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Symmetry

Pure Decoherence of the Jaynes–Cummings Model: Initial Entanglement with the Environment, Spin Oscillations and Detection of Non-Orthogonal States

Jerzy Dajka

Published Feb 18, 2024• 1 citation
Publisher

Abstract

A model based on pure decoherence for the Jaynes–Cummings spin–boson system, coupled through its integral of motion to an infinite bosonic bath, is proposed and examined. The properties of the spin oscillation process suggest an initial entanglement between the environment and the spin–boson degrees of freedom. The study demonstrates that the potential applicability of the Jaynes–Cummings model in detecting non-orthogonal bosonic states is preserved in the presence of pure decoherence.

DOI
10.3390/sym16020250

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A model based on pure decoherence for the Jaynes–Cummings spin–boson system, coupled through its integral of motion to an infinite bosonic bath, is proposed and examined. The properties of the spin oscillation process suggest an initial entanglement between the environment and the spin–boson degrees of freedom. The study demonstrates that the potential applicability of the Jaynes–Cummings model in detecting non-orthogonal bosonic states is preserved in the presence of pure decoherence.
Dissipative properties of a composite system interacting with an environment are studied in order to obtain insight into relaxation and decoherence phenomena. As a typical system with internal degree of freedom, a Jaynes–Cummings (JC) model is considered where a spin (qubit) interacts with a single bosonic mode. When the whole system is initially in a state of at most single excitation, the model becomes solvable for excitation number conserving Hamiltonians, even if the JC system interacts with its environment composed of harmonic oscillators. Effects of initial correlations between the system and the environment are also taken into account. Basic equations for the density matrix are solved exactly to determine dynamics of the reduced systems. Mutually related problems of initial correlations, entanglement and non-Markovian property are studied explicitly by examining the time evolution of the reduced density matrices, the concurrence and the trace distance.
We have shown that the Jaynes-Cummings model (JCM) with an environment-induced pure decoherence is an exactly solvable problem. Rabi oscillation of atomic population inversion and oscillation in the field population get trapped due to decoherence. But the decay of the coherence properties of the atom as well as of the field is comparatively slower than that of the population terms. It is also shown that although the fast oscillation in nonclassical properties are suppressed due to decoherence but an initial Poissonian field acquires a sub-Poissonian character in the steady state. So unlike the ordinary spontaneous emission all the nonclassical properties of the system are not erased.
Entanglement and decoherence arguably define the central issues of concern in present day quantum information theory. Decoherence occurs when a system interacts with its environment in an irreversible way; this prevents the quantum superposition of the system + environment's wavefunction from interfering with each other. A better understanding of environment-induced destruction of coherent superposition states is needed, as well as a clear description of the degree of entanglement between the quantum system and its environment. We quantitatively establish a correspondence between entanglement, decoherence, and spin dynamics for a two-state system coupled to a bath of harmonic oscillators, resulting in the celebrated spin-boson model. Applications to solid-state and cold atomic systems are also discussed.
In this paper, we investigate the decoherence of qubit due to its coupling to a Hermitian or a non-Hermitian bath within the pure dephasing spin-boson model. First, using this model, we analytically establish the previously anticipated similarity between the non-equilibrium and the equilibrium correlation functions Px(t)P_x(t)Px​(t) and Cx(t)C_x(t)Cx​(t). Then, in the short/long time asymptotic behaviors of Px(t)P_x(t)Px​(t), we find singular dependence on AAA (coupling strength) and sss (bath exponent) at their integer values. Finally, we find that the non-Hermitian bath tends to suppress the decoherence of qubit for all values of AAA and sss, in contrast to the conclusion of Dey et al. . Our results show the potential of non-Hermitian environment engineering in suppressing the decoherence of qubit.
The paradigmatic spin-boson model considers a spin degree of freedom interacting with an environment typically constituted by a continuum of bosonic modes. This ubiquitous model is of relevance in a number of physical systems where, in general, one has neither control over the bosonic modes, nor the ability to tune distinct interaction mechanisms. Despite this apparent lack of control, we present a suitable transformation that approximately maps the spin-boson dynamics into that of a tunable multiphoton Jaynes-Cummings model undergoing dissipation. Interestingly, the latter model describes the coherent interaction between a spin and a single bosonic mode via the simultaneous exchange of n bosons per spin excitation. Resorting to the so-called reaction coordinate method, we identify a relevant collective bosonic mode in the environment, which is then used to generate multiphoton interactions following the proposed theoretical framework. Moreover, we show that spin-boson models featuring structured environments can lead to non-Markovian multiphoton Jaynes-Cummings dynamics. We discuss the validity of the proposed method depending on the parameters and analyse its performance, which is supported by numerical simulations. In this manner, the spin-boson model serves as a good analogue quantum simulator for the inspection and realization of multiphoton Jaynes-Cummings models, as well as the interplay of non-Markovian effects and, thus, as a simulator of light-matter systems with tunable interaction mechanisms.