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Atomic beam deflection by the light of a tunable dye laser
Volume 5, number 5
OPTICS COMMUNICATIONS
ATOMIC BEAM DEFLECTION
BY THE LIGHT OF A TUNABLE
August 1972
DYE LASER
R. SCHIEDER, H. WALTHER and L. Wt3STE 1. Physikalisches Institut der UniversitiitK61n, Cologne, Germany Received 24 May 1972 The deflection of a sodium atomic beam by the radiation pressure of the light of a cw dye laser was investigated. From the deflection observed it is deduced that the linear momentum transferred corresponds to an average of 60 excitations per atom. The linewidth of the dye laser used for the measurements was smaller than 50 MHz.
The absorption and re-emission of resonance radiation by atoms is coupled with an exchange of linear momentum between the atoms and the radiation field. The linear m o m e n t u m of a photon of visible light is rather small and is o f no importance in the usual resonance experiment. However in certain experimental arrangements the transfer of linear m o m e n t u m can be observed. Frisch [1 ] * showed that a sharply collimated sodium atomic beam is deflected if the atoms are irradiated b y a sodium discharge lamp. But in this experiment only one third of the atoms of the beam were
oc
I Recorder
Amplifier
v I
\ Langmuir - Taylor - Detector Vo-Atomic Beam
t
Tunable cw Dye Laser I
Laser Beam Atomic Beam Oven
I
L
Fig. 1. Experimental setup.
excited and therefore the deflection observed was rather small. A much larger deflection can be expected if a tunable laser is used in order to excite the atoms. The laser is sufficiently intense so that the 3 2p, and 3 2P3 levels of Na I can be saturated. Therefore, the n u m b e r o f excitations of each atom, which may be on the order o f 100 or more, is determined by the interaction time between the atomic beam and the light beam. Furthermore it has been shown b y Ashkin [3] that for a convergent radiation field which is intense enough to produce saturation the radiation pressure is equivalent to the force in a central field in which atoms follow circular orbits. This enables one to velocity analyse the atomic beam. In this communication we describe an experiment in which the deflection of a sodium atomic beam by the radiation field of a cw dye laser was investigated. The experimental setup is shown in fig. 1. The sodium beam was well collimated with a collimation ratio o f 1 : 500. This implies a Doppler width of 3 MHz when the atoms are viewed at right angles to the beam. The absorption width of the beam was therefore mainly given b y the natural linewidth o f the excited 2p levels which is about 10 MHz. The atoms were detected using a Langmuir - Taylor detector. The signal was amplified and plotted by an x - y recorder. To measure the profile o f the atomic beam the detector could be moved in a direction perpendicular to the beam as shown in fig. 1. Using a helix potentiometer the posi* A more ref'med experiment:of this kind was recently performed by Picqu6 and Vialle [2]. 337
Volume 5, number 5
OPTICS COMMUNICATIONS
tion of the detector was coupled to the x axis of the recorder. Details of the cw dye laser dsed in our experiment will be described elsewhere [4]. The laser configuration was similar to that published by Hercher and Pike [5]. Single mode operation of the laser was achieved by the use of a birefringent filter made of a KDP crystal with a length of 6 cm [6] or by an intracavity etalon. The continuous tuning of the laser was performed by changing the cavity length. The output power of the laser was about 10 mW. The distance between laser interaction region and atomic beam detector was about 50 cm. Fig. 2 shows typical results obtained in our measurements. The signal current is plotted versus the position of the detector. At the zero point the slit of the atomic beam oven, the collimator, and the detector wire are all on a straight line. Curve (a) of fig. 2 was measured without laser excitation. Curve (b) was obtained wher~the dye laser was tuned to one hyperfine component of the Na D 2 line. Due to the transfer of linear momentum the center of the atomic beam is shifted in the direction of the laser beam.
August 1972
Curve (b) represents the average of 3 different measurements for the same experimental conditions. The fluctuation observed in an individual measurement was on the order of 5% and seems to be due to short time frequency variations of the laser. These frequency variations are mainly caused by mechanical instabilities of the laser cavity. The duration of one measurement was about 20 sec, the time constant of the recording system eas aproximately 0.2 sec. For curve (b) shown in fig. 2 the laser light was circularly (o ÷) polarized. Similar measurements have been performed using linearly polarized light. The result of the latter measurements was essentially the same as that shown in fig. 2 curve (b). In a quantitative discussion of the result the hyperfine splitting of the Na D 2 - line must be considered. Due to the nuclear spin of 23Na (J = 3) the 2S_~ground level is split into two levels with F 1,2 whereas the 2p~ level is split into four closely spaced levels with F = 0, 1,2, 3. In our experiment the laser was tuned to the hyperfine transition 2S_~,F = 2 ~ 2p~, F = 3. Statistically s of the atoms in the beam are in the 2S~, F = 2 level. This implies that about 63 percent of
Curve b
-4
-3
-2
- 1
0
1
2
3
,~
[mm]
Fig. 2. Typical results of the measurements. Curve (a): shape of the undeflected atomic beam. Curve (b): shape of the atomic beam with deflection by the resonance radiation pressure. 338
Volume 5, number 5
OPTICS COMMUNICATIONS
the atoms should be deflected by multiple excitations with the laser light. If the linewidth of the laser is comparable to the hyperfine splitting between the F = 3 and F = 2 levels of 2p_~ only a small deflection can be expected. In this case {he transition 2S_~,F = 2 ~ 2p], F = 2 is also excited and the atoms are pumped from the F = 2 to the F = 1 hyperfine level of 2S, since the 2p~, F = 2 can also decay into the 2S½, F = 1 level. These atoms are lost for further excitations and the average number of excitations for each atom will be very low. We will see below that in our experiment the average number of excitations per atom was about 60. From this one must conclude that the linewidth of the laser is small enough to excite the F = 3 and F = 2 hyperfine levels of 2p} separately. Since the hyperfine splitting between these levels is about 58 MHz [7] our laser linewidth must be smaller than 50 MHz. The signal shown in curve (b) of fig. 2 contains contributions from deflected and undeflected atoms. In order to determine the portion of the deflected atoms a fraction of curve (a), fig. 2 representing the undeflec-
August 1972
ted part of the beam must be subtracted from curve (b). This fraction was determined assuming that the left wing of curve (b) is influenced only by the undeflected atoms. The result of this analysis is shown in fig. 3. It follows that the ratio of the deflected atoms to the undeflected atoms is on the order of 0.4. This result deviates from the value of 1.67 expected theoretically. Several possible explanations may be offered for this discrepancy. (i) The short time frequency variations of the dye laser may cause that the average number of deflected atoms is reduced. (ii) In the atomic and laser beam interaction region the diameter of the laser beam was approximately 2 mm. The length of the collimator slit of the atomic beam was about 2 mm. Therefore the interaction region was longer for the atoms passing through the middle of the slit than for those passing through the two ends, causing a reduction in the average deflection. (iii) If the laser beam is not precisely perpendicular to the atomic beam direction the effective Doppler width of the atomic beam is increased so that it may be larger than the linewidth of the laser. This implies that only those atoms with
51 r
Curve e
//o " ° "~o o
\ o
Curve b
B/ H f ~ - - ~
~/~
\
/
\
p
-4
-3
-2
~
-1
Ok%
0"~0~
0
1
2
3
4
[mm]
Fig. 3. The measured atomic beam profile with deflection [curve (b) of fig. 2] as a superposition of the deflected [curve (b)] and undeflected part [curve (a)] of the beam.
339
Volume 5, number 5
OPTICS COMMUNICATIONS
the correct velocity component will be excited by the incident laser light. For example a deviation of 2 degrees from the perpendicular would be sufficient to explain the discrepancy observed in our experiment. In order to obtain the average number of excitations for each atom, the deflected beam profile was calculated using the velocity distribution o f the atoms and a trapezoidal shape for the undeflected beam. A best fit for curve (b) o f fig. 3 was obtained under the assumption that each atom was excited on an average of 60 times. This is in good agreement with the result one would expect from the average time the atoms spend in the interaction region with the laser beam.
340
August 1972
References [ 1] [2] [3] [4] [5] [6]
O.R. Frisch, Z. Physik ~6 (1933) 42, J.L. Picqu6 and J.L. Vialle, Opt. Commun. 5 (1972) 402. A. Ashkin, Phys. Rev. Letters 25 (1970) 1321. W. Hartig, R. Schieder and 14. Walther, to be published. M. Hercher and H.A. Pike, Opt. Commun. 3 (1971) 65. H. Walther and J.L. Hall, Appl. Phys. Letters 17 (1970) 239. [7] G. Copley, B.P. Kibble and G.W. Series, J. Phys. B 1 (1968) 724.
OPTICS COMMUNICATIONS
ATOMIC BEAM DEFLECTION
BY THE LIGHT OF A TUNABLE
August 1972
DYE LASER
R. SCHIEDER, H. WALTHER and L. Wt3STE 1. Physikalisches Institut der UniversitiitK61n, Cologne, Germany Received 24 May 1972 The deflection of a sodium atomic beam by the radiation pressure of the light of a cw dye laser was investigated. From the deflection observed it is deduced that the linear momentum transferred corresponds to an average of 60 excitations per atom. The linewidth of the dye laser used for the measurements was smaller than 50 MHz.
The absorption and re-emission of resonance radiation by atoms is coupled with an exchange of linear momentum between the atoms and the radiation field. The linear m o m e n t u m of a photon of visible light is rather small and is o f no importance in the usual resonance experiment. However in certain experimental arrangements the transfer of linear m o m e n t u m can be observed. Frisch [1 ] * showed that a sharply collimated sodium atomic beam is deflected if the atoms are irradiated b y a sodium discharge lamp. But in this experiment only one third of the atoms of the beam were
oc
I Recorder
Amplifier
v I
\ Langmuir - Taylor - Detector Vo-Atomic Beam
t
Tunable cw Dye Laser I
Laser Beam Atomic Beam Oven
I
L
Fig. 1. Experimental setup.
excited and therefore the deflection observed was rather small. A much larger deflection can be expected if a tunable laser is used in order to excite the atoms. The laser is sufficiently intense so that the 3 2p, and 3 2P3 levels of Na I can be saturated. Therefore, the n u m b e r o f excitations of each atom, which may be on the order o f 100 or more, is determined by the interaction time between the atomic beam and the light beam. Furthermore it has been shown b y Ashkin [3] that for a convergent radiation field which is intense enough to produce saturation the radiation pressure is equivalent to the force in a central field in which atoms follow circular orbits. This enables one to velocity analyse the atomic beam. In this communication we describe an experiment in which the deflection of a sodium atomic beam by the radiation field of a cw dye laser was investigated. The experimental setup is shown in fig. 1. The sodium beam was well collimated with a collimation ratio o f 1 : 500. This implies a Doppler width of 3 MHz when the atoms are viewed at right angles to the beam. The absorption width of the beam was therefore mainly given b y the natural linewidth o f the excited 2p levels which is about 10 MHz. The atoms were detected using a Langmuir - Taylor detector. The signal was amplified and plotted by an x - y recorder. To measure the profile o f the atomic beam the detector could be moved in a direction perpendicular to the beam as shown in fig. 1. Using a helix potentiometer the posi* A more ref'med experiment:of this kind was recently performed by Picqu6 and Vialle [2]. 337
Volume 5, number 5
OPTICS COMMUNICATIONS
tion of the detector was coupled to the x axis of the recorder. Details of the cw dye laser dsed in our experiment will be described elsewhere [4]. The laser configuration was similar to that published by Hercher and Pike [5]. Single mode operation of the laser was achieved by the use of a birefringent filter made of a KDP crystal with a length of 6 cm [6] or by an intracavity etalon. The continuous tuning of the laser was performed by changing the cavity length. The output power of the laser was about 10 mW. The distance between laser interaction region and atomic beam detector was about 50 cm. Fig. 2 shows typical results obtained in our measurements. The signal current is plotted versus the position of the detector. At the zero point the slit of the atomic beam oven, the collimator, and the detector wire are all on a straight line. Curve (a) of fig. 2 was measured without laser excitation. Curve (b) was obtained wher~the dye laser was tuned to one hyperfine component of the Na D 2 line. Due to the transfer of linear momentum the center of the atomic beam is shifted in the direction of the laser beam.
August 1972
Curve (b) represents the average of 3 different measurements for the same experimental conditions. The fluctuation observed in an individual measurement was on the order of 5% and seems to be due to short time frequency variations of the laser. These frequency variations are mainly caused by mechanical instabilities of the laser cavity. The duration of one measurement was about 20 sec, the time constant of the recording system eas aproximately 0.2 sec. For curve (b) shown in fig. 2 the laser light was circularly (o ÷) polarized. Similar measurements have been performed using linearly polarized light. The result of the latter measurements was essentially the same as that shown in fig. 2 curve (b). In a quantitative discussion of the result the hyperfine splitting of the Na D 2 - line must be considered. Due to the nuclear spin of 23Na (J = 3) the 2S_~ground level is split into two levels with F 1,2 whereas the 2p~ level is split into four closely spaced levels with F = 0, 1,2, 3. In our experiment the laser was tuned to the hyperfine transition 2S_~,F = 2 ~ 2p~, F = 3. Statistically s of the atoms in the beam are in the 2S~, F = 2 level. This implies that about 63 percent of
Curve b
-4
-3
-2
- 1
0
1
2
3
,~
[mm]
Fig. 2. Typical results of the measurements. Curve (a): shape of the undeflected atomic beam. Curve (b): shape of the atomic beam with deflection by the resonance radiation pressure. 338
Volume 5, number 5
OPTICS COMMUNICATIONS
the atoms should be deflected by multiple excitations with the laser light. If the linewidth of the laser is comparable to the hyperfine splitting between the F = 3 and F = 2 levels of 2p_~ only a small deflection can be expected. In this case {he transition 2S_~,F = 2 ~ 2p], F = 2 is also excited and the atoms are pumped from the F = 2 to the F = 1 hyperfine level of 2S, since the 2p~, F = 2 can also decay into the 2S½, F = 1 level. These atoms are lost for further excitations and the average number of excitations for each atom will be very low. We will see below that in our experiment the average number of excitations per atom was about 60. From this one must conclude that the linewidth of the laser is small enough to excite the F = 3 and F = 2 hyperfine levels of 2p} separately. Since the hyperfine splitting between these levels is about 58 MHz [7] our laser linewidth must be smaller than 50 MHz. The signal shown in curve (b) of fig. 2 contains contributions from deflected and undeflected atoms. In order to determine the portion of the deflected atoms a fraction of curve (a), fig. 2 representing the undeflec-
August 1972
ted part of the beam must be subtracted from curve (b). This fraction was determined assuming that the left wing of curve (b) is influenced only by the undeflected atoms. The result of this analysis is shown in fig. 3. It follows that the ratio of the deflected atoms to the undeflected atoms is on the order of 0.4. This result deviates from the value of 1.67 expected theoretically. Several possible explanations may be offered for this discrepancy. (i) The short time frequency variations of the dye laser may cause that the average number of deflected atoms is reduced. (ii) In the atomic and laser beam interaction region the diameter of the laser beam was approximately 2 mm. The length of the collimator slit of the atomic beam was about 2 mm. Therefore the interaction region was longer for the atoms passing through the middle of the slit than for those passing through the two ends, causing a reduction in the average deflection. (iii) If the laser beam is not precisely perpendicular to the atomic beam direction the effective Doppler width of the atomic beam is increased so that it may be larger than the linewidth of the laser. This implies that only those atoms with
51 r
Curve e
//o " ° "~o o
\ o
Curve b
B/ H f ~ - - ~
~/~
\
/
\
p
-4
-3
-2
~
-1
Ok%
0"~0~
0
1
2
3
4
[mm]
Fig. 3. The measured atomic beam profile with deflection [curve (b) of fig. 2] as a superposition of the deflected [curve (b)] and undeflected part [curve (a)] of the beam.
339
Volume 5, number 5
OPTICS COMMUNICATIONS
the correct velocity component will be excited by the incident laser light. For example a deviation of 2 degrees from the perpendicular would be sufficient to explain the discrepancy observed in our experiment. In order to obtain the average number of excitations for each atom, the deflected beam profile was calculated using the velocity distribution o f the atoms and a trapezoidal shape for the undeflected beam. A best fit for curve (b) o f fig. 3 was obtained under the assumption that each atom was excited on an average of 60 times. This is in good agreement with the result one would expect from the average time the atoms spend in the interaction region with the laser beam.
340
August 1972
References [ 1] [2] [3] [4] [5] [6]
O.R. Frisch, Z. Physik ~6 (1933) 42, J.L. Picqu6 and J.L. Vialle, Opt. Commun. 5 (1972) 402. A. Ashkin, Phys. Rev. Letters 25 (1970) 1321. W. Hartig, R. Schieder and 14. Walther, to be published. M. Hercher and H.A. Pike, Opt. Commun. 3 (1971) 65. H. Walther and J.L. Hall, Appl. Phys. Letters 17 (1970) 239. [7] G. Copley, B.P. Kibble and G.W. Series, J. Phys. B 1 (1968) 724.