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arXiv:quant-ph/0407124

Explicit formula for the external driving field used to eliminate the decoherence of a two-state system coupled to a noise field

Shen, Jian-Qi, Zhichao Ruan, Sailing He

Published Jul 16, 2004• 0 citations
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Abstract

The elimination of decoherence of a multiphoton two-state quantum system by using an appropriate external driving field is considered. The multiphoton process caused by the noise field has a supersymmetric Lie algebraic structure. The time-evolution equations for the off-diagonal elements of the density operator of the two-state system are derived in the interaction picture. A simple explicit formula is given for the time-dependent external driving field used to eliminate the decoherence of the multiphoton two-state system.

DOI
10.48550/arxiv.quant-ph/0407124

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The elimination of decoherence of a multiphoton two-state quantum system by using an appropriate external driving field is considered. The multiphoton process caused by the noise field has a supersymmetric Lie algebraic structure. The time-evolution equations for the off-diagonal elements of the density operator of the two-state system are derived in the interaction picture. A simple explicit formula is given for the time-dependent external driving field used to eliminate the decoherence of the multiphoton two-state system.
The elimination of decoherence of two-state quantum systems interacting with a thermal reservoir through an external controllable driving field is discussed in the present paper. The restriction equation with which the external controllable driving field should agree will be derived. Based on this, we obtain the time-development equation of the off-diagonal elements of density operator in the supersymmetric multiphoton two-state quantum systems, which is helpful for studying the polarization evolution in this two-state quantum model.
In this paper, the problem of the decoherence of two\|state quantum systems interacting with a bath through an external controllable driving field is discussed. The time evolution of the off-diagonal elements of the density operator in two\|state quantum systems is obtained. The relation between the decoherence and the external controllable driving field is also obtained. Thus we establish the restriction equation that must be satisfied by the external controllable driving field when the decoherence is to vanish.
The problem of decoherence of two-state quantum systems interacting with a bath through an external controllable driving field without rotating wave approximation is discussed.The off-diagonal elements of density operator in two-state quantum systems are obtained.The result reflects that decoherence of the two-state quantum systems has something to do with its original state,frequency of the bath and external controllable driving field.The relation between the decoherence and external controllable driving field is studied.Properties of an external controllable driving field are obtained when the two-state quantum systems of coherence is maintained.
Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics, are handled through master equations for the density matrix. Master equations such as the Lindblad equation preserve the trace of this matrix. Viewing them as first-order time-dependent operator equations for the elements of the density matrix, a unitary integration procedure can be adapted to solve for these elements. A simple model for decoherence preserves the Hermiticity of the density matrix. A single, classical Riccati equation is the only one requiring numerical handling to obtain a full solution of the quantum evolution. The procedure is general, valid for any number of levels, but is illustrated here for a three-level system with two driving fields. For various choices of the initial state, we study the evolution of the system as a function of the amplitudes, relative frequencies, and phases of the driven fields and of the strength of the decoherence. The monotonic growth of the entropy is followed as the system evolves from a pure to a mixed state. An example is provided by the n=3n=3n=3 states of the hydrogen atom in a time-dependent electric field, such degenerate manifolds affording an analytical solution.
We consider the quantized atom-field model and for the regime ; where , and respectively represent the self-Hamiltonians of the environment, the system, and the interaction between the system and the environment. Considering a single-mode quantized field we obtain the time evolution operator for the model. Using our time evolution operator we calculate the time-dependent pointer states of the system and the environment, which are characterized by their property of not entangling with states of another subsystem. We obtain a closed form expression for the off-diagonal element of the reduced density matrix of the system and study the decoherence of the central system in our model. We show that for the case where the system initially is not prepared in one of its pointer states, the off-diagonal element of the reduced density matrix of the system decays with a decoherence time that is inversely proportional to the square root of the mass of the bosonic field particles.