Optical sideband cooling

Assume that an ion in the Paul trap (absorption frequency coq for i = 0) performing a harmonic motion in the x-direction with the velocity Vx = vq cos coyt, is irradiated by a monochromatic wave propagating in the x-direction. In the frame of the oscillating ion, the laser frequency is modulated at the oscillation frequency due to the oscillating Doppler shift. If the linewidth y of the absorbing transition is smaller than cOy, the absorption spectrum of the oscillating ion consists of discrete lines at the frequencies com = coo mcoy. The relative line intensities are given by the mth-order Bessel function [1227, 1228], which depend on the velocity 

In a quantum-mechanical model, the ion confined to the trap can be described by a nearly harmonic oscillator with vibrational energy levels determined by the trap potential. Optical cooling corresponds to a compression of the population probability into the lowest levels. 

Optical sideband cooling is quite analogous to the Doppler cooling by photon recoil discussed in Sect. 9.1. The only difference is that the confinement of the ion within the trap leads to discrete energy levels of the oscillating ion, whereas the translational energy of a free atom corresponds to a continuous absorption spectrum within the Doppler width. 

Optical sideband cooling was demonstrated for Mg+ ions in a Penning trap [1227,1228] and for Ba+ ions in an RF quadrupole trap [1229]. The Mg+ ions were cooled below 0.5 K on the is Si/2- ip P3/2 transition by a frequency-doubled dye laser at X = 560.2 nm. The vibrational amplitude of the oscillating ions decreased to a few microns. With decreasing temperature the ions are therefore confined to a smaller and smaller volume around the trap center. 

The cooling can be monitored with a weak probe laser that is tuned over the absorption profile. Its intensity must be sufficiently small to avoid heating of the ions for frequencies tuprobe o. 

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If several ions are trapped in an ion trap and are cooled by optical sideband cooling, a phase transition may occur at the temperature Tc where the ions arrange into a stable, spatially symmetric configuration like in a crystal [14.88-14.91]. The distances between the ions in this Wigner crystal are about 10 — 10 times larger than those in an ordinary ion crystal such as NaCl. 

W. Neuhauser, M. Hohenstatt, RE. Toschek, H. Dehmelt Optical sideband cooling of visible atom cloud confined in a parabolic well. Phys. Rev. Lett. 41, 233... 

The lo- error includes uncertainties due to magnetic field extrapolations (0.40) and to the second-order Doppler shift (0.40), and could be diminished by better shielding of the magnetic field and by optical sideband cooling. The result of a classical optical pumping experiment was... 

Neuhauser, W., Hohenstatt, M., Toschek, P., and Dehmelt, H. (1978). Optical sideband cooling of visible atom cloud confined in particle well. Physical Review Letters, 41, 233-236. 

Optical sideband cooling has been used to cool Mg II ions to temperatures... 

Figure Cl.4.9. Usual cooling (carrier) and repumping (sideband) transitions when optically cooling Na atoms. The repumper frequency is nonnally derived from the cooling transition frequency with electro-optic modulation.

An alternative method for overcoming the Doppler tuning problem in laser cooling has been demonstrated by Ertmer et al. 52] Instead of using a spatially varying magnetic field these authors controlled the frequency of the laser by means of an electro-optic modulator, driven by a radiofrequency source. Varying the frequency of the r.f. field applied produces sidebands to the laser frequency and these can be swept in step with the Doppler shift. 

Fig. 9.13 Cooling, deflection and compression of atoms by photon recoil. The electro-optic modulators (EOM) and the acousto-optic modulator (AOM) serve for sideband generation and frequency tuning of the cooling laser sideband [1136]...

Instead of using counter-propagating laser beams with a and or polarization, one can also cool the atoms if the two beams have the same polarization but slightly different frequencies >+ = and > = atoms moving out of the trap are pushed back. These frequencies can be produced as the two sidebands generated by acousto-optic modulation of the incident laser beam tuned to the center fl-equency [Pg.497]

Polymer photophysics is determined by a series of alternating odd (B ) and even (Ag) parity excited states that correspond to one-photon and two-photon allowed transitions, respectively [23]. Optical excitation into either of these states is followed by subpicosecond nonradiative relaxation to the lowest excited state [90]. This relaxation is due to either vibrational cooling within vibronic sidebands of the same electronic state, or phonon-assisted transitions between two different electronic states. In molecular spectroscopy [146], the latter process is termed internal conversion. Internal conversion is usually the fastest relaxation channel that provides efficient nonradiative transfer from a higher excited state into the lowest excited state of the same spin multiplicity. As a result, the vast majority of molecular systems follow Vavilov-Kasha s rule, stating that FT typically occurs from the lowest excited electronic state and its quantum yield is independent of the excitation wavelength [91]. 

Fig.14,8. (a) Compression of the thermal velocity distribution of Na atoms by optical cooling into a narrow velocity range around v = 200 m/s. (h) The sharp resonance at v = 0 is caused by the probe laser perpendicular to the atomic beam. The arrow k gives the tuning range of the cooling laser, the arrow "us" that of the upper sideband, which pumps the transition F = 1 F = 2 [14.12]... 

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