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arXiv:1809.02964 · Physical Review A

Persistent currents by reservoir engineering

Maximilian Keck, Davide Rossini, Rosario Fazio

Published Nov 8, 2018• 28 citations
arXivHTMLPDF

Abstract

We demonstrate that persistent currents can be induced in a quantum system in contact with a structured reservoir, without the need of any applied gauge field. The working principle of the mechanism leading to their presence is based on the extension to the many-body scenario of nonreciprocal Lindblad dynamics, recently put forward by Metelmann and Clerk, Phys. Rev. X 5, 021025 (2015): Nonreciprocity can be generated by suitably balancing coherent interactions with their corresponding dissipative version, induced by the coupling to a common structured environment, so as to make the total interactions directional. Specifically, we consider an interacting spin- (or boson-) model in a ring-shaped one-dimensional lattice coupled to an external bath. By employing a combination of cluster mean-field, exact diagonalization, and matrix-product-operator techniques, we show that solely dissipative effects suffice to engineer steady states with a persistent current that survives in the limit of large systems. We also verify the robustness of such current in the presence of additional dissipative or Hamiltonian perturbation terms.

DOI
10.1103/physreva.98.053812

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We demonstrate that persistent currents can be induced in a quantum system in contact with a structured reservoir, without the need of any applied gauge field. The working principle of the mechanism leading to their presence is based on the extension to the many-body scenario of nonreciprocal Lindblad dynamics, recently put forward by Metelmann and Clerk, Phys. Rev. X 5, 021025 (2015): Nonreciprocity can be generated by suitably balancing coherent interactions with their corresponding dissipative version, induced by the coupling to a common structured environment, so as to make the total interactions directional. Specifically, we consider an interacting spin- (or boson-) model in a ring-shaped one-dimensional lattice coupled to an external bath. By employing a combination of cluster mean-field, exact diagonalization, and matrix-product-operator techniques, we show that solely dissipative effects suffice to engineer steady states with a persistent current that survives in the limit of large systems. We also verify the robustness of such current in the presence of additional dissipative or Hamiltonian perturbation terms.
We discuss two quantum simulation schemes in which the coupling to an external bath may give rise to novel and interesting many-body physics. Namely, we first address the effect of local Markovian baths on the quantum annealing dynamics of an Ising-like chain: deviations from adiabaticity may display a nonmonotonic trend as a function of the annealing time, as a result of the competition between nonadiabatic effects and dissipative processes. Secondly, we provide a framework to induce persistent currents through the coupling with a structured reservoir which generates nonreciprocity, without the need of any applied gauge field.
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 hard-core 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 state 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.
In a recent work [A. Metelmann and A. A. Clerk, Phys. Rev. X 5, 021025 (2015)], a general reservoir engineering approach for generating nonreciprocal quantum interactions and devices was described. We show here how in many cases this general recipe can be viewed as an example of autonomous feedforward: the full dissipative evolution is identical to the unconditional evolution in a setup where an observer performs an ideal quantum measurement of one system, and then uses the results to drive a second system. We also extend the application of this approach to nonreciprocal quantum amplifiers, showing the added functionality possible when using two engineered reservoirs. In particular, we demonstrate how to construct an ideal phase-preserving cavity-based amplifier which is fully nonreciprocal, quantum limited, and free of any fundamental gain-bandwidth constraint.
Reservoir engineering has proven to be a practical approach to control open quantum systems, preserving quantum coherence by appropriately manipulating the reservoir and system-reservoir interactions. In this context, for systems comprised of different parts, it is common to describe the dynamics of a subsystem of interest by performing an adiabatic elimination of the remaining components of the system. This procedure often leads to an effective master equation for the subsystem that is not in the diagonal form of the Gorini-Kossakowski-Lindblad-Sudarshan master equation (here called diagonal Lindblad form). Instead, it has a more general structure (here called non-diagonal Lindblad form), which explicitly reveals the dissipative coupling between the various components of the subsystem. In this work, we present a set of dynamical equations for the first and second moments of the canonical variables for linear Gaussian systems, bosonic and fermionic, described by non-diagonal Lindblad master equations. Our method is efficient and allows one to obtain analytical solutions for the steady state. We supplement our findings with a review of covariance matrix methods, focusing on those related to the measurement of entanglement. Notably, our exploration yields a surprising byproduct: the Duan criterion, commonly applied to bosonic systems for verification of entanglement, is found to be equally valid for fermionic systems. We conclude with a practical example, where we revisit two-mode mechanical entanglement in an optomechanical setup. Our approach, which employs adiabatic elimination for systems governed by time-dependent Hamiltonians, opens the door to examine physical regimes that have not been explored before.
Persistent currents circulate continuously without requiring external power sources. Here, we extend their theory to include dissipation within the framework of non-Hermitian quantum Hamiltonians. Using Green's function formalism, we introduce a non-Hermitian Fermi-Dirac distribution and derive an analytical expression for the persistent current that relies solely on the complex spectrum. We apply our formula to two dissipative models supporting persistent currents: (i) a phase-biased superconducting-normal-superconducting junction; (ii) a normal ring threaded by a magnetic flux. We show that the persistent currents in both systems exhibit no anomalies at any emergent exceptional points, whose signatures are only discernible in the current susceptibility. We validate our findings by exact diagonalization and extend them to account for finite temperatures and interaction effects. Our formalism offers a general framework for computing quantum many-body observables of non-Hermitian systems in equilibrium, with potential extensions to nonequilibrium scenarios.
Nonreciprocal quantum batteries harness reservoir engineering for controlled energy transfer, heralding a paradigm shift for quantum energy storage. A prior study utilizing the Metelmann-Clerk formalism reported a fourfold enhancement in nonreciprocal energy accumulation over reciprocal counterparts. This fourfold enhancement, however, appears to stem from a Lindblad master equation that exhibits fundamental inconsistencies, which may systematically understate the actual nonreciprocal advantage. Our approach is rooted in the rigorously established cascaded open quantum systems formalism, which ensures both mathematical consistency and physical fidelity. Remarkably, we surpass the previously reported fourfold benchmark, attaining a regime-independent sixteenfold steady-state nonreciprocal energy advantage over reciprocal systems. We further uncover a dissipation-dependent battery-to-charger efficiency, fourfold under symmetric damping, surpassing this benchmark when the battery is less dissipative, and lower otherwise. This work establishes the cascaded formalism as a mathematically rigorous and experimentally viable foundation for high-performance quantum energy storage.