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Chinese Physics B

Nonlinear interference dynamics and optimal control of quantum droplets in one-dimensional asymmetric double-well potential

Huilin Gong, Zhi 智 Tan 谭, Jintao Tan, Shufang Hu, and Honghua Zhong

Published Aug 17, 2026• 0 citations

Abstract

Abstract Interferometry with quantum droplets (QDs) has recently been investigated in several trapping configurations due to the robustness of QDs and their potential applications in quantum sensing and precision measurements. However, the effects of different splitting protocols and the optimal control of interference processes in asymmetric double-well potentials remain unclear. In this work, we investigate quantum interference and its optimal control for a QD confined in a one-dimensional asymmetric double-well potential. We show that asymmetric double-well potentials generated by two different splitting protocols can produce significantly different interference patterns. Furthermore, the interference dynamics strongly depend on the relative nonlinear interaction strength and the potential tilt. Specifically, a strong relative nonlinear interaction strength tends to induce dark solitons, whereas a large tilt favors the formation of breathing solitons. When the relative nonlinear interaction strength is much larger than the tilt, the droplet oscillates back and forth between the former double-well minima, and solitons gradually emerge in the overlapping regions during the interference process. Moreover, by choosing an appropriate adiabatic splitting velocity, we achieve optimal control of the splitting dynamics, such that the selected optimal-control state can reproduce the target interference pattern within a shorter evolution time, thereby significantly reducing the required adiabatic time. Our results provide an effective approach for realizing and optimally controlling QD interference in low-dimensional systems, and may offer useful insights for quantum-droplet-based matter-wave interferometry and coherent quantum manipulation.

DOI: 10.1088/1674-1056/ae9a66

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We investigate the nonlinearity-assisted quantum tunnelling and formation of nonlinear collective excitations in a matter-wave interferometer, which is realized by the adiabatic transformation of a double-well potential into a single-well harmonic trap. In contrast to the linear quantum tunnelling induced by the crossing (or avoided crossing) of neighbouring energy levels, the quantum tunnelling between different nonlinear eigenstates is assisted by the nonlinear mean-field interaction. When the barrier between the wells decreases, the mean-field interaction aids quantum tunnelling between the ground and excited nonlinear eigenstates. The resulting non-adiabatic evolution depends on the input states. The tunnelling process leads to the generation of dark solitons, and the number of the generated dark solitons is highly sensitive to the matter-wave nonlinearity. The results of the numerical simulations of the matter-wave dynamics are successfully interpreted with a coupled-mode theory for multiple nonlinear eigenstates.

We propose a variational shortcut-to-adiabaticity scheme for the fast dynamical control of one-dimensional quantum droplets in ultracold Bose-Bose mixtures. The control is implemented through time-dependent mean-field (MF) and beyond-mean-field (BMF) nonlinearities, which can be adjusted by tuning intra- and interspecies scattering lengths near Feshbach resonances. Using a bright-droplet variational ansatz, together with inverse engineering, we derive time-dependent interaction protocols that connect prescribed initial and target self-bound states while suppressing residual excitations. We analyze three representative settings: simultaneous control of the MF and BMF terms, control with fixed BMF nonlinearity and time-dependent MF interaction, and control with fixed MF nonlinearity and time-dependent BMF interaction. For the constrained cases, additional variational degrees of freedom are introduced to optimize the protocols while respecting the imposed restrictions. Direct numerical simulations of the extended Gross-Pitaevskii equation confirm final fidelities exceeding

0.99

on short time scales, and show that the optimised protocols are robust against finite calibration errors of the nonlinear control strength. Our results provide a route toward fast state-to-state manipulation of self-bound quantum fluids and may be useful for controlled matter-wave engineering in ultracold mixtures.

We consider the evolution of a single-atom wave function in a time-dependent double-well interferometer in the presence of a spatially asymmetric potential. We examine a case where a single trapping potential is split into an asymmetric double well and then recombined again. The interferometer involves a measurement of the first excited state population as a sensitive measure of the asymmetric potential. Based on a two-mode approximation a Bloch vector model provides a simple and satisfactory description of the dynamical evolution. We discuss the roles of adiabaticity and asymmetry in the double-well interferometer. The Bloch model allows us to account for the effects of asymmetry on the excited state population throughout the interferometric process and to choose the appropriate splitting, holding, and recombination periods in order to maximize the output signal. We also compare the outcomes of the Bloch vector model with the results of numerical simulations of the multistate time-dependent Schr\"odinger equation.

We adopt a nonlinear two-mode model to investigate the Rosen-Zener-St\"uckelberg (RZS) interferometry of an interacting Bose-Einstein condensate trapped in double-well potential with a periodically modulating barrier. For symmetric potential, we analyze the properties of interference patterns and derive the interference conditions. For asymmetric potential, we explore the resonance structures caused by destructive interference at the weakly coupling limit and obtain the resonance conditions. In particular, we find that the chaotic motions in the asymmetric case with low-frequency modulation, can destroy the formation of interference fringes. In the symmetric case with high-frequency modulation, we see Fano-line-like resonance structures and find that the reso- nance positions exactly correspond to the boundary of macroscopic quantum self-trapping. We show that the nonlinearity can significantly alter both the shape and position of interference fringes and resonance structures. We discuss the experimental feasibility by comparing the solution of the Gross-Pitaevskii equation with both the solution of the two-mode model and the truncated Wigner simulation as well. The results suggest important applications of nonlinear RZS interferometry both in precisely controlling the dynamics and in accurately measuring the parameters of interacting many-body systems.