Abstract We investigate signatures of a self-trapping transition in the driven-dissipative Bose Hubbard dimer, in presence of incoherent pump and single-particle losses. For fully symmetric couplings the stationary state density matrix is independent of any Hamiltonian parameter, and cannot therefore capture the competition between hopping-induced delocalization and the interaction-dominated self-trapping regime. We focus instead on the exact quantum dynamics of the particle imbalance after the system is prepared in a variety of initial states, and on the frequency-resolved spectral properties of the steady state, as encoded in the single-particle Green’s functions. We find clear signatures of a localization-delocalization crossover as a function of hopping to interaction ratio. We further show that a finite a pump-loss asymmetry restores a delocalization crossover in the steady-state imbalance and leads to a finite intra-dimer dissipation.
Abstract We investigate signatures of a self-trapping transition in the driven-dissipative Bose Hubbard dimer, in presence of incoherent pump and single-particle losses. For fully symmetric couplings the stationary state density matrix is independent of any Hamiltonian parameter, and cannot therefore capture the competition between hopping-induced delocalization and the interaction-dominated self-trapping regime. We focus instead on the exact quantum dynamics of the particle imbalance after the system is prepared in a variety of initial states, and on the frequency-resolved spectral properties of the steady state, as encoded in the single-particle Green’s functions. We find clear signatures of a localization-delocalization crossover as a function of hopping to interaction ratio. We further show that a finite a pump-loss asymmetry restores a delocalization crossover in the steady-state imbalance and leads to a finite intra-dimer dissipation.
We study a driven-dissipative Bose-Hubbard model in the presence of two-particle losses and an incoherent single-particle drive on each lattice site, leading to a finite-density stationary state. Using dynamical meanfield theory (DMFT) and an impurity solver based on exact diagonalization of the associated Lindbladian, we investigate the regime of strong two-particle losses. Here a stationary-state quantum Zeno effect emerges, as can be seen in the on-site occupation and spectral function. We show that DMFT captures this effect through its self-consistent bath. We show that, in the deep Zeno regime, the bath structure simplifies, with the occupation of all bath sites except one becoming exponentially suppressed. As a result, an effective dissipative hard-core Bose-Hubbard dimer model emerges, where the auxiliary bath site has single-particle dissipation controlled by the Zeno dissipative scale.
We analyze the classical and quantum dynamics of the driven dissipative Bose–Hubbard dimer. Under variation of the driving frequency, the classical system is shown to exhibit a bifurcation to the limit cycle, where its steady-state solution corresponds to periodic oscillation with the frequency unrelated to the driving frequency. This bifurcation is shown to lead to a peculiarity in the stationary single-particle density matrix of the quantum system. The case of the Bose–Hubbard trimer, where the discussed limit cycle bifurcates into a chaotic attractor, is briefly discussed.
We investigate the correlation properties in the steady state of driven-dissipative interacting bosonic systems in the quantum regime, as for example non-linear photonic cavities. Specifically, we consider the Bose-Hubbard model on a periodic chain and with spatially homogeneous one-body loss and pump within the Markovian approximation. The steady state is non-thermal and is formally equivalent to an infinite-temperature state with finite chemical potential set by the dissipative parameters. While there is no effect of interactions on the steady state, we observe a nontrivial behaviour of the space-time two-point correlation function, obtained by exact diagonalisation. In particular, we find that the decay width of the propagator is not only renormalised at increasing interactions, as it is the case of a single non-linear resonator, but also at increasing hopping strength. Furthermore, we numerically predict at large interactions a plateau value of the decay rate which goes beyond perturbative results in the interaction strength. We then compute the full spectral function, finding that it contains both a dispersive free-particle like dispersion at low energy and a doublon branch at energy corresponding to the on-site interactions. We compare with the corresponding calculation for the ground state of a closed quantum system and show that the driven-dissipative nature – determining both the steady state and the dynamical evolution – changes the low-lying part of the spectrum, where noticeably, the dispersion is quadratic instead of linear at small wavevectors. Finally, we compare to a high temperature grand-canonical equilibrium state and show the difference with respect to the open system stemming from the additional degree of freedom of the dissipation that allows one to vary the width of the dispersion lines.
We study the self-trapping transition in dissipative double wells using mean-field theory and exact diagonalization. We find that, similar to the conventional interaction-driven transition from oscillatory dynamics to self-trapping, dissipation alone can also induce self-trapping-like localization in one well. The resulting state, although transient and decaying, persists for a substantial time. At the mean-field level, the interaction- and dissipation-driven transitions are discontinuous and continuous, respectively. When interaction and dissipation both are present, their interplay produces three dynamical regimes: (i) at weak interaction, increasing dissipation drives a transition from oscillations to self-trapping; (ii) at moderate interaction, self-trapping at weak dissipation, oscillatory dynamics at intermediate dissipation, and re-entrant self-trapping at strong dissipation; and (iii) at strong interaction, self-trapping persists but is weakened by dissipation. We connect the transition with the Liouvillian spectrum. It is observed that purely dissipation-driven transition coincides with an exceptional point in the spectra, and a peak in the Liouvillian gap, marking the onset of the quantum-Zeno regime. In the presence of interactions, however, the onset of the Zeno regime is shifted to dissipation strengths larger than that required for the self-trapping transition.
We investigate steady-state properties of a two-dimensional incoherent-pumped dissipative Bose-Hubbard model, which describes a photon square lattice. This incoherent pumping exhibits an important environment-induced higher-order fluctuation effect, which induces a strong competition between the driven-dissipative channel, the photon-photon interaction, and the photon hopping in multi-photon processes. This new competition gives rise to a spontaneous breaking of the U(1) symmetry of system. As a result, we predict a many-body steady-state localized-delocalized phase transition and an anti-blockade effect, in which the increasing of the repulsive photon-photon interaction promotes the emergence of phase transition. These unconventional many-body steady-state phenomena can be understood by analyzing the single-cavity properties. Our results pave a new way to control many-body dynamics of driven-dissipative systems.
We study the dynamical properties in a non-Hermitian Bose-Hubbard dimer and show that the steady state consists mostly of the eigenstate whose eigenvalue has the largest imaginary part. A sharp phase transition occurs in the steady state and the phase transition occurs for a finite particle number, not for infinite ones, in contrast to the Hermitian system. We also investigate the quantum Fisher information and entanglement in two different phases. The results show that the steady state in the Josephson oscillation regime is fully N -particle entangled and the corresponding parameter sensitivity approaches the Heisenberg limit. In the self-trapping regime, the parameter sensitivity just scales as the shot-noise limit. Moreover, quantum Fisher information of the steady state is robust to the initial state, which indicates that the non-Hermitian dynamics takes more advantage than the Hermitian one for quantum metrology.