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Journal of the Physical Society of Japan

Pulse Control of Dephasing in Two-Level Quantum Systems

Yositake Takane, Takahiro Murakami

Published Aug 1, 2005• 6 citations
Publisher

Abstract

The pulse control of dephasing is studied for a two-level quantum system (qubit) interacting with a quantum environment. It has been shown that dephasing in a qubit due to qubit–environment interactions can be suppressed by a sequence of periodic π pulses with infinitely short duration. To study how the effectiveness of the pulse control is affected by finite pulse duration t d , we calculate the time evolution of the reduced density operator for a qubit under a sequence of π pulses. We show that the pulse control is effective even for not short t d if a suitable pulse sequence is adopted.

DOI
10.1143/jpsj.74.2243

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The pulse control of dephasing is studied for a two-level quantum system (qubit) interacting with a quantum environment. It has been shown that dephasing in a qubit due to qubit–environment interactions can be suppressed by a sequence of periodic π pulses with infinitely short duration. To study how the effectiveness of the pulse control is affected by finite pulse duration t d , we calculate the time evolution of the reduced density operator for a qubit under a sequence of π pulses. We show that the pulse control is effective even for not short t d if a suitable pulse sequence is adopted.
The pulse control of decoherence in a qubit interacting with a quantum environment is studied with focus on a general case where decoherence is induced by both pure dephasing and population decay. To observe how the decoherence is suppressed by periodic pi pulses, we present a simple method to calculate the time evolution of a qubit under arbitrary pulse sequences consisting of bit-flips and/or phase-flips. We examine the effectiveness of the two typical sequences: bb sequence consisting of only bit-flips, and bp sequence consisting of both bit- and phase-flips. It is shown that the effectiveness of the pulse sequences depends on a relative strength of the two decoherence processes especially when a pulse interval is slightly shorter than qubit-environment correlation times. In the short-interval limit, however, the bp sequence is always more effective than, or at least as effective as, the bb sequence.
We study the time evolution of a qubit linearly coupled with a quantum environment under a sequence of short π pulses.Our attention is focused on the case where qubit-environment interactions induce the decoherence with population decay.We assume that the environment consists of a set of bosonic excitations.The time evolution of the reduced density matrix for the qubit is calculated in the presence of periodic short π pulses.We confirm that the decoherence is suppressed if the pulse interval is shorter than the correlation time for qubit-environment interactions.
Reliable long-time storage of arbitrary quantum states is a key element of quantum information processing. In order to dynamically decouple a spin or quantum bit from a dephasing environment by non-instantaneous pulses, we introduce an optimized sequence of N control π pulses that are realistic in the sense that they have a finite duration and a finite amplitude. We show that optimized dynamical decoupling is still applicable and that higher-order decoupling can be reached if shaped pulses are implemented. The sequence suppresses decoherence up to the order , with T being the total duration of the sequence and τ mx the maximum length of the pulses. The exponent depends on the shape of the pulse. Based on existing experiments, a concrete setup for the verification of the properties of the advocated sequence is proposed.
An irreversible time evolution of a quantum system interacting with a surrounding environment is described by a quantum master equation. When an external field is applied to a quantum system, a non-Markovian master equation is derived in a rigorous way, where the relaxation terms in the quantum master equation include the effect of the external field that is ignored in the conventional treatment. It is shown that when the external field is a sequence of phase-modulation π-pulses, the decoherence of the quantum system can be suppressed. In particular, when the pulse separation is sufficiently short in comparison with the correlation time of the environmental system, dynamical decoupling takes place. To see the effect of the phase-modulation π-pulses, the time evolution of qubit entanglement is investigated in detail.
We examine the effect of multilevels on decoherence and dephasing properties of a quantum system consisting of a non-ideal two level subspace, identified as the qubit and a finite set of higher energy levels above this qubit subspace. The whole system is under interaction with an environmental bath through a Caldeira-Leggett type coupling. The model interaction we use can generate nonnegligible couplings between the qubit states and the higher levels upto N∼10N\sim 10N∼10. In contrast to the pure two-level system, in a multilevel system the quantum information may leak out of the qubit subspace through nonresonant as well as resonant excitations induced by the environment. The decoherence properties of the qubit subspace is examined numerically using the master equation formalism of the system's reduced density matrix. We numerically examine the relaxation and dephasing times as the environmental frequency spectrum, the environmental temperature, and the multilevel system parameters are varied. We observe the influence of all energy scales in the noise spectrum on the short time dynamics implying the dominance of nonresonant transitions at short times. The relaxation and dephasing times calculated, strongly depend on NNN for 4<N<104< N<104<N<10 and saturate for $10
We investigate the possibility to control quantum evolution speed of a single dephasing qubit for arbitrary initial states by the use of periodic dynamical decoupling (PDD) pulses. It is indicated that the quantum speed limit time (QSLT) is determined by initial and final quantum coherence of the qubit, as well as the non-Markovianity of the system under consideration during the evolution when the qubit is subjected to a zero-temperature Ohmic-like dephasing reservoir. It is shown that final quantum coherence of the qubit and the non-Markovianity of the system can be modulated by PDD pulses. Our results show that for arbitrary initial states of the dephasing qubit with non-vanishing quantum coherence, PDD pulses can be used to induce potential acceleration of the quantum evolution in the short-time regime, while PDD pulses can lead to potential speedup and slow down in the long-time regime. We demonstrate that the effect of PDD on the QSLT for the Ohmic or sub-Ohmic spectrum (Markovian reservoir) is much different from that for the super-Ohmic spectrum (non-Markovian reservoir).