Figure 1.12: Working principle of the optical conveyor belt. (a) If the counterpropa-gating beams are detuned with respect to each other, the reference frame in which both beams are Doppler shifted to the same frequency is moving at the velocity v. (b) In order to transport an atom over the distanced, we expose it to constant acceleration and deceleration.
1.4 An optical conveyor belt
To precisely control the position of an atom we use an optical conveyor belt [14, 23]. This device was designed to transport a desired number of atoms into the mode of an optical high-finesse resonator in a controlled manner. There they could interact via the exchange of single photons. This is a key technique for the implementation of a quantum logic gate.
Combining this tool with our imaging techniques, we demonstrated the first continued observation of controlled single atom transport [25].
1.4.1 A moving standing wave
The standing wave configuration of our dipole trap is well suited to transport trapped atoms. A mutual detuning of the counter-propagating beams by ∆ν =ν2−ν1 will cause the standing wave structure to move at the velocity v = λ∆ν/2. This can be seen by considering the Doppler shift which compensates this detuning in the reference frame moving atv, see Figure 1.12 (a). The time-dependent dipole potential
U(x, ρ, t) =−U0 w20 w2(x)e−
2ρ2
w2(x) cos2(π∆νt−kx) (1.17)
can therefore be used to transport trapped atoms along the dipole trap axis.
In order not to lose an atom during transport, it is important to smoothly accelerate and decelerate the potential. A simple way of transporting it over a desired distancedduring the time td is to uniformly accelerate it at a during the first half of the time interval followed by a uniform deceleration at −a during the second half. The velocity changes from 0 tovmax=atd/2 and back to 0 during this time, see Figure 1.12 (b).
Figure 1.13: Experimental setup of the optical conveyor belt. Each beam of the standing-wave dipole trap is frequency shifted by an acousto-optical modulator (AOM).
Both AOMs are driven by a phase-synchronous dual frequency RF-generator.
Experimental implementation
To implement this scheme experimentally, we installed an acousto-optical modulator (AOM) in each beam of the dipole trap, see Figure 1.13. They are both set up in double pass configuration to compensate beam walk-offs during frequency shifts. For the station-ary standing wave dipole trap both AOMs are operated at the same frequency of 100 MHz.
For the transport it is essential to change their frequency difference in a phase-continuous way, since their relative phase is directly translated to the spatial phase of the dipole trap. Any phase discontinuity could lead to the loss of the atom. We therefore use a custom built dual frequency synthesizer (APE Berlin, DFD 100) which drives both AOMs and performs phase-continuous frequency sweeps as programmed via an RS232 interface.
However, we found that remaining phase fluctuations of the two RF outputs on the order of 10−3 rad cause heating of the trapped atoms and reduce the lifetime in the trap from 25 s (see Section (1.2.3)) to about 3 s [57].
Using this setup we can transport a single atom over a distance as large as 1 cm with an efficiency of 80 % [14]. Since we monitor their relative phase and thus the total distance in units ofλby heterodyning the two AOM driving frequencies, we control this distance with an accuracy much smaller than 1µm. The maximum transportation distance is determined by the divergence of the Gaussian dipole trap laser beam. With increasing distance from the focus, the trap depth decreases. At a distance of 1.5 cm, gravity is stronger than the radial dipole force and pulls the atom out of the trap [23]. The minimum time required for a transport is limited by the maximum possible acceleration. If the accelerating force becomes stronger than the axial dipole force at typically amax = 5×105 m/s2 the atom
1.4 An optical conveyor belt 25
Figure 1.14: Continued imaging of the transport of single atoms. (a) Experimental sequence. Between successive images (exposure time: 1 s) the atoms are transported over a distance of 2 µm. (b) Screenshots of the transport of a single atom, where only every forth image is shown. (c) Synchronous transport of a string of three atoms. The direction of motion is changed twice. Here, every eighth image of the full movie presented in Reference [25] is shown. The exposure time per image was reduced to 0.5 s.
cannot follow the motion of the travelling standing wave any more. The finite bandwidth of the AOMs and a further heating effect due to abrupt changes of the acceleration limit the experimentally observed maximum acceleration to 105 m/s2 [23, 48]. With these parameters, the transport of an atom over 1 mm only takes 200 µs.
1.4.2 Imaging the controlled motion of a single atom
Combining our technique of imaging single atoms in the dipole trap with the optical conveyor belt we continuously image the transport of a single neutral atom [25]. An image sequence is recorded according to the scheme in Figure 1.14 (a). We first check the presence of one single atom in the MOT and take an image with an exposure time of 1 s. After transfer into the dipole trap we switch on the optical molasses and acquire the second image, again with an exposure time of 1 s. We then transport the atom over the distance of 2 µm within 2 ms and take the next picture. This sequence of transport and imaging is repeated and yields a series of pictures of the same atom. The resulting
“movie” (see Figure 1.14 (b)) shows the transport of the atom over a distance of 60 µm within one minute and ends with the loss of the atom. The long lifetime of the atom in the trap demonstrates that the continuous molasses cooling effectively counteracts the heating mechanism due to AOM-phase noise.
We employed this technique to precisely calibrate the magnification of our imaging system.
By comparing the positions of a single atom image on the ICCD chip before and after transport of the atom over the distance of 60 µm, we determine the magnification to be 14.0±0.1.
A second movie shows the transport of a string of three trapped atoms, see Figure 1.14 (c).
Here, we initiated the reversal of the transport direction by manually changing the sign of the relative detuning between the dipole trap laser beams. The average time before an atom is lost is of the order of 30 s which corresponds to the measured lifetime limited by background gas collisions [41, 63]. Both movies can be viewed online in Reference [25].