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arXiv:1605.00219 · Progress of Theoretical and Experimental Physics

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

Hiroo Azuma

Published Apr 12, 2017• 0 citations
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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. 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)].

DOI
10.1093/ptep/ptx056

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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 |\mboxT1\mbox{T}_{1}\mboxT1​| and |\mboxT2\mbox{T}_{2}\mboxT2​| decays. This paper is a sequel to [H. Azuma, Prog. Theor. Phys. 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. 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)].
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.
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.
In this paper, we study the multiphoton Jaynes-Cummings model (JCM) governed by the Milburn equation [G. J. Milburn, Phys. Rev. A 44, 5401 (1991); 47, 2415 (1993)], which models the decoherence of a quantum system as the quantum system evolves through intrinsic mechanisms beyond conventional quantum mechanics. We give an exact solution of this equation for the multiphoton Jaynes-Cummings Hamiltonian and apply it to investigate the influence of the intrinsic decoherence on nonclassical effects (atomic inversion, oscillations of the photon-number distribution, squeezing of the cavity field, and photon antibunching) in the JCM. It is shown that during the time evolution, the intrinsic decoherence in the atom-field interaction suppresses these nonclassical behaviors in the JCM.
In this paper, we study the influence of the intrinsic decoherence on quantum statistical properties of a generalized nonlinear interacting atom–field system, i.e., the nondegenerate two-photon f-deformed Jaynes–Cummings model governed by the Milburn equation. The model contains the nonlinearities of both the cavity–field and the atom–field coupling. Until now, very few exact solutions of nonlinear systems that include a form of decoherence have been presented. The main achievement of the present work is to find exact analytical solutions for the quantum dynamics of the nonlinear model under consideration in the presence of intrinsic decoherence. With the help of a supersymmetric transformation, we first put the model Hamiltonian into an appropriate form for treating the intrinsic decoherence. Then, by applying the superoperator technique, we find an exact solution of the Milburn equation for a nondegenerate two-photon f-deformed Jaynes–Cummings model. We use this solution to investigate the effects of the intrinsic decoherence on temporal evolution of various nonclassical properties of the system, i.e., atomic population inversion, atomic dipole squeezing, atom–field entanglement, sub-Poissonian photon statistics, cross correlation between the two modes and quadrature squeezing of the cavity field. Particularly, we compare the numerical results for three different cases of two-mode deformed, one-mode deformed, and nondeformed Jaynes–Cummings models. PACS Nos.: 42.50.Ct, 42.50.Dv, 03.65.Yz
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 phase fluctuations in the atom-field coupling coefficient. The fluctuations are modelled by random telegraph process and an equation for the density operator averaged over the distribution of fluctuations has been obtained. The solution of this equation is used to study the resulting decoherence effects in the dynamical behaviour of the atom and the statistical properties of the field.