Cooling and trapping of atoms and molecules by counterpropagating pulse trains

We discuss a possible one-dimensional trapping and cooling of atoms and molecules due to their nonresonant interaction with counterpropagating light pulse trains. The counterpropagating pulses form a one-dimensional trap for atoms and molecules and a properly chosen carrier frequency detuning from the transition frequency of the atoms or molecules keeps the temperature of the atomic or molecular ensemble close to the Doppler cooling limit. The calculation by the Monte Carlo wave-function method is carried out for the two-level and three-level schemes of the atom's and the molecule's interaction with the field, respectively. The models discussed are applicable to atoms and molecules with almost diagonal Frank-Condon factor arrays. Illustrative calculations are carried out for ensemble-averaged characteristics for sodium atoms and SrF molecules in the trap. The potential for the nanoparticle light pulses's trap formed by counterpropagating light pulse trains is also discussed.

Figure 1

Counterpropagating laser pulses form a trap for atoms near point $C$, where the pulses collide.

Figure 2

(a) Two-level scheme of the atom-field interaction and (b) three-level scheme of the molecule interaction with the field of laser radiation.

Figure 3

Example of the sodium atom's motion in the field of the counterpropagating sequences of light pulses: (a) $v\left(t\right)$ and (b) $z\left(t\right)$. The parameters are $\tau =1$ ps, $T=10$ ns, $\vartheta =0.05\pi ,\gamma =2\pi \times 10$ MHz, $\delta =2\pi \times 5$ MHz, $\lambda =589$ nm, and $M=23$ Da. The atom starts at the center of the trap with initial velocity $v_0=5$ m/s.

Figure 4

Dependence of the temperature of 1000 sodium atoms in the trap formed by the counterpropagating sequences of light pulses on the pulse's carrier frequency detuning on the atomic transition frequency. The parameters are $\tau =1$ ps, $T=10$ ns, $\vartheta =0.05\pi ,\gamma =2\pi \times 10$ MHz, $\lambda =589$ nm, and $M=23$ Da.

Figure 5

Dependence of the spatial capture range of the trap $\Delta z=\sqrt{\langle z^2\rangle -{\langle z\rangle }^2}$ on the frequency detuning $\delta$. The parameters are the same as in Fig. 4.

Figure 6

Dependence of the spatial capture range of the trap $\Delta z=\sqrt{\langle z^2\rangle -{\langle z\rangle }^2}$ on the pulse area for $\delta =0.5\gamma$. The other parameters are the same as in Fig. 4.

Figure 7

Example of the SrF molecule motion in the field of the counterpropagating sequences of light pulses: (a) $v\left(t\right)$ and (b) $z\left(t\right)$. The parameters are $\tau =1$ ps, $T=23.8$ ns, ${\vartheta }_1=0.1\pi ,{\vartheta }_2=0.014\pi ,\gamma =2\pi \times 7$ MHz, ${\delta }_1=2\pi \times 3.5$ MHz, ${\delta }_2=2\pi \times 7$ MHz, $\lambda =663.3$ nm, and $M=107$ Da. The molecule starts at the center of the trap with initial velocity $v_0=1$ m/s.

Figure 8

Time dependences of (a) average velocity $\overline{v}=〈v〉$ (thin line) and $\Delta v=\sqrt{\langle v^2\rangle -{\langle v\rangle }^2}$ (thick line) and (b) average coordinate $\overline{z}=〈z〉$ (thin line) and $\Delta z$ (thick line) for an ensemble of 400 molecules. The parameters are the same as in Fig. 7.

Figure 9

Example of a nanoparticle's motion in the field of the counterpropagating sequences of light pulses: (a) $v\left(t\right)$ and (b) $z\left(t\right)$. It is supposed that the mass of nanoparticle per every active atom is $30000$ Da. The parameters are $\tau =1$ ps, $T=10$ ns, $\vartheta =0.1\pi ,\gamma =2\pi \times 10$ MHz, $\delta =2\pi \times 5$ MHz, and $\lambda =600$ nm. The nanoparticle starts at the center of the trap with initial velocity $v_0=10$ cm/s.