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Physical Review A

Bichromatic force measurements using atomic beam deflections

M. R. Williams, F. Chi, M. Cashen, H. Metcalf

Published Jan 12, 2000• 37 citations
Publisher

Abstract

The spontaneous decay rate $\ensuremath{\gamma}$ of excited atomic states limits the radiative force on atoms to $\ensuremath{\Elzxh}k\ensuremath{\gamma}/2.$ This bottleneck in the dissipative exchange of momentum between atoms and light can be overcome by coherent control of the momentum exchange interactions. The bichromatic force provides such control by using stimulated instead of spontaneous emission to produce the force, while at the same time exploiting spontaneous emission to enable a dissipative interaction. It is implemented with two counterpropagating light beams, each containing two frequencies, whose phases, amplitudes, and frequency difference are carefully chosen. We have made precise measurements of the extremely large magnitude and velocity range of this bichromatic force, and have shown that its velocity dependence near the edge of its range is suitable for atomic beam slowing and laser cooling. Our measurements have corroborated various models and calculations of this bichromatic force.

DOI
10.1103/physreva.61.023408

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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.

Cambridge University Press eBooks•Dec 31, 2015•0 citations
The spontaneous decay rate \ensuremathγ\ensuremath{\gamma}\ensuremathγ of excited atomic states limits the radiative force on atoms to \ensuremath\Elzxhk\ensuremathγ/2.\ensuremath{\Elzxh}k\ensuremath{\gamma}/2.\ensuremath\Elzxhk\ensuremathγ/2. This bottleneck in the dissipative exchange of momentum between atoms and light can be overcome by coherent control of the momentum exchange interactions. The bichromatic force provides such control by using stimulated instead of spontaneous emission to produce the force, while at the same time exploiting spontaneous emission to enable a dissipative interaction. It is implemented with two counterpropagating light beams, each containing two frequencies, whose phases, amplitudes, and frequency difference are carefully chosen. We have made precise measurements of the extremely large magnitude and velocity range of this bichromatic force, and have shown that its velocity dependence near the edge of its range is suitable for atomic beam slowing and laser cooling. Our measurements have corroborated various models and calculations of this bichromatic force.
The limit of $\ensuremath{\Elzxh}k\ensuremath{\gamma}/2$ imposed on the magnitude of radiative forces by the spontaneous decay rate $\ensuremath{\gamma}$ of the excited state can be overcome by coherent control of the momentum exchange between atoms and the light field. This can be implemented with two light beams, each containing two frequencies whose phases, amplitudes, and frequency difference are carefully chosen. We have made precise measurements of the extremely large magnitude and velocity range of this bichromatic force, and have shown that its velocity dependence near the edge of its range is suitable for atomic beam slowing and laser cooling. Our measurements have corroborated various models and calculations of this bichromatic force.
We have demonstrated that coherent control of the momentum exchange between a light field and atoms can be implemented in frequency-modulated light. The optical parameters are chosen to drive the atoms between ground and excited states by adiabatic rapid passage in counterpropagating modulated light beams. We apply the optical force transversely to a thermal atomic beam, and the deflection provides a measure of the force. The modulation period is 2?/?s<<?, and each half-cycle exchanges momentum 2k, so the resulting force is much greater than the ordinary radiative force. Moreover, the velocity range of the force in such a light field is much greater than that of the radiative force. This constitutes another example of the huge range of capabilities of optical forces in non-monochromatic light.
Stimulated optical forces offer a simple and efficient method for providing optical forces far in excess of the saturated radiative force. The bichromatic force, using a counterpropagating pair of two-color beams, has so far been the most effective of these stimulated forces for deflecting and slowing atomic beams. We have numerically studied the evolution of a two-level system under several different bichromatic and polychromatic light fields, while retaining the overall geometry of the bichromatic force. New insights are gained by studying the time-dependent trajectory of the Bloch vector, including a better understanding of the remarkable robustness of bi- and polychromatic forces with imbalanced beam intensities. We show that a four-color polychromatic force exhibits great promise. By adding new frequency components at the third harmonic of the original bichromatic detuning, the force is increased by nearly 50% and its velocity range is extended by a factor of 3, while the required laser power is increased by only 33%. The excited-state fraction, crucial to possible application to molecules, is reduced from 41% to 24%. We also discuss some important differences between polychromatic forces and pulse trains from a high-repetition-rate laser.
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.
For cold samples of laser-cooled atoms to be useful in emerging technologies such as compact atomic clocks and sensors, it is necessary to achieve small sample sizes while retaining a large number of cold atoms. Achieving large atom numbers in a small system is a major challenge for producing miniaturized laser-cooled atomic clocks, since the number of captured atoms in a vapor-cell magneto-optical trap (MOT) scales as the fourth power of the laser beam diameter. This strong dependence on size is fundamentally set by the maximum spontaneous light force ħkγ/2, where ħk is the photon momentum and γ/2 is the maximum spontaneous photon scatter rate of a saturated transition of linewidth γ. We are attempting to surmount the limit imposed by spontaneous emission by using bichromatic cooling - a technique that uses stimulated emission to slow the atoms. We have built a table-top experiment that uses stimulated-emission bichromatic cooling to pre-cool rubidium atoms and dramatically enhance the trappable atom number in a small MOT. The apparatus lets us test how bichromatic cooling scales with miniaturization. Here we report on our first experimental results of cooling a thermal beam of rubidium atoms down to MOT capture velocities.
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.