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Register a new userQuantum stability of an ion in a Paul trap revisited
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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.
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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.
In this paper, direct observation of micromotion for multiple ions in a laser-cooled trapped ion crystal is discussed along with a novel measurement technique for micromotion amplitude. Micromotion is directly observed using a time-resolving, single-photon sensitive camera that provides both fluorescence and position data for each ion on the nanosecond time scale. Micromotion amplitude and phase for each ion in the crystal are measured, allowing this method to be sensitive to tilts and shifts of the ion chain from the null of the radiofrequency quadrupole potential in the linear trap. Spatial resolution makes this micromotion detection technique suitable for complex ion configurations, including two-dimensional geometries. It does not require any additional equipment or laser beams, and the modulation of the cooling lasers or trap voltages is not necessary for detection, as it is in other methods.
Simulations of the dynamics of ions trapped in a Paul trap with terms in the potential up to the order 10 have been carried out. The power series method is used to solve numerically the equations of motion of the ions. The stability diagram has been studied and the buffer gas cooling has been implemented by a Monte Carlo method. The dipole excitation was also included. The method has been applied to an existing trap and it has shown good agreement with the experimental results and previous simulations using other methods.
Using optical Ramsey interferometry, we precisely measure the laser-induced AC-stark shift on the $S_{1/2}$ -- $D_{5/2}$ quantum bit transition near 729 nm in a single trapped $^{40}$Ca$^+$ ion. We cancel this shift using an additional laser field. This technique is of particular importance for the implementation of quantum information processing with cold trapped ions. As a simple application we measure the atomic phase evolution during a $n times 2pi$ rotation of the quantum bit.
We present models for a heteronuclear diatomic molecular ion in a linear Paul trap in a rigid-rotor approximation, one purely classical, the other where the center-of-mass motion is treated classically while rotational motion is quantized. We study the rotational dynamics and their influence on the motion of the center-of-mass, in the presence of the coupling between the permanent dipole moment of the ion and the trapping electric field. We show that the presence of the permanent dipole moment affects the trajectory of the ion, and that it departs from the Mathieu equation solution found for atomic ions. For the case of quantum rotations, we also evidence the effect of the above-mentioned coupling on the rotational states of the ion.
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