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arXiv:2105.09093 · Physical Review A

Decoherence and objectivity in higher spin environments

Mateusz Kiciński, Jarosław K. Korbicz

Published Oct 21, 2021• 10 citations

Abstract

We analyze decoherence and objectivization processes in spin-spin models for arbitrary spins without interactions between different spins in the environment. We first derive the most general analytic form of the decoherence factor in the measurement limit, where the interaction Hamiltonian dominates the rest. We then analyze thermal environments and derive exact, analytic formulas for both the decoherence factor and the state fidelity of postinteraction environment states, conditioned on different states of the system. This allows us to analyze the objectivization process of the state of the central spin during the interaction. We do so using so-called spectrum broadcast structures (SBS), which are specific multipartite quantum states encoding a certain operation notion of objectivity. We analyze analytically (for short times) and numerically how higher spin influences the efficiency of decoherence and objectivization processes. As expected, the higher the spin of the environment, the more efficient decoherence and objectivization become. This work is a generalization of previous studies, limited to spin-$1/2$ systems only, and we hope will be useful in future objectivity experiments.

DOI: 10.1103/physreva.104.042216

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We analyze decoherence and objectivization processes in spin-spin models for arbitrary spins without interactions between different spins in the environment. We first derive the most general analytic form of the decoherence factor in the measurement limit, where the interaction Hamiltonian dominates the rest. We then analyze thermal environments and derive exact, analytic formulas for both the decoherence factor and the state fidelity of postinteraction environment states, conditioned on different states of the system. This allows us to analyze the objectivization process of the state of the central spin during the interaction. We do so using so-called spectrum broadcast structures (SBS), which are specific multipartite quantum states encoding a certain operation notion of objectivity. We analyze analytically (for short times) and numerically how higher spin influences the efficiency of decoherence and objectivization processes. As expected, the higher the spin of the environment, the more efficient decoherence and objectivization become. This work is a generalization of previous studies, limited to spin-

1/2

systems only, and we hope will be useful in future objectivity experiments.

We investigate quantum objectivity in the boson-spin model, where a central harmonic oscillator interacts with a thermal bath of spin-

\frac{1}{2}

systems. We analyze how information about a continuous position variable can be encoded into discrete, finite-dimensional environments. More precisely, we study conditions under which the so-called spectrum broadcast structures can be formed in the model. These are multipartite quantum-state structures, representing a mode-refined form of decoherence. Working in the recoil-less limit, we use the Floquet theory to show that despite its apparent simplicity, the model has a rich structure with different regimes, depending on the motion of the central system. In one of them, the faithful encoding of the position and hence objectivity are impossible irrespectively of the resources used. In another, large enough collections of spins will faithfully encode the position information. We derive the characteristic length scales, corresponding to decoherence and precision of the encoding.

In this paper, we contribute to the mathematical foundations of the recently established theory of Spectrum Broadcast Structures (SBS). These are multipartite quantum states, encoding an operational notion of objectivity and exhibiting a more advanced form of decoherence. We study SBS and asymptotic convergence to SBS in the case of a central system interacting with N environments via the von Neumann-type measurement interactions, ubiquitous in the theory of open quantum systems. We will be focusing on the case where the system is modeled by an infinite-dimensional Hilbert space and the operators associated with the system in the Hamiltonian have purely continuous spectrum. Such a setup yields mathematical complications that have hitherto not been addressed in the theory of SBS.

In this paper, we contribute to the mathematical foundations of the recently established theory of Spectrum Broadcast Structures (SBS). These are multipartite quantum states, encoding an operational notion of objectivity and exhibiting a more advanced form of decoherence. We study SBS in the case of a central system interacting with N environments via the von Neumann-type measurement interactions, ubiquitous in the theory of open quantum systems. We state and prove a novel sufficient condition for SBS to arise dynamically for finite-dimensional systems. The condition is based on the Gram–Schmidt orthogonalization rather than on the Knill–Barnum error estimation used in previous papers.

We revisit the decoherence process of a multiqubit register interacting with a thermal bosonic bath. We generalize the previous studies by considering not only the register's behavior but also a part of its environment. In particular, we are interested in information flow from the register to the environment, which we describe using recently introduced multipartite quantum state structures called spectrum broadcast structures. Working in two specific cases of (i) two-qubit register and (ii) collective decoherence, we identify the regimes where the environment acquires almost complete information about the register state. We also study in more detail the interesting causal aspects related to the finite propagation time of the field disturbances between the qubits. Finally, we describe quantum state structures which appear due to the presence of protected spaces.

We examine two exactly solvable models of decoherence---a central spin-system, (i) with and (ii) without a self-Hamiltonian, interacting with a collection of environment spins. In the absence of a self-Hamiltonian we show that in this model (introduced some time ago to illustrate environment-induced superselection) generic assumptions about the coupling strengths can lead to a universal (Gaussian) suppression of coherence between pointer states. On the other hand, we show that when the dynamics of the central spin is dominant a different regime emerges, which is characterized by a non-Gaussian decay and a dramatically different set of pointer states. We explore the regimes of validity of the Gaussian decay and discuss its relation to the spectral features of the environment and to the Loschmidt echo (or fidelity).

In spite of all of its successes, quantum mechanics leaves us with a central problem: How does nature create a bridge from fragile quanta to the objective world of everyday experience? Here we find that a basic structure within quantum mechanics that leads to the perceived objectivity is a so-called spectrum broadcast structure. We uncover this based on minimal assumptions, without referring to any dynamical details or a concrete model. More specifically, working formally within the decoherence theory setting with multiple environments (called quantum Darwinism), we show how a crucial for quantum mechanics notion of nondisturbance due to Bohr [N. Bohr, Phys. Rev. 48, 696 (1935)] and a natural definition of objectivity lead to a canonical structure of a quantum system-environment state, reflecting objective information records about the system stored in the environment.