### Description

Optical forces on atoms derive from the momentum exchange between the atoms and an incident light field [1]. Atoms cannot absorb the linear momentum of light into their internal coordinates the same way as energy ($\hbar \omega_{\ell}$) and angular momentum ($\Delta \ell = \pm 1$), so absorption or emission must involve atomic motion, usually in the form of a recoil momentum $\Delta p \equiv \hbar \omega_{\ell}/c \equiv \hbar k$. Since this is small compared to typical atomic momenta, it must be repeated many times to make a significant velocity change. Typically an excitation is followed by a spontaneous emission and then repeated to achieve the multiple momentum exchanges. The strength of such optical forces on atoms depends on the rate of this exchange and this is usually limited by the excited state lifetime $\tau$, so the force scales with $\Delta p/\Delta t = \hbar k/\tau \equiv \hbar k \gamma$. In practice, excitation also takes time so the maximum value of this radiative force is given by $F_{\mathrm{rad}} \equiv \hbar k \gamma/2$ for light tuned on resonance.

Instead of spontaneous emission, we have been using stimulated emission to increase the momentum exchange rate, where we choose the stimulating light to have a $\vec{k}$-vector opposite to that of the exciting light so that the net momentum transfer becomes $2 \hbar k$. A rapidly cycling, absorption-stimulated emission sequence from counter-propagating beams can lead to a very large force [2], $F_{\mathrm{ARP}} \gg F_{\mathrm{rad}} \equiv \hbar k \gamma/2$. We use a series of properly tailored pulses designed to cause absorption-stimulated emission cycles that produce a strong, unidirectional force. The optical frequency of each pulse is swept to enable adiabatic rapid passage (ARP) because such pulses invert populations more efficiently than $\pi$-pulses. Such ARP forces have been demonstrated for atoms initially at rest to be much stronger than ordinary radiative forces [3-7]. We have explored how this very strong force depends on atomic velocity and found surprising enhancement at certain regularly-spaced velocities [7,8]. These will be discussed, but they seem to occur when atoms travel approximately an integer number of wavelengths between ARP pulses.

In our experiments, a well-collimated beam of atoms is deflected by the ARP force and their spatial distribution is recorded by an MCP-phosphor-screen combination. Because the atoms have a significant longitudinal velocity spread that is unaffected by the light beams, their spatial distribution is spread out. Nevertheless, there are distinct, regularly spaced peaks at velocities that approximately correspond to "resonant" velocities.

An important criterion for a cooling force is a velocity dependence that is finite over some velocity range but vanishes at other velocities so that atoms accumulate in the region of velocity space where the force is zero or very small. Atomic motion in the lab frame corresponds to Doppler-shifted frequencies in the atomic frame, so we use oppositely detuned laser beams to simulate a velocity $v_{at}$. For large $v_{at}$ we use two different lasers, but the coherent momentum exchange requires phase locking them \footnote{J. Elgin, Ph.D Thesis, Stony Brook University, 2015.}. This has been implemented and the first results show that the force is nearly constant at low $v_{at}$ but decreases at higher $v_{at}$. For an ARP frequency sweep range of $\pm \, \delta_0$, one intuitively expects an effective force range of $v_{at}$ between 1/4 and 1/2 of $\pm \, \delta_0/k$, and our initial measurements corroborate this.

[1] H. Metcalf and P. van der Straten, Laser Cooling and Trapping (Springer Verlag, NY, 1999).

[2] A. Goepfert, I. Bloch, D. Haubrich, F. Lison, R. Schutze, R. Wynands, and D. Meschede, Phys. Rev. A 56, R3354 (1997).

[3] T. Lu, X. Miao, and H. Metcalf, Phys. Rev. A 71, R 061405 (2005).

[4] X. Miao, E. Wertz, M. G. Cohen, and H. Metcalf, Phys. Rev. A 75, 011402 (2007).

[5] X. Miao, Ph.D. thesis, Stony Brook University (2006).

[6] T. Lu, X. Miao, and H. Metcalf, Phys. Rev. A 75, 063422 (2007).

[7] We acknowledge laboratory help from Brian Arnold, Mike Dapolito and Eric Jones

[8] J. Elgin, Ph.D Thesis, Stony Brook University, 2015.

Presenter name | Harold Metcalf |
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