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Italian Quantum Information Science Conference (IQIS)

Manipulating Quantum Many-Body Systems in the Presence of Controllable Dissipation

Davide Rossini

Published Jun 25, 2019• 0 citations
Publisher

Abstract

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.

DOI
10.3390/proceedings2019012008

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•Oct 24, 2019•0 citations
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.
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.
Applications of quantum devices and simulators require an accurate understanding of their dynamics as well as the effects of environmental noise. While some sources of noise can be modeled as Markovian dissipation, coupling to resonators or vibrational modes often produces non-Markovian dynamics as well, making it difficult to characterize the system, particularly for interacting many-body systems. Here, we identify a broad class of exactly solvable many-body quantum systems with both non-Markovian dynamics and Markovian dissipation. We consider a prototypical model of spins coupled to lossy bosonic modes that mediate Ising-type interactions. We exclude a transverse field but allow local spin dissipation that need not commute with the interactions, including dephasing, relaxation, pumping, and even processes that generate coherences. Using an exact stochastic representation, we decouple the many-body dynamics into the evolution of individual spins, yielding exact spin observables and correlations without adiabatically eliminating the bosons. In the Markovian limit, our solutions describe Ising models with correlated dephasing and nonreciprocal interactions. An example of spin squeezing shows that both the achievable squeezing and its optimal preparation time depend strongly on the interplay between non-Markovian dynamics and Markovian dissipation.
We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to study the interplay between nonadiabatic transitions and dissipation in many-body quantum systems. After the adiabatic evolution, we evaluate the excess energy (the average value of the Hamiltonian) as a measure of the deviation from reaching the final target ground state. We compute the excess energy in a variety of different situations, where the nature of the bath and the Hamiltonian is modified. We find robust evidence of the fact that an optimal working time for the quantum annealing protocol emerges as a result of the competition between the nonadiabatic effects and the dissipative processes. We compare these results with the matrix-product-operator simulations of an Ising system and show that the phenomenology we found also applies for this more realistic case.
Quantum simulation of open quantum systems offers a pathway towards better understanding various non-equilibrium physics that would otherwise be challenging to study. While most open quantum systems studied are modeled as being memory-less (obeying the Markov approximation), real baths generally are influenced by the system-bath interaction, and some systems existing in structured non-Markovian environments can display novel behavior as a result. Here we utilize a trapped ion quantum simulator to simulate a single spin-1/21/21/2 driven-dissipative system with a non-Markovian dissipation channel, and experimentally compare steady-states to those from an analogous Markovian bath. We observe that a non-Markovian dissipative channel can shift the steady-state even for a single qubit, to a regime inaccessible for Markovian dissipation. The techniques used here are compatible with many-body extensions of the model, which can not be simulated efficiently on a classical computer in general. Our work also opens up new possibilities in quantum reservoir engineering beyond the Markovian regime.
In this thesis, the effect of dissipation is investigated in driven models of interest for quantum annealing and quantum topological pumping. Dissipation comes from coupling the system to a bosonic bath at thermal equilibrium, using the usual Caldeira-Leggett setting. The first original results presented deal with the dissipative Landau-Zener model, where we revisit the issue of whether dissipation can improve the final ground state probability. We shed light upon the importance of the coupling direction. Then, we move to dissipation effects in the quantum annealing of the Ising chain in transverse field: we study the conditions for the emergence or absence of an optimal annealing velocity, depending on system-bath interaction strength and bath temperature. Finally, we explore dissipation effects in topological pumping in the periodically-driven Rice-Mele model, where we find that a bath at low temperature can improve the pumping performance when adiabaticity is not perfectly fulfilled.