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arXiv:1007.2661 · Physical Review Letters

Decoherence due to Elastic Rayleigh Scattering

Hermann Uys, Michael J. Biercuk, Aaron P. VanDevender, C. Ospelkaus, D. Meiser, Roee Ozeri, J. J. Bollinger

Published Nov 8, 2010• 99 citations
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Abstract

We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of light off resonant with higher lying excited states. We demonstrate that under appropriate conditions, elastic Rayleigh scattering can be the dominant source of decoherence, contrary to previous discussions in the literature. We show that the elastic-scattering decoherence rate of a two-level system is given by the square of the difference between the elastic-scattering amplitudes for the two levels, and that for certain detunings of the light, the amplitudes can interfere constructively even when the elastic-scattering rates from the two levels are equal. We confirm this prediction through calculations and measurements of the total decoherence rate for a superposition of the valence electron spin levels in the ground state of 9Be+ in a 4.5 T magnetic field.

DOI
10.1103/physrevlett.105.200401

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We present theoretical and experimental studies of the decoherence of hyperfine ground-state superpositions due to elastic Rayleigh scattering of light off resonant with higher lying excited states. We demonstrate that under appropriate conditions, elastic Rayleigh scattering can be the dominant source of decoherence, contrary to previous discussions in the literature. We show that the elastic-scattering decoherence rate of a two-level system is given by the square of the difference between the elastic-scattering amplitudes for the two levels, and that for certain detunings of the light, the amplitudes can interfere constructively even when the elastic-scattering rates from the two levels are equal. We confirm this prediction through calculations and measurements of the total decoherence rate for a superposition of the valence electron spin levels in the ground state of 9Be+ in a 4.5 T magnetic field.
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 coherence of a hyperfine-state superposition of a trapped 9Be+ ion in the presence of off-resonant light is studied experimentally. It is shown that Rayleigh elastic scattering of photons that does not change state populations also does not affect coherence. We observe coherence times that exceed the average scattering time of 19 photons which is determined from measured Stark shifts. This result implies that, with sufficient control over its parameters, laser light can be used to manipulate hyperfine-state superpositions with very little decoherence.
We study a novel property of light scattering by Rb atoms confined in a far off-resonance optical dipole force trap. The trapping laser wavelength varies from 780 nm to 860 nm and its intensity is about 1 MW/cm{sup 2}. Spontaneous Raman scattering of photons from the trapping laser can change the ground-state hyperfine quantum number F of the atoms. We observe the relaxation time by measuring the population of the F=3 level after optically pumping the atoms into the F=2 level. Spontaneous photon scatter rates as low as 10{sup 3} s{sup -1} have been observed, corresponding to recoil heating rates below 1 mK/s. For detuning from resonance {Delta} greater than the excited-state fine-structure splitting the total scatter rate, including Rayleigh scattering, decreases as {Delta}{sup 2} while the spontaneous Raman scatter rate decreases as {Delta}{sup 4}. This is due to interference between the Raman scattering amplitudes from the two excited-state fine-structure levels in the Kramers-Heisenberg formula. Because Rayleigh scattering dominates, the atoms` F and M{sub F} quantum numbers are preserved even after many scattering events. This makes far off-resonance optical traps ideal for studies of state-selective collisions and collective phenomena.
Atoms are not two-level systems, and their rich internal structure often leads to complex phenomena in the presence of light. Here, we analyze off-resonant light scattering including the full hyperfine and magnetic structure. We find a set of frequency detunings where the induced atomic dipole is the same irrespective of the Zeeman state, and where two-photon transitions that alter the atomic state turn off. For alkali-metal atoms and alkaline-earth-metal ions, if the hyperfine splitting is dominated by the magnetic dipole moment contribution, these detunings approximately coincide. Therefore, at a given ``magical'' detuning, all Zeeman states in a hyperfine manifold behave almost identically, and can be traced out to good approximation. This feature prevents state decoherence due to light scattering, which impacts quantum optics experiments and quantum information applications.
In a three-level $\ensuremath{\Lambda}$ system, a bichromatic light field can induce a ground-state coherence that leads to vanishing absorption of the bichromatic field. Although this coherence is between ground states only, in a real atom it can nevertheless be influenced by the hyperfine structure of the excited state. We present experimental results which show that for suitable detunings of the bichromatic field from optical resonance, the specific contribution of each individual hyperfine level of the excited state can be distinguished through increased amplitude or width of the ground-state coherence.
In this paper we investigate the effect of many Rayleigh scattering events on decoherence of superpositions of chiral states of a molecule, by taking these events as measurement-like interactions in the sense that the scattered photon state depends on the state of the molecule—both its centre-of-mass position and its chirality. This gives rise to two contributions to decoherence: one due to the position measurement and the other due to the chirality measurement. It is found that under identical conditions, the decoherence timescale for chiral molecules can be different from that for achiral molecules depending on the chiral sensitivity of scattering.