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Modern Physics Letters B

Quantum evolution of a qubit state with decoherence and LFC

Chao Wang, Jian Luo

Published Feb 20, 2016• 0 citations
Publisher

Abstract

We study the Rabi oscillation of two-level system in double quantum dots, and found that the Rabi oscillation considering decoherence rate is a cycle attenuated oscillation when the qubit energy asymmetry [Formula: see text] ([Formula: see text] is the qubit energy asymmetry). The peak of Rabi oscillation alternatively changes in the case of the qubit energy asymmetry [Formula: see text] ([Formula: see text] is the qubit tunneling matrix element). Moreover, the local field correction (LFC) greatly affects the frequency of Rabi oscillation, in which the Rabi frequency changes fast with LFC increasing.

DOI
10.1142/s0217984916500275

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We study the Rabi oscillation of two-level system in double quantum dots, and found that the Rabi oscillation considering decoherence rate is a cycle attenuated oscillation when the qubit energy asymmetry [Formula: see text] ([Formula: see text] is the qubit energy asymmetry). The peak of Rabi oscillation alternatively changes in the case of the qubit energy asymmetry [Formula: see text] ([Formula: see text] is the qubit tunneling matrix element). Moreover, the local field correction (LFC) greatly affects the frequency of Rabi oscillation, in which the Rabi frequency changes fast with LFC increasing.
We present Investigation of the implications of decoherence on a single quantum dot two-level system’s dynamic by using the Jaynes-Cumming model (JCM). In addition to JCM, we use generalized Lindblad time evolution method for obtaining the reduced density matrix of master system, with time-dependent coherent energy transfer between atom and cavity quantum electrodynamics (CQED) field and total energy damping. Quantum to the classical transition of the master system and changes in the present amount of coherence in the system via coupling with the environment is reported by using Wigner function. The present investigation aims to numerically predict the quantum to classical shift and induced decoherence process of Rabi oscillation in a single quantum dot using the JC model. The obtained results have been explained with a different approach of entropy generation. Further, obtained result can be used for the development of third-generation semiconductor-based qubits.
We study the role of charge fluctuations in the decoherence of Rabi oscillations between spin states \ensuremath{\mid}\ensuremath{\uparrow}\ensuremath{\downarrow}⟩, \ensuremath{\mid}\ensuremath{\downarrow}\ensuremath{\uparrow}⟩ of two electrons in a double dot structure. We consider the effects of fluctuations in energy and in the quantum state of the system, both in the classical and quantum limits. The role of state fluctuations is shown to be of leading order at sufficiently high temperature, applicable to actual experiments. At low temperature, the low frequency energy fluctuations are the only dominant contribution.
Decoherence is a quantum-mechanical phenomenon severely limiting quantum information processing and storage capability in quantum computers. Decoherence refers to mechanisms that cause transfer of information from a quantum system to its bath. Typically, in theoretical and experimental considerations of different systems containing superconducting qubits, the coupling strength between a qubit and its bath has been assumed to be constant in time. In this case, many standard results in the dynamics of two-level systems follow. For example, due to decoherence, driven Rabi oscillations in a qubit have a characteristic decay time. In addition, the oscillations may take place at any phase. However, by considering time-dependent coupling to the bath, these phenomena may be absent. In this thesis, we demonstrate with numerical simulations of a time-dependent Lindblad master equation persistent Rabi oscillations in a qubit driven by a coherent drive tone. The persistent Rabi oscillations are induced by modulating the coupling of the qubit to the bath with a sinusoidal temporal shape. We observe that the temporal modulation enforces a limit cycle on the evolution of the dressed qubit state with a fixed phase relative to the phase of the sinusoidal modulation regardless of the initial state of the system. Through a synchronization-like phenomenon, the frequency of the Rabi oscillation adapts to match the frequency of the modulation. We determine the effect of different system parameters on the limit cycle and study how the amplitude of the persistent oscillation depends on the coupling modulation parameters. We also observe a similar effect in the freely evolving qubit precession. In addition, the qubit acts as a non-linear mixer, resulting in different linear combinations of the original modulation waveform appearing in the bath-induced Rabi oscillations. We also introduce a design for a physical system where our simulations can be verified experimentally.
We consider the quantum Rabi model as an open system that is subject to dissipation, dephasing, and sinusoidal qubit driving. One can change to an interaction picture where the qubit-driving term disappears at the expense of changing the free energy of the qubit which becomes time dependent. If the driving frequency is large with respect to the rest of the parameters with the exception of the driving strength, then one can obtain an effective Hamiltonian that accurately describes the dynamics of the system. The driving has two effects: the qubit-transition frequency is changed and the qubit has reduced dephasing. The driving strength can be chosen so that the qubit-transition frequency is reduced, made equal to zero, or even made negative so that the excited and ground states of the qubit are interchanged. Therefore, sinusoidal qubit driving offers another method to control the qubit-transition frequency and to reduce qubit dephasing. Adjusting the driving strength allows one to consider a qubit with degenerate energy levels. Not taking dissipation into account, the evolution operator of the qubit-harmonic oscillator system is given by a linear combination of the orthogonal projectors onto the eigenstates of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\sigma}}}_{x}$ followed by the evolution operator of a forced harmonic oscillator, the harmonic oscillator can be prepared in such a way that it is always found in a Schr\"odinger cat state, and the transition probability of the qubit can exhibit a collapse-revival behavior. In addition, the Born-Markov-secular master equation is deduced and the effects of dissipation are presented. In particular, smaller ultrastrong-coupling values are preferable over larger ultrastrong-coupling values and deep strong-coupling values in order to have long-lived, easily distinguishable Schr\"odinger cat states because the decoherence rate is inversely proportional to the square of the coupling. Finally, the qubit-harmonic oscillator system can be prepared in highly entangled states that are stable under dissipation.
We consider the problem of a qubit driven by a harmonically oscillating external field while it is coupled to a quantum two-level system (TLS). We perform a systematic numerical analysis of the problem by varying the relevant parameters. The numerical calculations agree with the predictions of a simple intuitive picture, namely one that takes into consideration the four-level energy spectrum, the simple principles of Rabi oscillations and the basic effects of decoherence. Furthermore, they reveal a number of other interesting phenomena. We provide explanations for the various features that we observe in the numerical calculations and discuss how they can be used in experiment. In particular, we suggest an experimental procedure to characterize an environment of TLSs.