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arXiv:cond-mat/0305510 · Physical Review B

Quantum impurity models of noisy qubits

Dmitri V. Khveshchenko

Published Apr 30, 2004• 23 citations
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Abstract

We demonstrate that the problem of coupled two-level systems (``qubits'') which are also subject to a generic (sub-)Ohmic dissipative environment belongs to the same class of models as those describing (non)magnetic impurities embedded in strongly correlated systems. A further insight into the generalized single- and two-impurity Bose/Fermi Kondo models enables one to make specific recommendations towards a systematic engineering of highly coherent multiqubit assemblies for potential applications in quantum information processing.

DOI
10.1103/physrevb.69.153311

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We demonstrate that the problem of coupled two-level systems (``qubits'') which are also subject to a generic (sub-)Ohmic dissipative environment belongs to the same class of models as those describing (non)magnetic impurities embedded in strongly correlated systems. A further insight into the generalized single- and two-impurity Bose/Fermi Kondo models enables one to make specific recommendations towards a systematic engineering of highly coherent multiqubit assemblies for potential applications in quantum information processing.
We demonstrate that the problem of coupled two-level systems ("qubits") which are also subject to a generic (sub-)Ohmic dissipative environment belongs to the same class of models as those describing (non)magnetic impurities embedded in strongly correlated systems. A further insight into the generalized single- and two-impurity Bose/Fermi Kondo models enables one to make specific recommendations towards a systematic engineering of highly coherent multiqubit assemblies for potential applications in quantum information processing.
We study a model of frustration of decoherence in an open quantum system. Contrary to other dissipative Ohmic impurity models, such as the Kondo model or the dissipative two-level system, the impurity model discussed here never presents overdamped dynamics even for strong coupling to the environment. We show that this unusual effect has its origins in the quantum-mechanical nature of the coupling between the quantum impurity and the environment. We study the problem using analytic and numerical renormalization group methods and obtain expressions for the frequency and temperature dependence of the impurity susceptibility in different regimes.
We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin density of a bosonic environment, leading to bosonic versions of the standard Kondo and Anderson impurity models. In a physical situation, these bosonic environments can correspond either to deconfined spinons in certain classes of Z2{Z}_{2}Z2​ frustrated antiferromagnets, or to particles in a multicomponent Bose gase (in which case the spin degree of freedom is attributed to hyperfine levels). Using renormalization group techniques, we establish that our impurity models, which feature an exchange interaction analogous to Kondo impurities in Fermi liquids, allow flow toward a stable strong-coupling state. Since the low-energy bosons exist around a single point in momentum space, and there is no Fermi surface, an impurity quantum phase transition occurs at intermediate coupling, separating screened and unscreened phases. This behavior is qualitatively different from previously studied spin-isotropic variants of the spin-boson model, which display stable intermediate-coupling fixed points and no screening.
The Kondo effect is a prototypical strongly correlated phenomenon, and it is usually discussed in the context of unitary dynamics. Here, we demonstrate that the Kondo effect can be induced through non-linear dissipative channels, without requiring any coherent interaction on the impurity site. Specifically, we consider a reservoir of noninteracting fermions that can hop on a few impurity sites that are subjected to strong two-body losses. In the simplest case of a single lossy site, we recover the Anderson impurity model in the regime of infinite repulsion, with a small residual dissipation as a perturbation. While the Anderson model gives rise to the Kondo effect, this residual dissipation competes with it, offering an instance of a nonlinear dissipative impurity where the interplay between coherent and incoherent dynamics emerges from the same underlying physical process. We further outline how this dissipative engineering scheme can be extended to two or more lossy sites, realizing generalizations of the Kondo model with spin 1 or higher. Our results suggest alternative implementations of Kondo models using ultracold atoms in transport experiments, where localized dissipation can be naturally introduced, and the Kondo effect observed through conductance measurements.
Zero temperature phase transitions not only occur in the bulk of quantum systems, but also at boundaries or impurities. We review recent work on quantum phase transitions in impurity models that are generalizations of the standard Kondo model describing the interaction of a localized magnetic moment with a metallic fermionic host. Whereas in the standard case the moment is screened for any antiferromagnetic Kondo coupling as T to 0, the common feature of all systems considered here is that Kondo screening is suppressed due to the competition with other processes. This competition can generate unstable fixed points associated with phase transitions, where the impurity properties undergo qualitative changes. In particular, we discuss the coupling to both non-trivial fermionic and bosonic baths as well as two-impurity models, and make connections to recent experiments.
We introduce a mapping between a variety of superconducting circuits and a family of Hamiltonians describing localized magnetic impurities interacting with conduction bands. This includes the Anderson model, the single impurity one- and two-channel Kondo problem, as well as the one-dimensional Kondo lattice. We compare the requirements for performing quantum simulations using the proposed circuits to those of universal quantum computation with superconducting qubits, singling out the specific challenges that will have to be addressed.