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arXiv:quant-ph/0504187

Note on "Hyperfine coherence in the presence of spontaneous photon scattering" (quant-ph/0502063) and minimum energy requirements for quantum logic

Julio R. Gea-Banacloche

Published Apr 25, 2005• 3 citations
arXivHTMLPDF

Abstract

The goal of this short note is to show that the formulas I derived originally in [Phys. Rev. A 65, 022308 (2002)] regarding the errors introduced in quantum logical operations by the quantum nature of the control fields apply even in the situation discussed recently by Ozeri et al. in quant-ph/0502063, where the decoherence-inducing spontaneous Raman scattering is considerably suppressed.

DOI
10.48550/arxiv.quant-ph/0504187

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The goal of this short note is to show that the formulas I derived originally in [Phys. Rev. A 65, 022308 (2002)] regarding the errors introduced in quantum logical operations by the quantum nature of the control fields apply even in the situation discussed recently by Ozeri et al. in quant-ph/0502063, where the decoherence-inducing spontaneous Raman scattering is considerably suppressed.
We investigate the decoherence of superpositions of hyperfine states of Be ions due to spontaneous scattering of off-resonant light. We find that, contrary to conventional wisdom, elastic Rayleigh scattering can have majour contributions to decoherence when compared to the effect of inelastic Raman scattering. 1. Summary Minimizing the effects of decoherence is a central challenge in many quantum physics experiments. In the case of ion trap quantum computing [1] a majour contribution to decoherence comes from the off-resonant scattering of the controlling light beams. It is often assumed that the decoherence process is dominated by in-elastic Raman scattering, since in that case the scattered photon has a different frequency from the incoming photon, and consequently carries with it information regarding the internal state of the ion [2, 3]. This leads to decoherence of that internal state. On the otherhand since Rayleigh scattering does not carry this information it is assumed to not lead to comparable decoherence. Here we show that under certain circumstances the Rayleigh scattering can dominate the ecoherence process even at large detunings from the excited state levels. We find excellent agreement between a masters theory approach and experimental measurements. Figure 1: Comparison of decoherence rates as a function of detuning from the Be cycling transition. Squares experiment, Blue/Red line full masters equation theory, Cyan line incomplete model sometimes used in literature. 2. References [1] D.J. Wineland, et al., Phil. Trans. R. Soc. Lond. A 361, 1349 (2003). [2] R. Ozeri, et al., Phys. Rev. A 75, 042329 (2007). [3] R. Ozeri, et al., Phys. Rev. Lett. 95, 030402 (2005).
The recently proposed idea to generate entanglement between photon states via exchange interactions in an ensemble of atoms (J.D. Franson and T.B. Pitman, Phys. Rev. A 60, 917 (1999) and J.D. Franson et al., (quant-ph/9912121)) is discussed using an S-matix approach. It is shown that if the nonlinear response of the atoms is negligible and no additional atom-atom interactions are present, exchange interactions cannot produce entanglement between photons states in a process that returns the atoms to their initial state. Entanglement generation requires the presence of a nonlinear atomic response or atom-atom interactions.
The quantum nature of the laser fields used in many proposed schemes for the manipulation of quantum information may have important consequences for some very large scale quantum computations. Some of these consequences are explored here, focusing especially on phase errors and their effects on error-correction schemes. Depending on the way the logical gates are performed, constraints are found on either the required number of photons per coherence time put out by the laser source, or the source's power