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arXiv:2609.01700

Tunneling assisted interference in double-well levitodynamics

Yue Ma, Endre Bokor, M. S. Kim

quant-phSubmitted Sep 1, 2026• Announced Sep 2, 2026• 0 citations
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Abstract

Levitated particles trapped in double-well potentials provide a promising platform for exploring quantum dynamics beyond the harmonic regime. We show that such systems exhibit a distinctive quantum signature arising from tunneling-assisted interference. Unlike classical dynamics, where the two wells are disconnected, in the quantum case, quantum tunneling enables eigenstates to delocalize into the other well, creating nonzero overlaps between adjacent eigenstates that introduce low-frequency components into the evolution of the mean particle position. By comparing quantum and classical dynamics of particles in one-dimensional double-well potentials, we demonstrate that this interference is uniquely quantum and can be identified through the oscillation of the average position alone. We further relate the observed spectral peaks to the structure of the energy eigenvalues. The effect provides a promising probe of the quantum signature of levitated particle motion, and has fundamental importance as it predicts the demonstration of two major phenomena of quantum mechanics, quantum tunneling and quantum interference, at the same time and on the same system.

Comments
4 pages, 5 figures, comments welcome

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Levitated particles trapped in double-well potentials provide a promising platform for exploring quantum dynamics beyond the harmonic regime. We show that such systems exhibit a distinctive quantum signature arising from tunneling-assisted interference. Unlike classical dynamics, where the two wells are disconnected, in the quantum case, quantum tunneling enables eigenstates to delocalize into the other well, creating nonzero overlaps between adjacent eigenstates that introduce low-frequency components into the evolution of the mean particle position. By comparing quantum and classical dynamics of particles in one-dimensional double-well potentials, we demonstrate that this interference is uniquely quantum and can be identified through the oscillation of the average position alone. We further relate the observed spectral peaks to the structure of the energy eigenvalues. The effect provides a promising probe of the quantum signature of levitated particle motion, and has fundamental importance as it predicts the demonstration of two major phenomena of quantum mechanics, quantum tunneling and quantum interference, at the same time and on the same system.
The familiar Rabi model, comprising a two-level system coupled to a quantum harmonic oscillator, continues to produce rich and surprising physics when the coupling strength becomes comparable to the individual subsystem frequencies. We construct approximate solutions for the eigenstates and energies in the regime in which the oscillator frequency is small compared to that of the two-level system and the coupling strength matches or exceeds the oscillator frequency. The resulting oscillator dynamics closely resembles that of a particle tunneling in a classical double-well potential. Relating our calculation to an earlier semiclassical approximation in which coupling to the two-level system creates an effective potential for the oscillator, we examine the extent to which this picture is valid. We find that, for certain parameter regimes, the interpretation of the oscillator dynamics in terms of tunneling holds to a good approximation despite the fundamentally entangled nature of the joint system. We assess the prospects for observation of oscillator tunneling in the context of nano- or micromechanical experiments and find that it should be possible if suitably high coupling strengths can be engineered.
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We study the full-fledged microscopic dynamics of two interacting, ultracold bosons in a one-dimensional double-well potential, through the numerically exact diagonalization of the many-body Hamiltonian. With the particles initially prepared in the left well, we increase the width of the right well in subsequent trap realizations and witness how the tunneling oscillations evolve into particle loss. In this closed system, we analyze the spectral signatures of single- and two-particle tunneling for the entire range of repulsive interactions. We conclude that for comparable widths of the two wells, pairwise tunneling of the bosons may be realized for specific system parameters. In contrast, the decay process (corresponding to a broad right well) is dominated by uncorrelated single-particle decay.
Since the early days of quantum mechanics, tunneling has been recognized as one of the hallmarks of the wave character of microscopic physics. The possibility of a quantum particle to penetrate an energetic barrier represents certainly one of the most spectacular implications of quantum theory and has led to various applications in nuclear, atomic, and molecular physics as well as in mesoscopic science. Typical scenarios in which tunneling manifests are the escape route of a quantum particle from a quasibounded region, the transition between two or more symmetry-related, but classically disconnected wells (which we shall focus on in the following), as well as scattering or transport through potential barriers. The spectrum of scenarios becomes even richer when the concept of tunneling is generalized to any kind of classically forbidden transitions in phase space, that is, to transitions that are not necessarily inhibited by static potential barriers but by some other constraints of the underlying classical dynamics (such as integrals of motion). Such “dynamical tunneling” processes arise frequently in molecular systems [1] and were realized with cold atoms propagating in periodically modulated optical lattices [2-4]. Moreover, the electromagnetic analog of dynamical tunneling was also obtained with microwaves in billiards [5].
We numerically investigate quantum dynamics in a one-dimensional double-well system emphasizing influence of a parametrically polychromatic perturbation on the dynamics. It is found that time dependence of transition probability for an initially localized wave packet between the wells shows two types of motion, coherent and incoherent motion, depending on the perturbation parameters. As the strength and/or the number of frequency components of the perturbation increase, coherent motion changes into incoherent one. The former is related to coherent tunneling of the wave packet due to coherence; the latter is related to a delocalized state caused by decoherence. In coherent motion, by virtue of coherence of the dynamics, the expectation value and the standard deviation of a dynamical variable such as the energy of the system show oscillatory time dependence around the initial values. On the contrary in incoherent motion, because of the decoherence, the time dependence fluctuates irregularly around a certain value after a rapid increase due to the resonance. We find that negativity of the Wigner function also show similar time dependence in each type of motion. We compare the classification of the quantum dynamics based on regularity of the time dependence with the one of corresponding classical dynamics based on the Lyapunov exponent. The classifications of the quantum and classical dynamics overlap well in the parameter space. Furthermore, we confirm decoherence of quantum dynamics in a kicked double-well system.
The study of quantum tunneling dates back to the early days of quantum mechanics, and has been a major topic of investigation in both theory and experiment. In recent years, there has been significant effort to understand tunneling phenomena for systems that exhibit chaos in their classical counterpart [13,15,18,29,42]. In particular, tunneling was predicted for mixed systems where chaotic and stable regions are intermingled [14]. The tunneling in this case is between two stable regions (referred to as nonlinear resonances, or islands of stability) in the classical phase space. The classical transport between these islands is forbidden by “dynamical barriers” in phase space. In contrast, quantum tunneling can couple the two islands so that a wave packet oscillates coherently between the two symmetry-related regions. This phenomenon is called dynamical tunneling because it occurs in phase space, without a fixed potential barrier. In the case of a mixed phase space, the presence of the chaotic region can enhance the rate of dynamical tunneling, a phenomenon known as chaos-assisted tunneling [53]. In this chapter, we review our experimental observation of chaosassisted tunneling with ultracold cesium atoms [48-51]. We first give a brief overview of some basic concepts and of earlier work in order to provide a context for our results.