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 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 ω _sec = 2π 620 kHz, we measure 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 phonons s⁻¹ μm⁻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 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.

我们研究了单个离子的运动模式和被困在线性射频 (rf) 保罗陷阱中的扩展离子晶体的加热，精度为声子 s ^-1。四年来，单离子轴向和径向加热速率一致，电场噪声一直稳定。在ω _sec = 2 π 620 kHz的长期频率下，我们针对最多 11 个离子的线性链的质心 (com) 模式测量每个离子的声子 s ^-1并且观察到没有明显加热-phase (oop) 模式。通过从节点线远离移动中的离子，诱导过量微动，射频噪声平方加热COM模式作为径向位移的函数[R通过每个离子的声子 s ^-1 μ m ^-2，而 oop 模式受到保护，免受线性链中 rf 噪声引起的加热。通过将谐振射频电路的品质因数从Q = 542 更改为Q = 204，我们观察到射频噪声增加了 3 倍。我们表明，射频噪声引起的扩展晶体运动模式的加热也取决于晶体的对称性和模式本身。例如，我们考虑几种 2D 和 3D 晶体配置。对于单个模式观察到高达 500 ph s ^{-1 的}加热速率，导致总动能增加，因此时间膨胀的分数偏移高达 -0.3 10 ^-18 s ^-1整个系统的。此外，我们详细介绍了如何由于德拜-沃勒效应降低单个离子的激发概率和增加退相干。