Dissipative Generation of Currents by Nonreciprocal Local and Global Environments

TL;DR

The paper tackles how nonreciprocal dissipation stabilizes quantum correlations in a 1D Bose-Hubbard system. It compares local kinetic dissipation to global, cavity-mediated dissipation, using matrix-product-state methods to reveal that a nonreciprocal global reservoir supports persistent currents and long-range current–current correlations, while local dissipation confines currents to a narrow region with rapidly decaying correlations. The work identifies how decoherence-free subspaces differ between the two schemes and demonstrates that cavity-induced dissipation can maintain complex long-range coherence, offering a pathway to robust non-equilibrium quantum states. These findings have direct relevance for ultracold atoms in optical cavities and broader hybrid quantum platforms where nonlocal dissipation can be engineered to control transport and correlations.

Abstract

We investigate the mechanisms necessary for the stabilization of complex quantum correlations by exploring dissipative couplings to nonreciprocal reservoirs. We analyze the role of locality in the coupling between the environment and the quantum system of interest, as we consider either local couplings throughout the system, or a single global coupling. We contrast the results obtained for the two scenarios in which a chain of strongly interacting hardcore bosonic atoms is coupled directly to Markovian kinetic dissipative processes, or experiences effective dissipation through the mediation of the field of a lossy optical cavity. To investigate the dissipative dynamics of the many-body quantum systems considered we perform numerical simulations employing matrix product states methods. We show that by coupling atomic tunneling terms to the global field of a dissipative cavity we can stabilize at long times both finite currents and current-current correlations throughout the atomic chain. This is in contrast to the setup in which dissipation acts directly via local tunneling processes, where currents arise in a narrow region of the system and the current-current correlations are rapidly decaying.

Figures (28)

• Figure 1: Sketches of the models: (a) An one-dimensional chain of interacting bosonic atoms under the action of directional kinetic dissipation. The coherent tunneling processes have the amplitude $t$, the repulsive on-site interactions strength $U$ and the dissipative rate is $\gamma$. (b) An one-dimensional chain of interacting bosonic atoms coupled to the field of an optical cavity. The atoms-cavity coupling is realized with the help of a retroreflected transverse pump beam and the strength of the coupling is $\Omega$. Photons are leaking out of the cavity with the dissipation strength $\Gamma$.
• Figure 2: The local density profile, $\langle \hat{n}_l \rangle$, at time $\tau t/\hbar=50$, for atoms with kinetic dissipation, Eqs. (\ref{['eq:Lindblad_atoms']})-(\ref{['eq:Hamiltonian_BH']}), and different values of the dissipation strength, $\hbar\gamma/t\in\{0.5,1,2,4,8\}$. We consider $L=32$ sites and $N=8$ particles.
• Figure 3: The time dependence of the local densities, $\langle \hat{n}_l \rangle$, for the first half of the chain, $1\leq l \leq 16$, for atoms with kinetic dissipation, Eqs. (\ref{['eq:Lindblad_atoms']})-(\ref{['eq:Hamiltonian_BH']}). The different panels correspond to different values of the dissipation strength, $\hbar\gamma/t\in\{0.5,1,2,4,8\}$. We consider $L=32$ sites and $N=8$ particles.
• Figure 4: The time dependence of the kinetic energy, $\hat{H}_{\text{kin}}$, for atoms with kinetic dissipation, Eqs. (\ref{['eq:Lindblad_atoms']})-(\ref{['eq:Hamiltonian_BH']}), and different values of the dissipation strength, $\hbar\gamma/t\in\{0.5,1,2,4,8\}$. We consider $L=32$ sites and $N=8$ particles.
• Figure 5: The time dependence of the current, $\langle\hat{J}_l\rangle$, for atoms with kinetic dissipation, Eqs. (\ref{['eq:Lindblad_atoms']})-(\ref{['eq:Hamiltonian_BH']}), and different values of the dissipation strength, $\hbar\gamma/t\in\{0.5,1,2,4,8\}$. The different panels correspond to the different sites for which the $\langle\hat{J}_l\rangle$ was computed, $l\in\{1,4,8,12\}$. We consider $L=32$ sites and $N=8$ particles.