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arXiv:0805.0962

Decoherence by Quantum Telegraph Noise

Benjamin Abel, Florian Marquardt

Published May 7, 2008• 2 citations
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Abstract

We investigate the time-evolution of a charge qubit subject to quantum telegraph noise produced by a single electronic defect level. We obtain results for the time-evolution of the coherence that are strikingly different from the usual case of a harmonic oscillator bath (Gaussian noise). When the coupling strength crosses a certain temperature-dependent threshold, we observe coherence oscillations in the strong-coupling regime. Moreover, we present the time-evolution of the echo signal in a spin-echo experiment. Our analysis relies on a numerical evaluation of the exact solution for the density matrix of the qubit.

DOI
10.48550/arxiv.0805.0962

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We investigate the time-evolution of a charge qubit subject to quantum telegraph noise produced by a single electronic defect level. We obtain results for the time-evolution of the coherence that are strikingly different from the usual case of a harmonic oscillator bath (Gaussian noise). When the coupling strength crosses a certain temperature-dependent threshold, we observe coherence oscillations in the strong-coupling regime. Moreover, we present the time-evolution of the echo signal in a spin-echo experiment. Our analysis relies on a numerical evaluation of the exact solution for the density matrix of the qubit.
We investigate the time evolution of a charge qubit subject to quantum telegraph noise produced by a single electronic defect level. We obtain results for the time evolution of the coherence that are strikingly different from the usual case of a harmonic-oscillator bath (Gaussian noise). When the coupling strength crosses a certain temperature-dependent threshold, we observe coherence oscillations in the strong-coupling regime. Moreover, we present the time evolution of the echo signal in a spin-echo experiment. Our analysis relies on a numerical evaluation of the exact solution for the density matrix of the qubit.
A qubit (containing two quantum states, 1 and 2), is coupled to a control register (state 3), which is subject to telegraph noise. We study the time evolution of the density matrix ρρρ of an electron which starts in some coherent state on the qubit. At infinite time, ρρρ usually approaches the fully decoherent state, with ρnm=δnm/3ρ^{}_{nm}=δ^{}_{nm}/3ρnm​=δnm​/3. However, when the Hamiltonian is symmetric under 1↔21\leftrightarrow 21↔2, the element ρ12ρ^{}_{12}ρ12​ approaches a non-zero real value, implying a partial coherence of the asymptotic state. The asymptotic density matrix depends only on Re[ρ12(t=0)]{\rm Re}[ρ^{}_{12}(t=0)]Re[ρ12​(t=0)]. In several cases, the information stored on the qubit is protected from the noise.
We present a general and exact formalism for finding the evolution of a quantum system subject to external telegraph noise. The various qubit decoherence rates are determined by the eigenvalues of a transfer matrix. The formalism can be applied to a qubit subject to an arbitrary combination of dephasing and relaxational telegraph noise, in contrast to existing nonperturbative methods that treat only one or the other of these limits. Hence we are able to investigate the crossover from pure dephasing noise to pure relaxational noise in detail. New results at strong coupling include the full qubit dynamics on time scales short compared with the environmental correlation times, which reveals unexpected oscillations and induced magnetization components and strong violations of the widely used relation $1∕{T}_{2}=1∕2{T}_{1}+1∕{T}_{\ensuremath{\phi}},$ which is a result of perturbation theory. We also discuss the effects of bang-bang and spin-echo controls of the qubit dynamics in general settings of the telegraph noises. Finally, we discuss the extension of the method to the cases of many telegraph noise sources and multiple qubits. The method still works when white noise is also present.
We analyze theoretically the decoherence of two interacting electrons in a double self-assembled quantum dot due to a random telegraph noise. For this purpose we have examined the pure dephasing rate by evaluating the decoherence factor. The latter has been shown to be different from that calculated within the Gaussian approximation in the strong coupling regime. In order to determine the influence of the random telegraph noise on the entanglement of the system states, the concurrence, the populations, and the entropy are evaluated as well. Our results show that telegraph noise can severely impact the coherence of charge qubits.
We analyze local spin-echo procedures for protecting entanglement between two non-interacting qubits, each subject to pure-dephasing random telegraph noise. For superconducting qubits, this simple model captures the characteristic features of the effect of bistable impurities coupled to the device. An analytic expression for the entanglement dynamics is reported. Peculiar features related to the non-Gaussian nature of the noise already observed in the single-qubit dynamics also occur in the entanglement dynamics for proper values of the ratio g = v / γ , between the qubit–impurity coupling strength and the switching rate of the random telegraph process, and of the separation between the pulses Δ t . We found that the echo procedure may delay the disappearance of entanglement, cancel the dynamical structure of entanglement revivals and dark periods and induce peculiar plateau-like behaviors of the concurrence.
The effects of a collection of classical two-level charge fluctuators on the coherence of a dynamically decoupled qubit are studied. Distinct dynamics is found at different qubit working positions. Exact analytical formulas are derived at pure dephasing and approximate solutions are found at the general working position, for weakly and strongly coupled fluctuators. Analysis of these solutions, combined with numerical simulations of the multiple random telegraph processes, reveal the scaling of the noise with the number of fluctuators and the number of control pulses, as well as dependence on other parameters of the qubit-fluctuators system. These results can be used to determine potential microscopic models for the charge environment by performing noise spectroscopy.