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arXiv:2610.16525

Bogoliubov excitations of a Bose-Einstein condensate in the presence of the non-Hermitian skin effect

Carlo Panu, Ulf Peschel, O. A. Egorov, Elena A. Ostrovskaya, Eliezer Estrecho

Published Oct 12, 2026• 0 citations
arXivHTMLPDF

Abstract

The non-Hermitian skin effect is one of the most remarkable topological features of non-conservative physics. It causes a macroscopic accumulation of states at the boundaries of a confined system, opening new ways for controlling and directing waves in non-Hermitian settings. This effect has recently been observed in experiments with Bose-Einstein condensates of exciton polaritons and ultracold bosonic quantum gases. The underlying physics is captured by a mean-field Hamiltonian with a trapping potential and an imaginary gauge field. While prior work has examined the effect of the imaginary gauge field term on the condensate itself, its effect on the collective excitations on top of the condensate remained unexplored. Here, we develop a new theory for the Bogoliubov excitations in a non-Hermitian framework and systematically study their spectrum across different interaction regimes. By analysing the position expectation values, we find that while the repulsive interactions oppose the localisation of the condensate due to the skin effect, the excitations remain strongly affected by the imaginary gauge field. As a consequence, in the presence of harmonic confinement, we predict a strong shift in the dipole oscillation frequency, which can be observed in experiments. This is in contrast to Hermitian systems, where this frequency is fixed by the trap dimensions. Furthermore, we develop a consistent second-quantised field theory of the collective excitations in this non-Hermitian system. Strikingly, we find that a second-quantised treatment removes the shift of the dipole oscillation frequency entirely. This intriguing discrepancy between the two theoretical approaches to the treatment of elementary excitations in a non-Hermitian system can be resolved in experiments.

DOI
10.48550/arxiv.2610.16525

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The non-Hermitian skin effect is one of the most remarkable topological features of non-conservative physics. It causes a macroscopic accumulation of states at the boundaries of a confined system, opening new ways for controlling and directing waves in non-Hermitian settings. This effect has recently been observed in experiments with Bose-Einstein condensates of exciton polaritons and ultracold bosonic quantum gases. The underlying physics is captured by a mean-field Hamiltonian with a trapping potential and an imaginary gauge field. While prior work has examined the effect of the imaginary gauge field term on the condensate itself, its effect on the collective excitations on top of the condensate remained unexplored. Here, we develop a new theory for the Bogoliubov excitations in a non-Hermitian framework and systematically study their spectrum across different interaction regimes. By analysing the position expectation values, we find that while the repulsive interactions oppose the localisation of the condensate due to the skin effect, the excitations remain strongly affected by the imaginary gauge field. As a consequence, in the presence of harmonic confinement, we predict a strong shift in the dipole oscillation frequency, which can be observed in experiments. This is in contrast to Hermitian systems, where this frequency is fixed by the trap dimensions. Furthermore, we develop a consistent second-quantised field theory of the collective excitations in this non-Hermitian system. Strikingly, we find that a second-quantised treatment removes the shift of the dipole oscillation frequency entirely. This intriguing discrepancy between the two theoretical approaches to the treatment of elementary excitations in a non-Hermitian system can be resolved in experiments.
The non-Hermitian skin effect (NHSE), the accumulation of eigen-wave functions at boundaries of open systems, underlies a variety of exotic properties that defy conventional wisdom. While the NHSE and its intriguing impact on band topology and dynamics have been observed in classical or photonic systems, their demonstration in a quantum gas system remains elusive. Here we report the experimental realization of a dissipative Aharonov-Bohm chain-non-Hermitian topological model with NHSE-in the momentum space of a two-component Bose-Einstein condensate. We identify signatures of the NHSE in the condensate dynamics, and perform Bragg spectroscopy to resolve topological edge states against a background of localized bulk states. Our Letter sets the stage for further investigation on the interplay of many-body statistics and interactions with the NHSE, and is a significant step forward in the quantum control and simulation of non-Hermitian physics.
We study a Bose-Einstein condensate of ultracold atoms subject to a non-Hermitian spin-orbit coupling, where the system acquires the non-Hermitian skin effect under the interplay of spin-orbit coupling and laser-induced atom loss. The presence of the non-Hermitian skin effect is confirmed through its key signatures in terms of the spectral winding under the periodic boundary condition, the accumulation of eigen wavefunctions at boundaries under an open boundary condition, and bulk dynamics signaled by a directional flow. We show that bulk dynamics, in particular, serves as a convenient signal for experimental detection. The impact of interaction and trapping potentials is also discussed based on the non-Hermitian Gross-Pitaevskii equations. Our work demonstrates that the non-Hermitian skin effect and its rich implications in topology, dynamics, and beyond are well within the reach of current cold-atom experiments.
Interaction between matter field and gauge field plays a fundamental role in many areas of physics. Recently, a non-abelian gauge field has been successfully synthesized in laboratory for ultracold neutral bosonic atoms, yielding the coupling between the pseudo-spin of an atom and its orbital motion. This new superfluid has many unconventional properties remaining to be explored. Here we study the collective oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. We find that the frequency of dipole oscillation deviates from the harmonic trap frequency and depends on the oscillation amplitude. Such an unharmonic behavior reveals the nonabelain character of the gauge field. We also observe that a magnetization oscillation is induced by the dipole motion, as a manifestation of the absence of the Galilean invariance of this system. We develop a variational wave-function method that well describes the dipole oscillation, except in the regime with two degenerate single-particle energy minima separated by a low barrier. In this regime, since the harmonic trapping potential plays an analogous role as kinetic energy in a real-space double-well potential, macroscopic quantum tunneling in momentum space is observed in the dipole oscillation.
The non-Hermitian skin effect (NHSE), featured by the collapse of bulk-band eigenstates into the localized boundary modes of the systems, is one of most striking properties in the fields of non-Hermitian physics. Unique physical phenomena related to the NHSE have attracted a lot of interest, however, their experimental realizations usually require nonreciprocal hopping, which faces a great challenge in ultracold-atom systems. In this work, we propose to realize the NHSE in a 1D optical lattice by periodically-driven ultracold atoms in the presence of staggered atomic loss. By studying the effective Floquet Hamiltonian in the high-frequency approximation, we reveal the underlying mechanism for the periodic-driving-induced the NHSE. We found that the robust NHSE can be tuned by driving phase, which is manifested by the dynamical localization. Most remarkably, we uncover the periodic-driving-induced critical skin effect for two coupled chains with different driving phases, accompanied by the appearance of size-dependent topological in-gap modes. Our studies provide a feasible way for observing the NHSE and exploring corresponding unique physical phenomena due to the interplay of non-Hermiticity and many-body statistics in ultracold-atom systems.
Fractionalization in ideal Chern bands and non-Hermitian topological physics are two active but so far separate research directions. Merging these, we generalize the notion of ideal Chern bands to the non-Hermitian realm and uncover several striking consequences both on the level of band theory and in the strongly interacting regime. Specifically, we show that the lowest band of a Kapit--Mueller lattice model with an imaginary gauge potential satisfies a generalized ideal condition with complex Berry curvature in sync with a complex quantum metric. The ideal band remains purely real and exactly flat on both the torus and cylinder: eigenstates are extended on the torus, while on the cylinder all right and left eigenstates localize at the boundaries, yielding a non-Hermitian skin effect without spectral winding. In the interacting regime, we find that the generalized ideal condition stabilizes an incompressible liquid at fractional fillings, retaining intrinsic non-Hermitian features on both cylinder and torus, while strikingly distinct on different manifolds. On the cylinder, the ground states are always skin-Laughlin states. In contrast, on the torus, we instead observe an unconventional competition between topologically ordered Laughlin-like states and negative collective modes, arising purely from non-Hermiticity.
The non-Hermitian skin effect (NHSE), characterized by the collapse of bulk-band eigenstates into the localized boundary modes of the systems, is one of most striking properties in the field of non-Hermitian physics. Unique physical phenomena related to the NHSE have attracted a great deal of interest; however, their experimental realization usually requires nonreciprocal hopping, which faces a great challenge in ultracold-atom systems. In this work we propose the realization of the NHSE in a one-dimensional optical lattice by periodically driven ultracold atoms in the presence of staggered atomic loss. By studying the effective Floquet Hamiltonian in the high-frequency approximation, we reveal the underlying mechanism for the periodic-driving-induced NHSE. We find that the robust NHSE can be tuned by the driving phase, which is manifested by the dynamical localization. Most remarkably, we uncover the periodic-driving-induced critical skin effect for two coupled chains with different driving phases, accompanied by the appearance of size-dependent topological in-gap modes. Our study provides a feasible way to observe the NHSE and explore the corresponding unique physical phenomena due to the interplay of non-Hermiticity and many-body statistics in ultracold-atom systems.