. Here we present a straightforward approach for a partial suppression of the nonadiabatic transitions applicable for any set of available Hamilton operators. We illustrate the method on several examples including interacting spin systems, interacting bosons in a double-well potential, a particle in an expanding box and a system of atoms interacting via a Rydberg-blockade. Whenever suitable compensating operators are available, the system may be evolved faster or with higher fidelity along an eigenstate of the original time-dependent Hamiltonian.
This paper investigates the dynamic suppression of quantum noise within the framework of quantum control theory. The core challenge in implementing precise quantum operations lies in the significant influence of environmental noise, which introduces uncertainties and degrades control fidelity. We propose a novel approach utilizing real-time feedback control, leveraging quantum sensors to monitor the noise levels within a quantum system. Based on this continuous assessment, control parameters are dynamically adjusted to mitigate the impact of noise. The effectiveness of this method is demonstrated through theoretical analysis and mathematical modeling. We aim to enhance the accuracy and stability of quantum control processes, ultimately contributing to the reliable execution of complex quantum operations. The system is described by the following Hamiltonian: H=H0+HIH = H_0 + H_IH=H0​+HI​, where H0H_0H0​ is the system Hamiltonian and HIH_IHI​ represents the interaction Hamiltonian. The time evolution of the system is governed by the equation: d∣ψ(t)>dt=iℏ[H,∣ψ(t)]\frac{d|ψ(t)>}{dt} = \frac{i}{\hbar} [H, |ψ(t)]dtd∣ψ(t)>​=ℏi​[H,∣ψ(t)]. Noise is modeled as a stochastic term, adding to the Hamiltonian: H=H0+HI+HNH = H_0 + H_I + H_NH=H0​+HI​+HN​, where HNH_NHN​ represents the noise Hamiltonian. The control pulse can be described as: U(t)=∑i=1Nαi e−iωitU(t) = \sum_{i=1}^N \alpha_i \, e^{-i\omega_i t}U(t)=∑i=1N​αi​e−iωi​t, where αi\alpha_iαi​ are the amplitudes and ωi\omega_iωi​ are the carrier frequencies. The fidelity of the quantum operation is evaluated using the overlap between the initial and final states: Fidelity=∣∣2Fidelity = ||^2Fidelity=∣∣2. The control parameters are optimized to maximize the fidelity. The quantum state evolution is described by the equation: ∣ψ(t+δt)>=U(t)∣ψ(t)>|ψ(t+\delta t)> = U(t) |ψ(t)>∣ψ(t+δt)>=U(t)∣ψ(t)>, where U(t) is the control pulse. The time-dependent Schrodinger equation is: i/ħ ∂/∂t |ψ(t)> = H|ψ(t)>. The noise introduces uncertainties which can be represented as: σ2=−2\sigma^2 = - ^2σ2=−2, where N is the noise operator.