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arXiv:2605.21900

Dissipation-Selected Resonant Fronts in a Driven-Dissipative Bose-Hubbard Lattice

Wei-Guo Ma, Heng Fan

cond-mat.quant-gasquant-phSubmitted May 21, 2026• Announced May 22, 2026• 0 citations
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Abstract

Spatially structured dissipation organizes driven quantum matter beyond Hamiltonian control. We show that a dissipation gradient combined with a Stark-induced detuning ramp selects a nonlinear resonance slice in a two-dimensional driven-dissipative Bose-Hubbard lattice, producing a pinned density front in generalized Gross-Pitaevskii simulations. The underlying resonance condition fixes the front position, while its Airy-like profile obeys a width scaling set by tunneling stiffness and the effective detuning slope. Treating the front as an emergent interface explains how tuning the selected resonance toward the minimum-loss side yields Peierls-Nabarro depinning steps, discrete transverse pattern locking, spatiotemporal chaos, and minimum-loss localization. Center-of-mass and generalized-imbalance diagnostics map these outcomes into a dynamical phase diagram as detuning-ramp slope and dissipation-gradient strength vary. The results suggest structured dissipation as a mechanism for reconfigurable transport barriers and nonequilibrium interfaces in programmable bosonic lattices.

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Spatially structured dissipation organizes driven quantum matter beyond Hamiltonian control. We show that a dissipation gradient combined with a Stark-induced detuning ramp selects a nonlinear resonance slice in a two-dimensional driven-dissipative Bose-Hubbard lattice, producing a pinned density front in generalized Gross-Pitaevskii simulations. The underlying resonance condition fixes the front position, while its Airy-like profile obeys a width scaling set by tunneling stiffness and the effective detuning slope. Treating the front as an emergent interface explains how tuning the selected resonance toward the minimum-loss side yields Peierls-Nabarro depinning steps, discrete transverse pattern locking, spatiotemporal chaos, and minimum-loss localization. Center-of-mass and generalized-imbalance diagnostics map these outcomes into a dynamical phase diagram as detuning-ramp slope and dissipation-gradient strength vary. The results suggest structured dissipation as a mechanism for reconfigurable transport barriers and nonequilibrium interfaces in programmable bosonic lattices.
Driven-dissipative light-matter systems can exhibit collective nonequilibrium phenomena due to loss and gain processes on the one hand and effective photon-photon interactions on the other hand. As a generic example we study a bosonic lattice system implemented via an array of driven-dissipative coupled nonlinear resonators with linearly increasing resonance frequencies across the lattice. The model also describes a driven-dissipative Bose-Hubbard model in a tilted potential without a particle-conservation constraint. We numerically predict a diverse range of stationary and nonstationary states resulting from the interplay of the tilt, tunneling, on-site interactions, and loss and gain processes. Our key finding is that, under weak on-site interactions, the bosons mostly condense into a selected, single-particle Wannier-Stark state without exhibiting the expected Bloch oscillations. As the strength of the on-site interactions increase, a nonstationary regime emerges which, surprisingly, exhibits periodic Bloch-type oscillations. As a direct consequence of the driven-dissipative nature of the system we predict a highly nontrivial phase diagram including regular oscillating as well as chaotic dynamical regimes. While a straightforward photonic implementation using microwave or optical modes is possible, such dynamics might also be observable for an ultracold gas in a vertical lattice with gravity or a tilted external potential.
Modern experimental platforms such as superconducting circuit arrays call for the exploration of bosonic tight-binding models in unconventional situations with no counterpart in real materials. Here we investigate one such situation in which excitations are driven and damped by pairs, leading to pattern formation and exotic bosonic states emerging from a nonequilibrium quantum many-body system. Focusing on a two-dimensional driven-dissipative Bose-Hubbard model, we find that its steady states are characterized by the condensation of bosons around momenta lying on a "Bose surface," a bosonic analog of the Fermi surface in solid-state systems. The interplay between instabilities generated by the driving, the nonlinear dissipative mode coupling, and the underlying lattice effect allows the system to equilibrate into an exotic superfluid state of bosons condensed on a closed ring in momentum space instead of discrete points. Such an unconventional state with a spatially uniform density distribution goes beyond the traditional scope of pattern formation and thus has no counterpart in the classical literature. In addition, it is a state connected to several open problems in modern condensed-matter physics. Here we provide the means to stabilize it, opening the way to its experimental study. Moreover, we also provide a concrete experimental implementation of our model in currently available superconducting circuit arrays. We also investigate the relaxation spectrum around the condensate, which shows a characteristic purely diffusive behavior.
The emergence of equilibrium universality from intrinsically nonequilibrium dynamics is a fundamental open problem. Bose-Hubbard lattices realized in photonic and circuit-QED platforms provide a versatile setting to engineer nonlinear interactions, dissipation, and multiphoton processes. Here we investigate a Bose-Hubbard lattice subject to three-photon parametric driving, whose nonequilibrium steady state spontaneously breaks a Z3\mathbb Z_3Z3​ symmetry and realizes the criticality of the three-state Potts model, a three-state generalization of the Ising model. Using a variational phase-space approach with systematically controllable accuracy based on a Variational Multi-Gaussian ansatz, we perform finite-size scaling analyses in one and two spatial dimensions. We find that, in two-dimensional lattices with single-photon losses, the nonequilibrium steady-state transition belongs to the universality class of the 2D classical three-state Potts model. In contrast, in one-dimensional lattices with three-photon losses, the transition is governed by the one-dimensional quantum three-state Potts universality class. These results establish driven-dissipative bosonic lattices as a platform for emergent Potts criticality and identify multiphoton dissipation as a mechanism that promotes nonequilibrium critical behavior from classical to quantum universality classes.
Self-sustained oscillations combine finite-amplitude stabilization with a neutral phase degree of freedom. We develop this bifurcation-based framework for driven-dissipative collective spins and show that the microscopic structure of the U(1)-covariant dissipation selects the background attractor, while the explicit U(1)-breaking channel governs its local bifurcation response. In the thermodynamic-limit mean-field dynamics, a single linear U(1)-covariant jump produces only polar fixed-point backgrounds, whereas nonlinear covariant dissipation provides amplitude-dependent saturation and stabilizes a finite-latitude self-sustained-oscillator manifold through a supercritical Hopf bifurcation. Under coherent U(1) breaking, exact resonance leads to a reversible double-zero degeneracy with vanishing critical frequency rather than a standard Hopf onset. Finite detuning unfolds this singularity into a genuine finite-frequency Hopf boundary, which exists only on the self-sustained-oscillator side and can be either supercritical or subcritical. By contrast, a single linear dissipative U(1)-breaking jump cannot generate a standard Hopf instability: when its phase-pinning invariant vanishes the azimuthal direction remains neutral, whereas otherwise the phase-locked fixed points have a purely real Jacobian spectrum. These results establish a general design principle: nonlinear covariant dissipation selects the selfsustained background, while the structure of the symmetry-breaking channel determines whether the resulting local response is double-zero, genuinely Hopf, or non-Hopf.
In this thesis, we study interacting bosons on lattices consisting of a few sites. The main focus is on their response to external driving fields, their transport and decay properties. We address fundamental questions of quantum classical correspondence and investigate the implications of interactions in the transport properties of (ultra-)cold atom devices. Quantum mechanically, we describe bosons on lattices using a parametric Bose-Hubbard Hamiltonian while the corresponding classical limit is described by the discrete nonlinear Schrödinger equation.In the first part of this thesis we focus on the chaotic regime of the Bose-Hubbard Hamiltonian. We investigate the parametric change of eigenstates as the coupling strength between neighboring sites is varied, using perturbative and semiclassical methods. We then turn to the quantum evolution of driven interacting bosonic systems and study the resulting quantum dynamics and the irreversibility (fidelity) of the quantum motion.In the second part we initiate the study of quantum pumping/stirring in Bose-Einstein condensates with the aim to identify optimal pumping cycles and propose such a device in order to probe the interatomic interactions. Finally, in the last part we focus on the interplay of intrinsic dynamics with coupling to the continuum and investigate the structure of the resonance widths of a Bose-Hubbard dimer which is coupled to the continuum at one of the sites using an effective non-Hermitian Hamiltonian formalism.
Dissipation is ubiquitous in nature and plays a crucial role in quantum systems such as causing decoherence of quantum states. Recently, much attention has been paid to an intriguing possibility of dissipation as an efficient tool for the preparation and manipulation of quantum states. We report the realization of successful demonstration of a novel role of dissipation in a quantum phase transition using cold atoms. We realize an engineered dissipative Bose-Hubbard system by introducing a controllable strength of two-body inelastic collision via photoassociation for ultracold bosons in a three-dimensional optical lattice. In the dynamics subjected to a slow ramp-down of the optical lattice, we find that strong on-site dissipation favors the Mott insulating state: The melting of the Mott insulator is delayed, and the growth of the phase coherence is suppressed. The controllability of the dissipation is highlighted by quenching the dissipation, providing a novel method for investigating a quantum many-body state and its nonequilibrium dynamics.