Spatially selective loading of an optical lattice by light-shift engineering using an auxiliary laser field

We report on a method of light-shift engineering where an auxiliary laser is used to tune the atomic transition frequency. The technique is used to selectively load a specific region of an optical lattice. The results are explained by calculating the differential light-shift of each hyperfine state. We conclude that the remarkable spatial selectivity of light-shift engineering using an auxiliary laser provides a powerful technique to prepare ultra-cold trapped atoms for experiments on quantum gases and quantum information processing.

We report on a method of light-shift engineering where an auxiliary laser is used to tune the atomic transition frequency. The technique is used to selectively load a specific region of an optical lattice. The results are explained by calculating the differential light-shift of each hyperfine state. We conclude that the remarkable spatial selectivity of light-shift engineering using an auxiliary laser provides a powerful technique to prepare ultra-cold trapped atoms for experiments on quantum gases and quantum information processing. Optical dipole traps and optical lattices are finding an ever increasing range of applications in experiments on Bose-Einstein condensation (BEC) [1,2,3,4], optical clocks [5], single-atom manipulation [6,7], and quantum information processing (QIP) [8,9]. In many applications, one is interested not only in the light-shift of the ground state, which determines the trap depth, but also the relative shift of a particular excited state. One has some control over this differential shift as the ground and excited states have different resonances, and the laser can be tuned to a 'magic' wavelength where the ground and excited state polarizabilities are the same [5,7,10]. However, using a 'magic' wavelength is not always appropriate either because one is no longer free to select the laser wavelength to minimize spontaneous emission, or because of the unavailability of suitable light sources.
In this paper, we report on a different method of lightshift engineering where a second laser field is used to control the excited state polarizability. One such method for controlling ground-state hyperfine polarizabilities is discussed in Ref. [11]. Light-shift engineering using an independent laser could have significant advantages over the use of a 'magic' wavelength for some applications, as it can be applied to specific regions of a trap. For example, we show how the technique can be used to selectively load a well defined region of an optical lattice. Specifically, we consider the case of loading 85 Rb atoms into a deep CO 2 laser lattice. A quasi-electrostatic lattice based on a CO 2 laser (wavelength 10.6 µm) is particulary attractive for trapping cold atoms or molecules as it combines low light scattering [12] with a lattice constant sufficiently large to allow single-site addressability [13]. We show that by focussing an additional laser (a Nd:YAG laser with wavelength 1.064 µm) on a specific region of the lattice we can selectively load only into sites in this region. This spatially selective loading is most effective when the cooling light is blue-detuned relative to the unperturbed atomic resonance. We explain the effect by calculating the differential light-shifts between the ground and excited states in the presence of two light fields. We show that only in the light-shift engineered region where the CO 2 and Nd:YAG laser beams overlap, is the differential shift negative allowing efficient laser cool-ing. In addition, we show that for red-detuned cooling light, light-shift engineering produces a significant enhancement in the number of atoms loaded into a deep optical trap.
The experimental set-up employed to demonstrate controlled loading by light-shift engineering is shown in Fig. 1. An octagonal vacuum chamber, fitted with home-made Zinc Selenide (ZnSe) UHV viewports [14] to accommodate the CO 2 laser beams, provides a background pressure of 1.2×10 −10 Torr. A focussed Nd:YAG laser beam, with variable power, locally heats an alkali metal dispenser to provide a controllable source of thermal 85 Rb atoms [15]. A CO 2 laser beam, (propagating along the z-axis in Fig. 1) with power 45 W, is focussed to form a waist (1/e 2 radius) of 70 µm at the center of the chamber. The beam is collimated and retroreflected to form a 1D optical lattice. The intensity of the CO 2 laser is controlled using an acousto-optic modulator (AOM). The intensity at the center of the lattice, I 0 = 2.3 × 10 6 Wcm −2 , gives a ground state light-shift is the ground-state polarizability at 10.6 µm in atomic units. A Nd:YAG laser beam (propagating at +45 • to the y axis in the xy plane) with power 7.8 W is focussed by a f = 150 mm lens to overlap with the CO 2 lattice in the trapping region. The Nd:YAG laser has a circular focus with a beam waist of 30 µm in the overlap region. This gives an intensity of I 0 = 5.5 × 10 5 Wcm −2 leading to a ground state light-shift U 0 = h(−18.6 MHz) using our calculated value of α 0 = 722 a 3 0 at 1.064 µm. The CO 2 and Nd:YAG laser beams are linearly polarized along the x and z axes, respectively.
Loading of a CO 2 laser lattice is carried out as follows: The CO 2 and Nd:YAG laser beams are left on throughout the loading stage. We load a magneto-optical trap (MOT), centered on the dipole trap, with 2 × 10 7 85 Rb atoms in typically 3 seconds. After the magnetic field is switched off, the cooling laser beam intensities are reduced from 55 mWcm −2 to 10 mWcm −2 and the detuning is increased to ∆ = −8Γ, where Γ = 2π(6 MHz) is the natural linewidth of the transition, to create an optical molasses. After 10 ms of molasses, the atom cloud has a typical temperature of 40 µK, measured by time- of-flight. During the molasses phase the hyperfine repumping laser intensity is lowered from 6 mWcm −2 to 200 µWcm −2 and then switched off completely with a shutter for the final 5 ms such that atoms are pumped in the lower hyperfine state [16]. After the molasses phase, the cooling light and the Nd:YAG laser are extinguished for a few hundred milliseconds, then the CO 2 laser is turned off and the MOT beams (tuned to resonance) are turned back on to image the cloud. A CCD camera collects the fluorescence to give a spatial profile of the trapped atoms. A typical atom distribution viewed approximately perpendicular to the CO 2 and Nd:YAG beam axes is shown in Fig. 1(b). One sees that the CO 2 lattice loads efficiently out in the wings where the trap depth is smaller. This effect has been widely observed in experiments on far-off resonance optical dipole traps [13,17,18] and arises due to the smaller differential light-shift between the ground and excited states away from the focus. We also see that the loading is greatly enhanced in the region where the Nd:YAG laser intersects the CO 2 laser lattice.
Remarkably, if we detune the cooling light slightly to the blue of the unperturbed atomic resonance such that neither the CO 2 nor the Nd:YAG laser beams alone trap any atoms, then we still observe that the region where the two beams intersect is efficiently loaded, see Fig. 2(b). This spatial selectivity provides a very clear demonstration of the power of light-shift engineering using an auxiliary laser field. In addition, it demonstrates that the enhanced loaded observed in Fig. 1 and Fig. 2(a) cannot be explained by a 'dimple' effect [19], where atoms from the wings of a trap rethermalise in the deeper overlap region [20]. Finally, we should add that the enhanced loading observed in the overlap region cannot be explained simply by the fact that the trap is deeper in this region. To demonstrate this we have reduced the CO 2 laser power by a factor of four such that the depth in the combined CO 2 plus Nd:YAG trap is less than a CO 2 lattice alone at full power. Typical column densities are shown in Fig.  3. We see that the density in the combined trap is still significantly higher than for a deeper CO 2 lattice.
To explain the spatially selective loading for bluedetuned cooling light, we have calculated the polarizability of the 5s ground and 5p excited states as a function of wavelength. The details of the calculation will be explained elsewhere [21]. Briefly, the scalar polarizability α 0 is the average of the dipole polarizabilities α xx , α yy and α zz for an atom exposed to a laser field polarized, respectively, in the x, y, and z-directions: α 0 = (α xx + α yy + α zz )/3. The scalar polarizability is the same for all m-components of the 5p state. In addition, there is a tensor polarizabilty α 2 = (α xx − α zz ) /3 which lifts the degeneracy of different m-states. In order to obtain these quantities, we represent the interaction of the valence electron with the core by the model potential proposed by Klapisch [22]. The polarizabilities are calculated by the implicit summation method [23]. Thus α xx (and similarly for α yy and α zz ) is obtained as α xx = −e( 0|x|1 + 0|x| − 1 )/F , where |0 represents the state vector of the unperturbed 5s, or 5p −1,0,1 states, and | ± 1 are such that Here H 0 is the Hamiltonian of the field-free model atom and E 0 is the eigenenergy of the unperturbed state, i.e. H 0 |0 = E 0 |0 , and F is an arbitrary electric field. These equations are solved in position space by expanding the wave functions on a discrete basis of radial Sturmian functions and spherical harmonics [24]. In the zerofrequency limit, the resulting values of α 0 [5s], α 0 [5p] and α 2 [5p] converge towards 333a 3 0 , 854a 3 0 , and −151a 3 0 , respectively, in satisfactory agreement with previous experimental and theoretical work [25]. The dynamic polarizabilities as functions of wavelength are shown in Fig. 4. We find that α 0 = 722a 3 0 at 1.064 µm, which agrees well with experiment and other theoretical work [26,27,28].
For our purposes the most important result of Fig. 4 is that the polarizabilities of the 5s state at the CO 2 laser wavelength (λ = 10.6 µm) and the Nd:YAG wavelength (λ = 1.064 µm) have the same sign, whereas the polarizabilities of the 5p state have opposite signs. It follows that one can use a combination of CO 2 and Nd:YAG lasers to tune the differential light-shift between the 5s and 5p states through zero. To calculate the light-shift experienced by atoms in the combined CO 2 plus Nd:YAG trap we calculate the eigenvalues of the matrix [29,30] where U 0 is a diagonal matrix with components corresponding to the hyperfine splitting, the index i denotes the CO 2 and Nd:YAG lasers, and Q i is a ma- µ − J(J + 1)]/J(2J − 1) and J µ being the electronic angular momentum operator in the direction of laser field i. The differential light-shift between the ground state and the 5p 2 P 3/2 (F = 4) state for the CO 2 laser alone is shown in Fig. 5(a). As a single laser beam splits the states according to the magnitude of m F , there are five curves corresponding to |m F | = 0, . . . , 4. We see that all the levels are far blue-detuned (positive differential shift) at the centre of the lattice, making laser cooling ineffective unless the cooling light is detuning to the red by an amount larger than the differential light-shift. Adding the Nd:YAG laser produces the shifts shown in Fig. 5(b). The Nd:YAG laser lifts the degeneracy between the ±m F components, although two pairs of states remain close to degenerate. More importantly, one pair of states is pulled down into the region of negative differential shift. This allows efficient laser cooling in the center of the overlap region, even when the cooling light is slightly blue-detuned relative to the unperturbed resonance frequency. Note that, efficient loading for blue-detuning can only be explained if one includes the tensor polarizability term α 2 . Although α 2 is smaller than the scalar polarizability (by a factor of 4 or 5), it dramatically alters whether states see the cooling light as red or blue detuned and therefore completely determines whether the trap is loaded or not.
As light-shift engineering allows laser cooling to work as efficiently as in free space one might expect to load atoms at lower temperature than in conventional loading schemes. To address this issue we need to increase the sensitivity and the resolution of our imaging system to allow accurate density and temperature measurements. This will be the focus of future work.
To conclude, we have shown how light-shift engineering using an auxiliary laser field can be used to implement spatially selective loading of deep far-off resonance optical lattices. We have performed theoretical calculations of the atomic polarizabilities and have shown that the addition of a second laser field induces a splitting of the excited state which is crucial in determining the efficiency of loading into the combined trap. The technique could be applied to load a single-site in 3D CO 2 lattice, with the interesting prospect of BEC in the limit of high trap frequency. In addition one could adapt the technique to perform patterned loading of optical lattices [31] for applications in QIP experiments.
We thank E. Riis, I. G. Hughes, and S. L. Cornish for stimulating discussions, M. J. Pritchard for experimental assistance and EPSRC for financial support.