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Register a new userDynamics and control of fast ion crystal splitting in segmented Paul traps
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We theoretically investigate the process of splitting two-ion crystals in segmented Paul traps, i.e. the structural transition from two ions confined in a common well to ions confined in separate wells. The precise control of this process by application of suitable voltage ramps to the trap segments is non-trivial, as the harmonic confinement transiently vanishes during the process. This makes the ions strongly susceptible to background electric field noise, and to static offset fields in the direction of the trap axis. We analyze the reasons why large energy transfers can occur, which are impulsive acceleration, the presence of residual background fields and enhanced anomalous heating. For the impulsive acceleration, we identify the diabatic and adiabatic regimes, which are characterized by different scaling behavior of the energy transfer with respect to time. We propose a suitable control scheme based on experimentally accessible parameters. Simulations are used to verify both the high sensitivity of the splitting result and the performance of our control scheme. Finally, we analyze the impact of trap geometry parameters on the crystal splitting process.
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We experimentally demonstrate fast separation of a two-ion crystal in a microstructured segmented Paul trap. By the use of spectroscopic calibration routines for the electrostatic trap potentials, we achieve the required precise control of the ion trajectories near the textit{critical point}, where the harmonic confinement by the external potential vanishes. The separation procedure can be controlled by three parameters: A static potential tilt, a voltage offset at the critical point, and the total duration of the process. We show how to optimize the control parameters by measurements of ion distances, trap frequencies and the final motional excitation. At a separation duration of $80 mu$s, we achieve a minimum mean excitation of $bar{n} = 4.16(0.16)$ vibrational quanta per ion, which is consistent with the adiabatic limit given by our particular trap. We show that for fast separation times, oscillatory motion is excited, while a predominantly thermal state is obtained for long times. The presented technique does not rely on specific trap geometry parameters and can therefore be adopted for different segmented traps.
We present and derive analytic expressions for a fundamental limit to the sympathetic cooling of ions in radio-frequency traps using cold atoms. The limit arises from the work done by the trap electric field during a long-range ion-atom collision and applies even to cooling by a zero-temperature atomic gas in a perfectly compensated trap. We conclude that in current experimental implementations this collisional heating prevents access to the regimes of single-partial-wave atom-ion interaction or quantized ion motion. We determine conditions on the atom-ion mass ratio and on the trap parameters for reaching the s-wave collision regime and the trap ground state.
We study the quantum stability of the dynamics of ions in a Paul trap. We revisit the results of Wang et al. [Phys. Rev. A 52, 1419 (1995)], which showed that quantum trajectories did not have the same region of stability as their classical counterpart, contrary to what is obtained from a Floquet analysis of the motion in the periodic trapping field. Using numerical simulations of the full wave-packet dynamics, we confirm that the classical trapping criterion are fully applicable to quantum motion, when considering both the expectation value of the position of the wave packet and its width.
Using numerical simulations of the time-dependent Schrodinger equation, we study the full quantum dynamics of the motion of an atomic ion in a linear Paul trap. Such a trap is based on a time-varying, periodic electric field, and hence corresponds to a time-dependent potential for the ion, which we model exactly. We compare the center of mass motion with that obtained from classical equations of motion, as well as to results based on a time-independent effective potential. We also study the oscillations of the width of the ions wave packet, including close to the border between stable (bounded) and unstable (unbounded) trajectories. Our results confirm that the center-of-mass motion always follow the classical trajectory, that the width of the wave packet is bounded for trapping within the stability region, and therefore that the classical trapping criterion are fully applicable to quantum motion.
We study the stochastic dynamics of a particle in a periodically driven potential. For atomic ions trapped in radio-frequency Paul traps, noise heating and laser cooling typically act slowly in comparison with the unperturbed motion. These stochastic processes can be accounted for in terms of a probability distribution defined over the action variables, which would otherwise be conserved within the regular regions of the Hamiltonian phase space. We present a semiclassical theory of low-saturation laser cooling applicable from the limit of low-amplitude motion to large-amplitude motion, accounting fully for the time-dependent and anharmonic trap. We employ our approach to a detailed study of the stochastic dynamics of a single ion, drawing general conclusions regarding the nonequilibrium dynamics of laser-cooled trapped ions. We predict a regime of anharmonic motion in which laser cooling becomes diffusive (i.e., it is equally likely to cool the ion as it is to heat it), and can also turn into effective heating. This implies that a high-energy ion could be easily lost from the trap despite being laser cooled; however, we find that this loss can be counteracted using a laser detuning much larger than Doppler detuning.
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