Relaxation and decoherence of a qubit coupled to the environment and driven by a resonant ac field are investigated by analytically solving the Bloch equation of the qubit. We found that the decoherence of a driven qubit can be decomposed into intrinsic and field-dependent decoherence. The intrinsic decoherence time equals the decoherence time of the qubit in a free decay while the field-dependent decoherence time is identical with the relaxation time of the qubit in driven oscillation. Analytical expressions of the relaxation and decoherence times are derived and applied to study a microwave-driven SQUID flux qubit. The results are in excellent agreement with those obtained from directly numerically solving the master equation. The relations between the relaxation and decoherence times of a qubit in free decay and driven oscillation can be used to extract the decoherence and thus dephasing times of the qubit by measuring its population evolution in free decay and resonantly driven oscillation.Relaxation and decoherence of a qubit coupled to the environment and driven by a resonant ac field are investigated by analytically solving the Bloch equation of the qubit. We found that the decoherence of a driven qubit can be decomposed into intrinsic and field-dependent decoherence. The intrinsic decoherence time equals the decoherence time of the qubit in a free decay while the field-dependent decoherence time is identical with the relaxation time of the qubit in driven oscillation. Analytical expressions of the relaxation and decoherence times are derived and applied to study a microwave-driven SQUID flux qubit. The results are in excellent agreement with those obtained from directly numerically solving the master equation. The relations between the relaxation and decoherence times of a qubit in free decay and driven oscillation can be used to extract the decoherence and thus dephasing times of the qubit by measuring its population evolution in free decay and resonantly driven oscillation.

arXiv:cond-mat/0604191Journal of Physics B Atomic Molecular and Optical PhysicsFeb 12, 200815 citations

Spin relaxation and decoherence of two-level systems

X. R. Wang, Yanzhe Zheng, Yin Sun

We revisit the concepts of spin relaxation and spin decoherence of two-level (spin- $1∕2$ ) systems. From two toy models, we clarify two issues related to the spin relaxation and decoherence: (1) For an ensemble of two-level particles each subjected to a different environmental field, there exists an ensemble relaxation time ${T}_{1}^{*}$ , which is fundamentally different from ${T}_{1}$ . When the off-diagonal coupling of each particle is in a single mode with the same frequency but a random coupling strength, we show that ${T}_{1}^{*}$ is finite while the spin-relaxation time of a single-spin ${T}_{1}$ and the usual ensemble decoherence time ${T}_{2}^{*}$ are infinite. (2) For a two-level particle under only a random diagonal coupling, its relaxation time ${T}_{1}$ shall be infinite, but its decoherence time ${T}_{2}$ is finite.We revisit the concepts of spin relaxation and spin decoherence of two-level (spin-$1∕2$) systems. From two toy models, we clarify two issues related to the spin relaxation and decoherence: (1) For an ensemble of two-level particles each subjected to a different environmental field, there exists an ensemble relaxation time ${T}_{1}^{*}$, which is fundamentally different from ${T}_{1}$. When the off-diagonal coupling of each particle is in a single mode with the same frequency but a random coupling strength, we show that ${T}_{1}^{*}$ is finite while the spin-relaxation time of a single-spin ${T}_{1}$ and the usual ensemble decoherence time ${T}_{2}^{*}$ are infinite. (2) For a two-level particle under only a random diagonal coupling, its relaxation time ${T}_{1}$ shall be infinite, but its decoherence time ${T}_{2}$ is finite.

arXiv:cond-mat/0509395Physical Review BSep 15, 200519 citations

We revisit the concepts of spin relaxation and spin decoherence of two-level (spin-

1∕2

) systems. From two toy models, we clarify two issues related to the spin relaxation and decoherence: (1) For an ensemble of two-level particles each subjected to a different environmental field, there exists an ensemble relaxation time

{T}_{1}^{*}

, which is fundamentally different from

{T}_{1}

. When the off-diagonal coupling of each particle is in a single mode with the same frequency but a random coupling strength, we show that

{T}_{1}^{*}

is finite while the spin-relaxation time of a single-spin

{T}_{1}

and the usual ensemble decoherence time

{T}_{2}^{*}

are infinite. (2) For a two-level particle under only a random diagonal coupling, its relaxation time

{T}_{1}

shall be infinite, but its decoherence time

{T}_{2}

is finite.