Sideband cooling of small ion Coulomb crystals in a Penning trap

We have recently demonstrated the laser cooling of a single 40 Ca + ion to the motional ground state in a Penning trap using the resolved-sideband cooling technique on the electric quadrupole transition S 1/2 ↔ D 5/2 . Here we report on the extension of this technique to small ion Coulomb crystals made of two or three 40 Ca + ions. Efficient cooling of the axial motion is achieved outside the Lamb-Dicke regime on a two-ion string along the magnetic field axis as well as on two- and three-ion planar crystals. Complex sideband cooling sequences are required in order to cool both axial degrees of freedom simultaneously. We measure a mean excitation after cooling of n COM for the centre of mass (COM) mode and n B for the breathing mode of the two-ion string with corresponding heating rates of 11(2)s -1 and 1(1)s -1 at a trap frequency of 162 kHz. The occupation of the ground state of the axial modes (n tilt = n COM = 0) is above 75% for the two-ion planar crystal and the associated heating rates 0.8(5)s -1 at a trap frequency of 355 kHz

Sideband cooling of the radial modes of motion of a single ion in a Penning trap

Doppler and sideband cooling are long-standing techniques that have been used together to prepare trapped atomic ions in their ground state of motion. In this paper we study how these techniques can be extended to cool both radial modes of motion of a single ion in a Penning trap. We numerically explore the prerequisite experimental parameters for efficient Doppler cooling in the presence of an additional oscillating electric field to resonantly couple the radial modes. The simulations are supported by experimental data for a single 40 Ca + ion Doppler cooled to ∼ 100 phonons in both radial modes at a magnetron frequency of 52 kHz and a modified cyclotron frequency of 677 kHz. For these frequencies, we then show that mean phonon numbers of 0.35(5) for the modified cyclotron and 1.7(2) for the magnetron motions are achieved after 68 ms of sideband cooling

Fine structure of Vavilov-Cherenkov radiation near the Cherenkov threshold

We analyze the Vavilov-Cherenkov radiation (VCR) in a dispersive nontransparent dielectric air-like medium both below and above the Cherenkov threshold, in the framework of classical electrodynamics. It is shown that the transition to the subthreshold energies leads to the destruction of electromagnetic shock waves and to the sharp reduction of the frequency domain where VCR is emitted. The fine wake-like structure of the Vavilov-Cherenkov radiation survives and manifests the existence of the subthreshold radiation in the domain of anomalous dispersion. These domains can approximately be defined by the two phenomenological parameters of the medium, namely, the effective frequency of oscillators and the damping describing an interaction with the other degrees of freedom.Comment: 9 pages, 6 figure

Coherence properties of highly-excited motional states of a trapped ion

We present a study of the coherence properties of a variety of motional states of a single ion confined in a Penning ion trap. We demonstrate that the motion of the ion has a coherence time of the order of 1 s, using Ramsey interferometry. We introduce a technique for preparing the ion in an incoherent superposition of highly-excited motional states using a simple modification of optical sideband cooling. Coherent manipulation of these states allows measurements of optical and motional coherence to be carried out. We show that these highly-excited motional state superpositions have long coherence times despite the incoherent preparation of the states. Such states can be useful for sensitive motional dephasing measurements

Population dynamics in sideband cooling of trapped ions outside the Lamb-Dicke regime

We present the results of simulations of optical sideband cooling of atomic ions in a trap with a shallow potential well. In such traps, an ion cannot be Doppler cooled near to the Lamb-Dicke regime [ η 2 ( 2 ⟨ n ⟩ + 1 ) ≪ 1 ] . Outside the Lamb-Dicke regime, the sideband cooling dynamics are altered by the existence of various Fock states with weak coupling where the cooling becomes very slow. A 40 Ca + ion trapped in our Penning trap realizes such a situation; hence single stage cooling is inefficient to prepare the ion in the motional ground state. For these systems, it is necessary to study the cooling dynamics in detail and we show that it is possible to implement an optimized cooling sequence to achieve efficient ground-state cooling. We also present the simulated cooling dynamics of two ions trapped in a Penning trap, where the presence of an additional motional mode requires a complicated cooling sequence in order to cool both axial modes to the ground state simultaneously. Additionally, we demonstrate the dissipative preparation of Fock states outside the Lamb-Dicke regime by sideband heating a single ion in a Penning trap

Observation of the interference of two transition radiations emitted by ultra-relativistic lead ions in a gas close to the Vavilov- Cherenkov radiation threshold

The interference of two transition radiations emitted by ultra- relativistic lead ions in a gas near the Vavilov-Cherenkov radiation threshold was observed. The experiment was performed at 158 A GeV lead ion beam of CERN SPS. The experimental results are in good agreement with Tamm's theory. (6 refs)