Observation of a Phase Transition of Stored Laser-Cooled Ions

Abstract

Clouds of two to about fifty simultaneously stored, laser-cooled Mg + ions in a Paul trap were observed in two phases, which are clearly distinguishable by their excitation spectra. Transitions between these phases can be induced either by a variation of the power of the laser radiation used to cool the ions or by a change of the size of the radio-frequency voltage applied to the trap. Transitions between a "crystalline" phase and a "gaseous" phase can be repeatedly observed by variation of the appropriate parameters. The two phases and the transitions between them have also been recorded by a photon-counting image system.There is growing interest in the use of particle traps for high-resolution spectroscopy. The ultimate resolution limits which can be achieved in principle are beyond all other known experimental possibilities. It seems quite probable that particle traps will be the basis of future frequency standards. 1,2 The traps most extensively employed to date for ions are the static Penning trap and especially the dynamic Paul trap. Storage in the Penning trap is achieved by use of a strong magnetic field; the Paul trap uses an oscillating electric quadrupole field. 2 ' 3In the Paul trap a single ion can, in principle, be kept at rest at a point of vanishing field amplitude in the center of the trap. By cooling of single Mg + , Ba + , and Hg + ions 4 " 7 in the millikelvin range, previous experiments have demonstrated that this ideal situation can be realized in very good approximation. In these experiments the kinetic energy of the ions («1 eV after the loading cycle) was reduced by radiation-pressure cooling. This was done by the excitation of a strong dipole transition with laser light whose frequency was detuned from resonance towards longer wavelengths. In this way a single Ba + ion may be localized in a region with dimensions small compared with the optical wavelength of the exciting light. 6 In this so-called Lamb-Dicke regime, the first-order Doppler effect is suppressed and, in addition, the second-order Doppler effect is negligible, so that single laser-cooled ions have been proposed as the basis for frequency standards. 8 The Lamb-Dicke regime can easily be obtained for microwave transitions. Because of the longer wavelength, even clouds of 10 5 ions can be confined to a space-charge-limited spatial region which is inside the Lamb-Dicke regime. 2 In this connection the question arises of how a cloud of ions behaves when cooled to low temperatures. Crystallization is expected when the Coulomb coupling constant T, which corresponds to the ratio of the Coulomb energy to the kinetic energy of a particle, is much bigger than l. 9 Experiments with laser-cooled Be + ions have shown that the observation of such a phase transition in a Penning trap should be possible. I0 The cooling of an ion crystal is predicted by theory to be as efficient as the cooling of independent particles. 11

Ion Traps as a testbed of classical and quantum statistical mechanics

“…This has provided researchers with the ability to cool ions to temperatures that permit the formation of stable crystalline phases. The first crystallisation of ions via laser cooling was achieved in the 1980s [10]. This seminal work has triggered a considerable body of experimental and theoretical work on the properties of ionic Coulomb crystals [11].…”

Rapid crystallization of externally produced ions in a Penning trap

“…The geometric properties of ion plasmas and the formation of ion Coulomb crystals have been described in detail, for example, in [7,8,[20][21][22][23][24]46,[49][50][51][52]. For the present ion numbers of the order of 1 × 10 3 to 1 × 10 5 ("mesoscopic"), and aspect ratios (axial extension to radial extension) of typically α 1, the so-called planar-shell model is a good approximation to describe the geometry of the confined plasmas.…”

“…For magnesium ions, this has been demonstrated under various confinement conditions [5][6][7][8][9]. Such cooling is beneficial for the stable confinement in traps over extended periods of time [1,10], and essential for precision spectroscopy as it reduces spectral line broadening caused by the Doppler effect [3,4].…”

Optically induced structural phase transitions in ion Coulomb crystals

“…Ty, 37.10.Vz, 64.70.kp, 36.40.Ei When an ensemble of confined ions with the same sign of charge is cooled to a sufficiently low temperature, the ionic system forms a crystalline structure [1], often referred to as an ion Coulomb crystal. Since the first experimental realizations of ion Coulomb crystals through laser cooling of atomic ions into the milli-Kelvin regime in electromagnetic traps [2,3], there has been growing theoretical [4][5][6][7][8][9][10][11][12][13][14] and experimental [15][16][17][18][19][20][21][22][23][24] interest in studying the structural and dynamic properties of these crystals under different trapping conditions and for various ion compositions.The unique localization and isolation of the individual ions constituting the crystals have already led to a large number of amazing results within precision measurements [25], cavity quantum electrodynamics (CQED) [26][27][28][29][30], quantum information science [31][32][33][34][35], and cold molecular science [36][37][38][39]. For experiments involving larger three-dimensional ion Coulomb crystals, such as CQED related experiments [26,27] with the interesting prospect of creating quantum memories and other quantum devices, ...…”

“…Ty, 37.10.Vz, 64.70.kp, 36.40.Ei When an ensemble of confined ions with the same sign of charge is cooled to a sufficiently low temperature, the ionic system forms a crystalline structure [1], often referred to as an ion Coulomb crystal. Since the first experimental realizations of ion Coulomb crystals through laser cooling of atomic ions into the milli-Kelvin regime in electromagnetic traps [2,3], there has been growing theoretical [4][5][6][7][8][9][10][11][12][13][14] and experimental [15][16][17][18][19][20][21][22][23][24] interest in studying the structural and dynamic properties of these crystals under different trapping conditions and for various ion compositions.…”