The results of a recent experiment on the mechanical interaction of a bichromatic light beam with a single three-level ion serve to redefine laser cooling of ions in a trap and of atoms in standing light waves. Novel variants of light forces are demonstrated. They are caused by stimulated Raman-type two-photon transitions combined with spontaneous Raman scattering and by all-stimulated parametric interaction. These efficient processes parallel the generation of a stimulated light force in a standing wave and the operation of a free-electron laser, respectively. The latter force imposes no natural limit on the residual excitation energy of trapped particles.
The results of a recent experiment on the mechanical interaction of a bichromatic light beam with a single three-level ion serve to redefine laser cooling of ions in a trap and of atoms in standing light waves. Novel variants of light forces are demonstrated. They are caused by stimulated Raman-type two-photon transitions combined with spontaneous Raman scattering and by all-stimulated parametric interaction. These efficient processes parallel the generation of a stimulated light force in a standing wave and the operation of a free-electron laser, respectively. The latter force imposes no natural limit on the residual excitation energy of trapped particles.
Limits for the laser cooling of a trapped ion and some experimental observations are summarized. The final temperature is low when a dipole‐forbidden line is two‐photon excited, e.g. by way of an electronic Raman process. Now, the two light modes also support dispersive interaction by stimulated Raman‐like scattering. A simplified model in terms of the vibrational Raman effect identifies processes analogous to those known from atoms in a standing light wave, and it reveals novel parametric interaction of ion vibration and light. In the diabatic limit, when dephasing by spontaneous decay is small, the ion approaches the dynamics of an electron in a free‐electron laser.
The usual form of electromagnetic forces is given by but for neutral atoms q = 0. The next order of force is the dipole term, but this also vanishes because neutral atoms have no inherent dipole moment. However, a dipole moment can be induced by a field, and this is most efficient if the field is alternating near the atomic resonance frequency. Since these frequencies are typically in the optical range, dipole moments are efficiently induced by shining nearly resonant light on the atoms. Laser cooling and trapping rely on the interaction between laser light and atoms to exert a controllable force on the atoms, and many sophisticated schemes have been developed using the special properties of the interaction. This chapter begins with the simplest schemes for exerting optical forces on atoms, namely a single-frequency light field interacting with a two-level atom. Although this is the simplest possible scheme, it is pedagogically valuable because it shows many of the features that will be encountered further on. The ultimate temperature using such a scheme is limited, but lower temperatures can be achieved with multilevel atoms. This topic is addressed later in the chapter. Two kinds of optical forces When an atom absorbs nearly resonant light, it makes a transition to the excited state, and its subsequent return to the ground state can be either by spontaneous or by stimulated emission. The nature of the optical force that arises from these two different processes is quite different, and will be described separately [1]. The spontaneous emission case is different from the familiar quantum mechanical calculations using state vectors to describe the state of the system, because spontaneous emission causes the state of the system to evolve from a pure state into a mixed state (see Exercise 6.9). Spontaneous emission is an essential ingredient for the dissipative nature of the optical forces in monochromatic light, and the density matrix is needed to describe it (see Chap. 6). When an atom absorbs light, its energy excites the atom and its angular momentum changes the electron's orbit. Both of these are internal atomic properties. However, the linear momentum of the light, can change only the external, translational motion of the atom.
It is widely believed that spontaneous emission (SE) is necessary to remove entropy from an atomic sample during laser cooling. In fact, SE is needed for energy removal when laser cooling is done with single-frequency light, but with more than one frequency, both energy and entropy can be removed using only stimulated processes. Our experimental demonstration of this phenomenon works by restricting the atom–light interaction to a time short compared to a cycle of absorption followed by natural decay [Phys. Rev. Lett.114, 043002 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.043002]. We present here additional information on these results, in particular, simulations of the motion of atoms under the bichromatic force that compare well with our data. This accomplishment is of interest to direct laser cooling of molecules or in experiments where working space or time is limited.
It is widely believed that spontaneous emission (SE) is necessary to remove entropy from an atomic sample during laser cooling. In fact, SE is needed for energy removal when laser cooling is done with single-frequency light, but with more than one frequency, both energy and entropy can be removed using only stimulated processes. Our experimental demonstration of this phenomenon works by restricting the atom–light interaction to a time short compared to a cycle of absorption followed by natural decay [Phys. Rev. Lett.114, 043002 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.043002]. We present here additional information on these results, in particular, simulations of the motion of atoms under the bichromatic force that compare well with our data. This accomplishment is of interest to direct laser cooling of molecules or in experiments where working space or time is limited.
The bichromatic force allows laser cooling using stimulated processes only. We provide details of our simulations of the bichromatic force when the effects of spontaneous emission are suppressed by restricting the atom-light interaction time to be short enough that there cannot be a significant number of spontaneous emission events. This short interaction time requires that the simulation include dynamics of the atomic motion through the light field that is coupled to the internal state dynamics that determine the force on the atom. The simulation is first tested with several standard optical field configurations to confirm its accuracy. Then the results, using conditions that match our experiment, are presented and compared with our measurements. The simulation shows that the resolution of the experiment greatly obscures the degree of cooling. Our simulation predicts an observed velocity distribution reduced by up to a factor of 4 in width over a time comparable to the excited state lifetime. This technique can allow the direct laser cooling of atoms and molecules without closed cycling transitions.
We have observed a new type of sub-Doppler laser cooling with neither polarization gradients nor magnetic fields. All known sub-Doppler laser cooling methods require one of these two to resdistribute the atomic population among the energy levels. This allows the irreversible processes of optical pumping vels. This allows the irreversible processes of optical pumping (OP) to manipulate the conservative force of light shifts (e.g. resonant exchange between the two beams comprising a standing wave) into a damping force. Our scheme employs stimulated Raman transitions between ground state hyperfine levels of Rb with a bichromatic standing wave, accompanied by a momentum change of {Delta}p = 2{h_bar}k. OP, with {Delta}p = 1{h_bar}k, creates a population imbalance allowing repetition of the Raman process. When the detuning of the light from Raman resonance {delta} is properly chosen, the net momentum exchange damps the atomic motion. Changing {delta} by only {gamma}/6(1 MHz) replaces cooling by heating. This process separates the velocity selective Raman resonance and OP processes differently from others, and helps clarify the role of these different mechanisms.