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Ukrainian Journal of Physics

Decoherence in a PT -Symmetric Qubit

Junaid Majeed Bhat, Muzaffar Qadir Lone, Sanjoy Datta, Ghulam Nabi Dar, Ahmed Farouk

Published Apr 20, 2023• 2 citations
Publisher

Abstract

We investigate the decoherence in a PT -symmetric qubit coupled with a bosonic bath. Using canonical transformations, we map the non-Hermitian Hamiltonian representing the PT-symmetric qubit to a spin boson model. Identifying the parameter α that demarcates the hermiticity and non-hermiticity in the model, we show that the qubit does not decohere at the transition from the real eigen spectrum to a complex eigen spectrum. Using a general class of spectral densities, the strong suppression of the decoherence is observed due to both vacuum and thermal fluctuations of the bath, and the initial correlations hold, as we approach the transition point.

DOI
10.15407/ujpe68.2.101

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Decoherence in a PT\mathcal{PT}PT-symmetric qubit
We investigate the decoherence in a PT\mathcal{PT}PT-symmetric qubit coupled with a bosonic bath. Using cannonical transformations, we map the non-Hermitian Hamiltonian representing thePT\mathcal{PT}PT-symmetric qubit to a spin boson model. Identifying the parameter α that demarcates the hermiticity and non-hermiticity in the model, we show that the qubit does not decohere at the transition from real eigen spectrum to complex eigen spectrum. Using a general class of spectral densities, the strong suppression of decoherence is observed due to both vaccum and thermal fluctuations of the bath, and initial correlations as we approach the transition point.
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We have introduced PT-symmetry to a central spin model by adding a PT-symmetric interaction with a tunable hermiticity parameter γγγ. Using the pseudo-Hermitian formalism, we applied a Dyson map to transform the non-Hermitian Hamiltonian to its Hermitian representation. We have found that the decoherence slows down as γγγ increases, eventually ceasing at γ=1γ=1γ=1. We define a pseudo-Hermitian observable that commutes with the metric operator to add as the self-Hamiltonian. Einselection gradually forced the system to select the eigenstates of the self-Hamiltonian as γ→1γ\rightarrow1γ→1. The steady-state purity of the central spin states in the strong environment regime exhibits a paradoxical decrease as γγγ increases. However, a turning point (minimum) corresponding to a maximum information dissipation to the spin bath is found. Finally, the Breuer-Laine-Piilo (BLP) measure, which is used to quantify the non-Markovianity of a quantum system, was evaluated for a finite time. The BLP measure in the strong environment regime exhibited similar turning point behavior, which means that the information backflow reaches a saturation point before declining. This decline signifies the point where PT-symmetry starts shielding the central spin from the environment.
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.
PT\mathcal{PT}PT-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics
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Abstract In this paper, we investigate the decoherence of qubit due to its coupling to a Hermitian or a non-Hermitian environment within the pure dephasing spin-boson model. 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). We find that integer values of AAA (coupling strength) or sss (bath exponent) has distinctive long time asymptotic behaviors of Px(t)P_x(t)Px​(t) and Cx(t)C_x(t)Cx​(t) from those of the non-integer values, accompanied with a diverging crossover time scale. We also find that the non-Hermitian environment tends to suppress the decoherence of qubit for all values of AAA and sss, in contrast to the conclusion of Dey et al . [Phys. Lett. A 383, 125931 (2019)]. Our results show the potential of the non-Hermitian environmental engineering for suppressing the decoherence of qubit.