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Decoherence of the quantum logic gate implemented with the Jaynes-Cummings model

Hiroo Azuma

Published May 1, 2016• 0 citations
OpenAlex

Abstract

In this paper, we investigate decoherence of Knill, Laflamme, and Milburn's nonlinear sign-shift gate that is implemented with the Jaynes-Cummings model. We analyze it by two methods. In the first method, we introduce a stochastic variable as an external magnetic field, and we let it couple with a magnetic dipole moment of a two-level atom. We examine this model using a semiclassical theory. The results of the Monte Carlo simulations under the semiclassical approximation correspond well with those obtained with the quantum mechanical perturbation theory for the stochastic process. In the second method, we study a master equation of the Jaynes-Cummings model with cavity losses in a fully quantum mechanical manner. We solve the master equation numerically with the Runge-Kutta method. For both semiclassical and fully quantum mechanical analyses, we can observe both the $\mbox{T}_{1}$ and $\mbox{T}_{2}$ decays. This paper is a sequel of the reference [H.~Azuma, Prog. Theor. Phys. {\bf 126}, 369 (2011)].

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Decoherence of the quantum logic gate implemented with the Jaynes–Cummings model: A semiclassical approach

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In this paper, we investigate decoherence of Knill, Laflamme, and Milburn’s nonlinear sign-shift gate that is implemented with the Jaynes–Cummings model. Introducing a stochastic variable as an external electric field, we let it couple with a dipole moment of a two-level atom. We examine this model using a semiclassical theory. Results of the Monte Carlo simulations under the semiclassical approximation correspond well with those obtained with quantum mechanical perturbation theory for the stochastic process. In the results of the simulations, we observe both the |$\mbox{T}_{1}$| and |$\mbox{T}_{2}$| decays. This paper is a sequel to [H. Azuma, Prog. Theor. Phys. 126, 369 (2011)].

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Coherence Loss of Two-Photon Jaynes–Cummings Model in Dispersive Approximation

Zhou Ling, Yanqing Guo, He‐Shan Song +1 more

Completely solving the dissipative dynamics of nonlinear Jaynes–Cumming model is a very difficult task. In our recent work (Phys. Lett. A284 (2001) 156), we just obtained analytical results of the field dissipative dynamics of the nonlinear JCM. In the present paper, employing the perturbative expansion of master equation, we obtain the density operator of the system (field +atom). The coherence losses of the system and of the atom are investigated when two-photon process is involved. We also study the effect of different atomic initial states and the influence of the field amplitude on the atomic coherence loss.

Communications in Theoretical Physics•Jan 15, 2004•1 citation
In this paper, we investigate decoherence of Knill, Laflamme, and Milburn's nonlinear sign-shift gate that is implemented with the Jaynes-Cummings model. We analyze it by two methods. In the first method, we introduce a stochastic variable as an external magnetic field, and we let it couple with a magnetic dipole moment of a two-level atom. We examine this model using a semiclassical theory. The results of the Monte Carlo simulations under the semiclassical approximation correspond well with those obtained with the quantum mechanical perturbation theory for the stochastic process. In the second method, we study a master equation of the Jaynes-Cummings model with cavity losses in a fully quantum mechanical manner. We solve the master equation numerically with the Runge-Kutta method. For both semiclassical and fully quantum mechanical analyses, we can observe both the \mboxT1\mbox{T}_{1}\mboxT1​ and \mboxT2\mbox{T}_{2}\mboxT2​ decays. This paper is a sequel of the reference [H.~Azuma, Prog. Theor. Phys. {\bf 126}, 369 (2011)].
In this paper, we investigate decoherence of Knill, Laflamme, and Milburn’s nonlinear sign-shift gate that is implemented with the Jaynes–Cummings model. Introducing a stochastic variable as an external electric field, we let it couple with a dipole moment of a two-level atom. We examine this model using a semiclassical theory. Results of the Monte Carlo simulations under the semiclassical approximation correspond well with those obtained with quantum mechanical perturbation theory for the stochastic process. In the results of the simulations, we observe both the |$\mbox{T}_{1}$| and |$\mbox{T}_{2}$| decays. This paper is a sequel to [H. Azuma, Prog. Theor. Phys. 126, 369 (2011)].
In this paper, we propose a method for building a two-qubit gate with the Jaynes-Cummings model (JCM). In our scheme, we construct a qubit from a pair of optical paths where a photon is running. Generating Knill, Laflamme and Milburn's nonlinear sign-shift gate by the JCM, we construct the conditional sign-flip gate, which works with small error probability in principle. We also discuss two experimental setups for realizing our scheme. In the first experimental setup, we make use of coherent lights to examine whether or not our scheme works. In the second experimental setup, an optical loop circuit made out of the polarizing beam splitter and the Pockels cell takes an important role in the cavity.
Decoherence of the dispersive Jaynes–Cummings model which is placed in a lossy cavity is studied by means of the time-convolutionless non-Markovian quantum master equation. The effect of the interaction between a two-level atom and photon field on the damping operator of the quantum master equation is made clear by calculating the decay of coherence and entanglement of the relevant system. It is shown that although the interaction effect on the damping operator is small when the cavity loss has the Markovian property, it becomes significantly large when the cavity loss is subject to the non-Markovian process. Furthermore, the quantum channel of the two-level atom derived by the dispersive Jaynes–Cummings model is investigated. The decay of entanglement of the two two-level atoms is examined to show the importance of the interaction effect on the damping operator.
The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic fluctuations in atom-field coupling. The coupling coefficient is assumed to fluctuate in phase and/or in amplitude. The phase fluctuations are described by a Wiener-Levy process and the amplitude fluctuations by a colored Gaussian noise. A secular approximation and the theory of the multiplicative stochastic processes are invoked to derive the master equation for the density operator averaged over both phase and amplitude ensembles. The solution of this equation is used to study the resulting decoherence effects in the dynamical behavior of the atom and the statistical properties of the field.
Completely solving the dissipative dynamics of nonlinear Jaynes-Cumming model is a very difficult task. In our recent work(Phys.Lett.A284(2001)156),we just obtained analytical results of the field dissipative dynamics of the nonlinear JCM.In the present paper,employing the perturbative expansion of master equation,we obtain the density operator of the system(field+atom).The coherence losses of the system and of the atom are investigated when two-photon process is involved.We also study the effect of different atomic initial states and the influence of the field amplitude on the atomic coherence loss.
Completely solving the dissipative dynamics of nonlinear Jaynes–Cumming model is a very difficult task. In our recent work (Phys. Lett. A284 (2001) 156), we just obtained analytical results of the field dissipative dynamics of the nonlinear JCM. In the present paper, employing the perturbative expansion of master equation, we obtain the density operator of the system (field +atom). The coherence losses of the system and of the atom are investigated when two-photon process is involved. We also study the effect of different atomic initial states and the influence of the field amplitude on the atomic coherence loss.