Rotating optical tubes for vertical transport of atoms

The classical dynamics of a cold atom trapped inside a vertical rotating helical optical tube (HOT) is investigated by taking also into account the gravitational field. The resulting equations of motion are solved numerically. The rotation of the HOT induces a vertical motion for an atom initially at rest. The motion is a result of the action of two inertial forces, namely, the centrifugal force and the Coriolis force. Both inertial forces force the atom to rotate in a direction opposite to that of the angular velocity of the HOT. The frequency and the turning points of the atom's global oscillation can be controlled by the value and the direction of the angular velocity of the HOT. However, at large values of the angular velocity of the HOT the atom can escape from the global oscillation and be transported along the axis of the HOT. In this case, the rotating HOT operates as an optical Archimedes’ screw for atoms.

Figure 1

A rotating HOT that is formed by LG beams with $l=1$ and $p=0$.

Figure 2

The trajectory of a ${}^{85}\mathrm{Rb}$ atom with respect to the HOT frame of reference: (a) ${\mathrm{\Omega }}_R=70\mathrm{kHz}$, represented by the black line and (b) ${\mathrm{\Omega }}_R=-70\mathrm{kHz}$, represented by the red line.

Figure 3

The trajectory of a ${}^{85}\mathrm{Rb}$ atom with respect to the lab frame of reference: (a) ${\mathrm{\Omega }}_R=70\mathrm{kHz}$, represented by the black line and (b) ${\mathrm{\Omega }}_R=-70\mathrm{kHz}$, represented by the red line.

Figure 4

The variation of the average of the transferred angular momentum (in units of $\hslash )$ to a ${}^{85}\mathrm{Rb}$ atom as a function of the angular velocity of the HOT, where the atomic initial velocity is $\left(v_x=0,v_y=0,v_z=0\right),w_0=5\mu \mathrm{m}$, and $l=1$.

Figure 5

The variation of a ${}^{85}\mathrm{Rb}$ atom elevation (the initial velocity of the atom is $v_x=5\mathrm{cm}/s,v_y=-5\mathrm{cm}/s,v_z=0)$ for different angular rotation velocities of the HOT ${\mathrm{\Omega }}_R$: $70\mathrm{krad}/\mathrm{s}$ (red solid line), static HOT (black dashed line), $-70\mathrm{krad}/\mathrm{s}$ (blue dash-dotted line), and $-97\mathrm{krad}/\mathrm{s}$ (brown dotted line).

Figure 6

The variation of the first turning point of a ${}^{85}\mathrm{Rb}$ atom as a function of the angular velocity of the HOT for different initial atomic velocities: $\left(v_x=7.6\mathrm{cm}/\mathrm{s},v_y=-7.6\mathrm{cm}/\mathrm{s},v_z=0\right)$ pink dash-dotted line, $\left(v_x=5\mathrm{cm}/\mathrm{s},v_y=-5\mathrm{cm}/\mathrm{s},v_z=0\right)$ red dashed line, $\left(v_x=2.4\mathrm{cm}/\mathrm{s},v_y=-2.4\mathrm{cm}/\mathrm{s},v_z=0\right)$ blue dash-dot-dotted line, $\left(v_x=0,v_y=0,v_z=0\right)$ black line, and $\left(v_x=-5\mathrm{cm}/\mathrm{s},v_y=5\mathrm{cm}/\mathrm{s},v_z=0\right)$ green dotted line $(w_0=5\mu \mathrm{m}$ and $l=1)$.

Figure 7

The variation of a ${}^{85}\mathrm{Rb}$ atom elevation with initial velocity $\left(v_x=5\mathrm{cm}/\mathrm{s},v_y=-5\mathrm{cm}/\mathrm{s},v_z=0\right)$ for different angular rotation velocities of the HOT: $147\mathrm{krad}/\mathrm{s}$ (black solid line), $146\mathrm{krad}/\mathrm{s}$(red dashed line), $-151\mathrm{krad}/\mathrm{s}$ (blue dash-dotted line), and $-150\mathrm{krad}/\mathrm{s}$ (brown dotted line) $(w_0=5\mu \mathrm{m}$ and $l=1)$.

Figure 8

The variation of a ${}^{85}\mathrm{Rb}$ atom radial wiggling with initial velocity $\left(v_x=5\mathrm{cm}/\mathrm{s},v_y=-5\mathrm{cm}/\mathrm{s},v_z=0\right)$ for different angular rotation velocities of the HOT:$307\mathrm{krad}/\mathrm{s}$ (red dotted line), $308\mathrm{krad}/\mathrm{s}$ (blue dash-dotted line), $-279\mathrm{krad}/\mathrm{s}$ (brown dash-dotted-dotted line), and $-280\mathrm{krad}/\mathrm{s}$ (dashed pink line) (the black solid line represents radial minima of the potential; $w_0=5\mu \mathrm{m}$ and $l=1)$.

Figure 9

The variation of ${\omega }_s^{\prime }$ (red dashed line) and ${\omega }_r^{\prime }$ (black solid line) of a trapped ${}^{85}\mathrm{Rb}$ atom as a function of ${\mathrm{\Omega }}_R$. The atom started the motion from rest, the beam waist of LG beams is $w_0=5\mu \mathrm{m}$, and the orbital angular momentum number is $l=1$.

Figure 10

The variation of ${\mathrm{\Omega }}_R^r$ and ${\mathrm{\Omega }}_R^s$ as a function of the orbital angular momentum number $l$ for a ${}^{85}\mathrm{Rb}$ atom initially at rest, where $w_0=5\mu \mathrm{m},P=80\mathrm{mW}$, and $\mathrm{\Delta }=-25.7\mathrm{THz}$.

Figure 11

The variation of ${\mathrm{\Omega }}_R^r$ and ${\mathrm{\Omega }}_R^s$ as a function of the beam waist $w_0$ for a ${}^{85}\mathrm{Rb}$ atom initially at rest, where $l=1,P=80\mathrm{mW}$, and $\mathrm{\Delta }=-25.7\mathrm{THz}$.

Figure 12

The variation of ${\mathrm{\Omega }}_R^r$ and ${\mathrm{\Omega }}_R^s$ as a function of the beam power $P$ for a ${}^{85}\mathrm{Rb}$ atom initially at rest, where $l=1,w_0=5\mu \mathrm{m}$, and $\mathrm{\Delta }=-25.7\mathrm{THz}$.

Figure 13

The variation of ${\mathrm{\Omega }}_R^r$ and ${\mathrm{\Omega }}_R^s$ as a function of the detuning $\mathrm{\Delta }$ for a ${}^{85}\mathrm{Rb}$ atom initially at rest, where $l=1,w_0=5\mu \mathrm{m}$, and $P=80\mathrm{mW}$.