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Modern Physics Letters B

Temperature Effect on Cirac and Zoller Model Using Two-Time Green's Function

Wei Li, Zhao Hong-min, Jia-tih Lin

Published Jun 20, 2003• 0 citations
Publisher

Abstract

Using the two-time Green's function method, we analyze the temperature effect on the famous Cirac and Zoller model. Formulas for the average number of different mode phonons and the deviation of its internal state from its ground state are derived. The influence of the internal state energy and trap frequency on the number of phonons is also discussed. The upper limit of temperature for regular quantum computation in the Cirac and Zoller model is obtained.

DOI
10.1142/s0217984903005391

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Using the two-time Green's function method, we analyze the temperature effect on the famous Cirac and Zoller model. Formulas for the average number of different mode phonons and the deviation of its internal state from its ground state are derived. The influence of the internal state energy and trap frequency on the number of phonons is also discussed. The upper limit of temperature for regular quantum computation in the Cirac and Zoller model is obtained.
Using two-time Green's function we analyze the effect of temperature on the Mølmer and Sørensen (M–S) model of cold trapped ion quantum computer. A formula for the deviation of an internal state from its ground state is derived in the first-order approximation. The fluctuation of internal state caused by thermal motion is also discussed. The deviation of internal state when different trap parameters changes with the temperature are given too. The upper temperature limit for regular quantum computation is obtained and our result is in agreement with experiment.
We analyzed the influence of the thermal motion from the environment on the internal states of trapped ions and the center-of-mass mode phonon using a Green's-function method. The deviation of the internal states and the variational rules of the phonon number with different trap parameters changing with the temperature are given. The upper limit of the temperature at which the gate operation can be performed safely is convenient to be found out according to different error correction capability.
. The theory of interactions between lasers and cold trapped ions as it pertains to the design of Cirac--Zoller quantum computers is discussed. The mean positions of the trapped ions, the eigenvalues and eigenmodes of the ions' oscillations, the magnitude of the Rabi frequencies for both allowed and forbidden internal transitions of the ions, and the validity criterion for the required Hamiltonian are calculated. Energy level data for a variety of ion species are also presented. PACS: 32.80.Qk; 42.50.Vk; 89.80.+h A quantum computer is a device in which data can be stored in a network of quantum mechanical two-level systems, such as spin-1/2 particles or two-level atoms. The quantum mechanical nature of such systems allows the possibility of a powerful new feature to be incorporated into data processing, namely, the capability of performing logical operations upon quantum mechanical superpositions of numbers. Thus in a conventional digital computer each data register is, throughout an...
Within unitary transformed Hamiltonian of Fröhlich type, using the Green's functions method, exact renormalized energy spectrum of quasiparticle strongly interacting with two-mode polarization phonons is obtained at T=0 K in a model of the system with limited number of its initial states. Exact analytical expressions for the average number of phonons in ground state and in all satellite states of the system are presented. Their dependences on a magnitude of interaction between quasiparticle and both phonon modes are analyzed.
The intrinsic decoherence from vibrational coupling of the ions in the Cirac-Zoller quantum computer [Phys. Rev. Lett. 74, 4091 (1995)] is considered. Starting from a state in which the vibrational modes are at a temperature TTT, and each ion is in a superposition of an excited and a ground state, an adiabatic approximation is used to find the inclusive probability P(t)P(t)P(t) for the ions to evolve as they would without the vibrations, and for the vibrational modes to evolve into any final state. An analytic form is found for P(t)P(t)P(t) at T=0T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0T=0, and the decoherence time is found for all TTT. The decoherence is found to be quite small, even for 1000 ions.