Light-induced drift of rubidium upon optically thin regime

 

A. Lucchesini, S. Gozzini and L. Moi


 

 

Light-induced drift (LID) has been deeply studied during these last years with special attention to the alkali-noble gas systems [1]. The LID effect consists in a macroscopic diffusion of an active gas immersed in a buffer gas. This diffusion, that may reach velocities of the order of 10-50 m/s, appears when both a velocity selective excitation and a transport property depen­dence on the atomic internal states are present. The diffusion is along the laser beam propagation and its direction depends on the laser frequency detuning. The LID pressure, which is due to atomic momentum transfer and not to photon momentum ex­change, can be orders of magnitude larger than the radiation pressure and, for this reason, it is suitable for many applications. Isotope separation seems to be the more promising and convenient when diode lasers can be used, and among the alkali atoms, rubidium is the best candidate. It has two stable isotopes 85Rb and 87Rb, with relative concentrations equal to 72% and 28% respectively. The absorption spectrum, as shown in fig. 1 in the case of D2 excitation, has four well sepa­rated lines, each one being due to the absorption of one isotope at a time. Streater et al. [2] calculated the drift velocity as a function of the laser detuning and they found that at some frequencies the two isotopes can also diffuse to opposite directions. Therefore the approach seems straightforward: the laser can be slightly detuned with respect to the absorption line of one of the two isotopes, which is then pushed away and collected. In the prac­tice many problems come out and an effective isotope separation seems more troublesome.

The analysis of the cell wall contribution to the vapor dynamics is stressed out by taking into account the new light-induced atom desorption effect (LIAD), recently observed.

Fig. 1.  D2 absorption spectrum of both rubidium isotopes.

 

 

LID VELOCITY CALCULATION

 

The drift velocity can be calculated by considering the atom level structure and the impact parameters with the buffer gas. In principle the complete level structure should be taken into ac­count, but, as shown by Haverkort et al. [3], a simplified atom model can be conveniently adopted. This numerical model has been first developed and checked for a four-level alkali atom model based on realistic Keilson-Storer collision kernels. This gives a good agreement between theory and experimental results in the case of sodium, as discussed by Werij et al. [4]. The four levels are the two hyperfine ground states and the two excited fine-structure states. For heavier alkali atoms like Rb, the colli­sion transfer rate between the two fine-structure levels can be neglected and in this specific case, when only one of the two up­per levels is optically excited [5], a simpler three-level descrip­tion is possible. Rb atom is then described by the two ground hy­per­fine states (labelled 1 and 2) and by one excited state (labelled 3). The rate equations can be written in the form:

 

                                                                                                   (1)

 

where

 

                                                                                                           (2)

 

is the population distribution, A and B are 3x3 matrices,

 

                                                                                                                                (3)

 

with

 

                                                                                                             (4)

 

and

                                                                                                 (5)

 

By remembering that the drift velocity is given by

 

                                                                                                                   (6)

 

it results

                                                         (7)

 

 

where

               (8)

and

 

                                                                                         (9)

 

hij are the excitation rates at a given velocity, Bij and Aij the Einstein coefficients, gi the statistical weights of the levels, I the laser power density, gi the collision rates.

 

Table I.  Common parameter values.

Parameter

Ref.

Value

g1,2

3, 6

3.18×107 Hz

g3

3, 6

4.15×107 Hz

A3

5

3.66×107 Hz

Is

7

361.88 W×m-2

k

 

0.8055×107m-1

G

7

2.93×108 Hz

T

 

333 K

 

 

Table II.  Specific parameter values. DHFS is the hyperfine energy level distance.

Parameter

Ref.

85Rb value

87Rb value

A31

5

2.135×107 Hz

2.288×107 Hz

A32

5

1.525×107 Hz

1.372×107 Hz

g1/g3

5

7/24

5/16

g2/g3

5

5/24

3/16

DHFS

5

3.0 GHz

6.8 GHz

 

The equation (7) has been numerically integrated by adopting the parameter values re­ported in tables I and II, and by assuming that the cell is filled with 5 Torr of Kr as a buffer gas. In fig. 2 the drift velocity v calculated as a function of the laser detuning is shown for the two isotopes. The laser power density is assumed equal to WL= 10 W/cm2 and the laser is single mode.

 

Fig. 2.  Drift velocity of the two Rb isotopes calculated as a function of the laser detuning, when the laser power density is 10 W/cm2

 

In fig. 3 v is shown as function of the laser power density WL, at the frequency detuning  DnL = -0.5 GHz. With this frequency detuning the two isotopes drift to opposite directions, with a relative ve­locity of about 40 cm/s when the laser power density is equal to 10 W/cm2. These calculations clearly show that, upon our experimental conditions, both rubidium LID and isotope de­pending velocities can be obtained. The only limitation set with this approach is the “optically thin condition” imposed to the vapor.

 

Fig. 3.  Drift velocity of both isotopes as function of the laser power density at a fixed laser detuning equal to -0.5 GHz.

 

 

LID VELOCITY MEASUREMENTS

 

Fig. 4.  Sketch of the experimental apparatus for the LID effect. D.L.: diode laser, P.M.: photomultiplier, B.S. beam splitter.

 

The experimental apparatus is sketched in fig. 4. AlGaAs single mode diode lasers, operating in free running mode, are used for excitation and monitoring of Rb vapor. Their gross fre­quency tuning is achieved by driving the diode laser temperature by using the Melles Griot thermoelectric cooler 06 DTC 001. The Melles Griot current generator 06 DLD 201 controls the fine tun­ing by the laser injection current. The LID laser, tuned to the D2 line of rubidium, is sent to a capillary cell (2 mm inter­nal diameter, 15 cm long and filled with 5 Torr of Kr). The cell is coated by an ether solution of dimethylpolysiloxane that reduces the vapor friction at the cell walls as described in ref. [8].

The LID effect is recorded by detecting the fluorescence coming from a given point along the capillary. The laser pushes or pulls the atoms and the detected fluorescence variations can be related to the vapor diffusion. Two different ap­proaches have been adopted, with the aim of well displaying the LID effect. In the first one the laser frequency is kept fixed and the laser is switched on at a given time. The fluorescence decay allows us to derive the drift velocity. In the second one the laser is always on, but its fre­quency is swept across the resonance. Depending on the different contribution of optical pumping and LID, the spectrum results modified by changing the scanning velocity. It is possible to separate these two contributions and extract the LID effect only; in such a way a continuous dependence of the drift velocity on the laser frequency is obtained. In these measurements only the total dif­fusion of the vapor, related to both isotopes, has been studied.

The macroscopic diffusion of the vapor is described by the differential equation

 

                                                                                                     (10)

 

where D is the diffusion coefficient of the ground state atoms. The solution of this equation for an optically thin vapor and for the boundary conditions

      and                                                                     (11)

 

has been already given and checked for sodium [2]. The solution having the form:

 

                                                                                                                       (12)

 

where

 

                                                                                                                   (12a)

 

and

 

 

                                                                             (12b)

with x= (v/D)×z.

The A term value varies between 0 and 1 and assumes the value of 0.5 after a time t*= z0/v, where z0 is the observation point and v the drift velocity. The B term contributes by a van­ishing quantity, depending on the parameter S = z0v/D. When S = 1, B is about 0.08 and when S becomes larger, B goes rapidly to zero. Therefore, when the B term is negligible, v can be directly derived by measuring z0 and t*. In our experimental conditions S = 0.2 v, and a drift velocity of a few cm/s is enough to give a B term of only a few per cent, therefore the drift velocity can be obtained with a reasonably good accuracy. In fig. 5 the fluo­rescence variations as a function of time are reported for two different laser detunings. The signals correspond to the drift of both iso­topes. The bottom line comes from the stray light and permits an absolute evaluation of the vapor density variation.

 

Fig. 5. Fluorescence signals as function of time for two laser detunings.

 

The results shown in fig. 6 are obtained by continuously vary­ing the laser frequency and by looking at the fluorescence spec­trum as a function of the laser frequency scan rate nR. Due to both op­tical pumping and LID, the fluorescence spectrum depends on nR, and in place of the four well separated peaks as reported in fig. 1, only three peaks appear, whose relative inten­sities again de­pend on nR. When nR is decreased to about nR = 1 Hz, the optical pumping dominates and the three peaks have the intensities shown in fig. 6a. When nR is further decreased, the induced vapor diffusion becomes important and LID overcomes the optical pumping. Then the relative peak intensities change as shown in fig. 6b. Ought to the much higher laser power and to the much larger drift velocity, that case showed a so strong LID effect that no evidence of optical pumping was ob­tained.

 

Fig. 6.  Fluorescence spectrum of Rb D2 as a function of the laser frequency scan rate. a) nR = 0.5 Hz; b) nR = 0.0048 Hz.

 

By subtracting curve b) from curve a) the LID contribu­tion is obtained as a function of the laser frequency and the re­sult is reported in fig. 7, where also the calculated drift velocity and the absorption spectrum without optical pumping are shown for comparison.

 

Fig. 7.  Drift velocity of Rb, measured and calculated at different laser detunings from the D2 line. Ilaser = 0.25 W/cm2.

(■) measured velocity, (—) calculated velocity, (---) absorption feature.

 

 

REFERENCES

 

1. See for example the Proceedings of The International Work­shop on Light Induced Kinetic Effects on Atoms, Ions and Molecules, Marciana Marina, Elba Island, 2 - 5 May, 1990, (Ed. L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, F. Strumia, E.T.S., Pisa, Italy, 1991), ISBN 88-7741-560-6

2. A.D. Streater, J. Mooibroek, J.P. Woerdman, Optics Commun. 64, 137 (1987)

3. W.A. Hamel, J.E.M. Haverkort, H.G.C. Werij, J.P. Woerdman, J. Phys. B: At. Mol. Phys. 19, 4127 (1988)

4. H.G.C. Werij, J.P. Woerdman, Phys. Rep. 169,145 (1988)

5. A.D. Streater, J.P. Woerdman, J. Phys. B: At. Mol. Opt. Phys. 22,  677 (1989)

6. J.E.M. Haverkort, Ph.D. Thesis, Leiden (1987)

7. E.L. Lewis, Phys. Rep. 58, 1 (1980)

8. J.H. Xu, M. Allegrini, S. Gozzini, E. Mariotti, L. Moi, Optics Commun. 63, 43 (1987).