Decoherence of Bell states by local interactions with a suddenly quenched spin environment

Wendenbaum, Pierre; Taketani, Bruno G.; Karevski, Dragi

doi:10.1103/physreva.90.022125

Cited by 6 publications

(17 citation statements)

References 49 publications

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“…From the non equilibrium study of the LE following offcritical quenches, we show that the initial fall of the LE is completely governed by the coupling strength. Such observation fairly agrees with the earlier analytical conjectures in Refs [39,44]. Our numerical investigation suggests that the quantitative nature of the initial fall of LE cannot be explain by a single exponential function.…”

Section: Discussionsupporting

confidence: 93%

“…One can now write LE (5) in terms of covariant matrices [39] L λ (t) = EN Π λ (t)|Ψ Ψ † |Π λ (t) EN given by…”

Section: Modelmentioning

confidence: 99%

“…The Loschmidt echo can act as an indicator of quantum phase transition in the equilibrium [2]. This is also true for non-equilibrium situation where derivative of LE with respect to a parameter of the quantum Hamiltonian shows a singular behavior at QCP [39]. The question we ask here is that whether for a disordered chain the derivative of LE still shows a peak around the QCP of the clean chain.…”

Section: A Existence Of Griffith Phasementioning

confidence: 99%

“…The ∆ dependent initial exponential fall is consistent with the analytical results in Refs. [39,44]. The analytical treatments suggest the decay rate is of the order of ∆ 2 .…”

Section: B Quenching Dynamics Of the Spin Chainmentioning

confidence: 99%

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Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain

Mukherjee¹,

Nag²

2019

J. Stat. Mech.

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We study the non-equilibrium evolution of concurrence of a Bell pair constituted of two qubits, through the measurement of Loschmidt echo (LE) under the scope of generalized central spin model. The qubits are locally coupled to a one dimensional disordered Ising spin chain. We first show that in equilibrium situation the derivative of LE is able to detect the extent of Griffiths phase that appeared in presence of disordered transverse field only. While in the non-equilibrium situation, the spin chain requires a temporal window to realize the effect of disorder. We show that within this timescale, LE falls off exponentially and this decay is maximally controlled by the initial states and coupling strength. Our detail investigation suggests that there actually exist three types of exponential decay, a Gaussian decay in ultra short time scale followed by two exponential decay in the intermediate time with two different decay exponents. The effect of the disorder starts appearing in the late time power law fall of LE where the power law exponent is strongly dependent on disorder strength and the final state but almost independent of initial states and coupling strength. This feature allows us to indicate the presence of Griffiths phase. To be precise, continuously varying critical exponent and wide distribution of relaxation time imprint their effect in LE in the late time limit where the power law fall is absent for quenching to a Griffiths phase. Here, LE vanishes following the fast exponential fall. Interestingly, for off-critical quenching LE attains a higher saturation value for increasing disorder strength, otherwise vanishes for a clean spin chain, referring to the fact that disorder prohibits the rapid decay of entanglement in long time limit. Moreover, we show that disorder is also able to destroy the light cone like nature of post quench quasi-particles as LE does not sense the singular time scales appearing for clean spin chain with qubits coupled at symmetric positions.

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Section: Discussionsupporting

confidence: 93%

“…One can now write LE (5) in terms of covariant matrices [39] L λ (t) = EN Π λ (t)|Ψ Ψ † |Π λ (t) EN given by…”

Section: Modelmentioning

confidence: 99%

Section: A Existence Of Griffith Phasementioning

confidence: 99%

“…The ∆ dependent initial exponential fall is consistent with the analytical results in Refs. [39,44]. The analytical treatments suggest the decay rate is of the order of ∆ 2 .…”

Section: B Quenching Dynamics Of the Spin Chainmentioning

confidence: 99%

See 2 more Smart Citations

Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain

Mukherjee¹,

Nag²

2019

J. Stat. Mech.

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show abstract

“…(8). One can the use the covariance matrix formalism to determine time evolution of DF associated with the different DCs governed by two different Hamiltonians [53,57]. These different Hamiltonians H αβ shown in Eq.…”

Section: And H Is Given Bymentioning

confidence: 99%

Generation of concurrence between two qubits locally coupled to a one-dimensional spin chain

Nag

Dutta

2016

Phys. Rev. A

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We consider a generalized central spin model, consisting of two central qubits and an environmental spin chain (with periodic boundary condition) to which these central qubits are locally and weakly connected either at the same site or at two different sites separated by a distance d. Our purpose is to study the subsequent temporal generation of entanglement, quantified by concurrence, when initially the qubits are in an unentangled state. In the equilibrium situation, we show that the concurrence survives for a larger value of d when the environmental spin chain is critical. Importantly, a common feature observed both in the equilibrium and the non-equilibrium situations while the latter is created by a sudden but global change of the environmental transverse field, is that the two qubits become maximally entangled for the critical quenching. Following a non-equilibrium evolution of the spin chain, our study for d = 0, indicates that there exists a threshold time above which concurrence attains a finite value. Additionally, we show that the number of independent decohering channels (DCs) is determined by d as well as the local difference of the transverse field of the two underlying Hamiltonians governing the time evolution. The qualitatively similar behavior displayed by the concurrence for critical and off-critical quenches, as reported here, is characterized by analyzing the non-equilibrium evolution of these channels. The concurrence is maximum when the decoherence factor or the echo associated with the most rapidly DC decays to zero; on the contrary, the condition when the concurrence vanishes is determined non-trivially by the associated decay of one of the intermediate DCs. Analyzing the reduced density of a single qubit, we also explain the observation that the dephasing rate is always slower than the unentanglement rate. We further show that the maximally and minimally decohering channels show singular behavior which can be explained by invoking upon a quasi-particle picture.

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Quantum optics in visual sensors and adaptive optics by quantum vacillations of laser beams wave propagation apply in data mining

Alkawak¹,

Ozturk

Jabbar³

et al. 2023

Optik

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Decoherence of Bell states by local interactions with a suddenly quenched spin environment

Cited by 6 publications

References 49 publications

Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain

Dynamics of decoherence of an entangled pair of qubits locally connected to a one-dimensional disordered spin chain

Generation of concurrence between two qubits locally coupled to a one-dimensional spin chain

Quantum optics in visual sensors and adaptive optics by quantum vacillations of laser beams wave propagation apply in data mining

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