Motional heating of spatially extended ion crystals

We study heating of motional modes of a single ion and of extended ion crystals trapped in a linear radio frequency (rf) Paul trap with a precision of Delta(n) over bar approximate to 0.1 phonons s(-1). Single-ion axial and radial heating rates are consistent and electric field noise has been stable over the course of four years. At a secular frequency of omega(sec) = 2 pi x 620 kHz, we measure (n) over bar = 0.56(6) phonons s(-1) per ion for the center-of-mass (com) mode of linear chains of up to 11 ions and observe no significant heating of the out-of-phase (oop) modes. By displacing the ions away from the nodal line, inducing excess micromotion, rf noise heats the com mode quadratically as a function of radial displacement r by (n) over bar (r)/r(2) = 0.89(4) phonons s(-1) mu m(-2) per ion, while the oop modes are protected from rf-noise induced heating in linear chains. By changing the quality factor of the resonant rf circuit from Q = 542 to Q = 204, we observe an increase of rf noise by a factor of up to 3. We show that the rf-noise induced heating of motional modes of extended crystals also depends on the symmetry of the crystal and of the mode itself. As an example, we consider several 2D and 3D crystal configurations. Heating rates of up to 500 ph s(-1) are observed for individual modes, giving rise to a total kinetic energy increase and thus a fractional time dilation shift of up to -0.3 x 10(-18) s(-1) of the total system. In addition, we detail how the excitation probability of the individual ions is reduced and decoherence is increased due to the Debye-Waller effect.

Automated summary

The study demonstrates consistent heating rates in a linear radio frequency Paul trap for single ions and extended ion crystals, stable electric field noise, and a quadratic relationship between ion displacement and radio frequency noise-induced heating for the center-of-mass mode in linear chains. Additionally, changing the quality factor of the resonant rf circuit can impact the level of rf noise, and the heating of motional modes in extended crystals is influenced by crystal symmetry and the specific mode being studied.