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Optical observations on3He-B superfluid
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Physica B 194-196 (1994) 757-758 North-Holland
Optical observations on 3He-B superfluid J. P. O. Ruutu, H. Alles, A. V. Babkin, G. M. Kira,* A. J. Manninen, J. P. Pekola,* and O. V. Lounasmaa Low Temperature Laboratory, Heisinki University of Technology, 02150 Espoo, Finland
Optical observations on the free surface of superfluid 3He-B have been made usin~ an interferometer. The change in viscosity was seen at the superfluid transition, and the fountain effect in He-B was observed directly. The equilibrium average density of vortices was ascertained by looking at the reflection of light from the free surface of the rotating superfluid. Heat leaks due to illumination were investigated. Our results will be illustrated by a video film showing the similarities and differences between the superfluid and the normal liquid.
Before our experiments it had not been possible to reach temperatures low enough to study superfluid 3He optically [1,2].The main problem was thermal radiation through conventionally used windows that connected the sample cell optically to room temperature. We have removed this difficulty by employing fibers instead of windows and by selecting carefully the optical components [3]. Using the new techniques, we built an interferometer (Fig. 1) inside our rotating nuclear demagnetization cryostat ROTA 2 for studying the shape of the free surface of superfluid 3He [4]. A He-Nelaser LA produces a light beam through a singlemode optical fiber F inside the vacuum jacket VJ of the cryostat. Lens BE expands the parallel beam to a diameter of 2 mm. The light is then guided through a beam splitter BS, mirrors M1 and M2, and a pair of lenses L1 and L2 to the optical cell OC. Main part of the beam passes through upper window UW and reference window RW of the cell and is reflected by mirror M3 out of the coldest part of the cryostat. Only about 0.01% of the illuminating beam is reflected from the surface of liquid helium HE and about 1% from the antireflection-coated RW. These beams interfere with each other while they return up to BS and pass through it. The image beam is next guided through the fiber bundle FB, which consists of 30000 single optical fibers. Finally, the image is reflected by mirror M4 and it then passes through window W and lens L3 to a CCD-camera that is connected to a video recorder and a computer. The power of the beam is on the order of 60 gW in the sample cell. Continuous illumination causes a heat leak of 2 gW into the nuclear stage, i.e., 3% of the light is absorbed. The main heat load comes
probably from secondary reflections and scattered light, because the measured heat absorption of the fused silica windows in the optical cell is only about 0.15%. For this reason the sample is illuminated typically using 50 ms pulses every 5 seconds, so the average heat load is about 20 nW. ~
kl
1 -
-,-
I,w
-
1
- , 7 - - 2 - - - - ' - - - - -
Fig. 1. The interferometer. For explanations, see text. Lateral motion of the image allowed us to detect the superfluid transition. We rotated the slightly tilted cryostat and monitored the light beam reflected from the liquid surface. When the 3He-liquid is in the superfluid state, gravity determines the ori-
* Present address: Department of Physics, University of Jyv~iskyla,P.O. Box 35, 40351 Jyv~iskyl~i,Finland. 0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved S S D I 0921-4526(93)E0958-J
158
~2 = 2.1 rad/s (a)
ii
f2
0 rad/s
....
f2 = 2.0 rad/s
f2 =2.3 rad/s
f2
2.6 radls
(b)
Figure 2. Focusing of light reflected from the surface of (a) normal liquid and (b) superfluid 3He. The interference pattern can be seen shrinking to its minimum at about 2.3 rad/s. entation of the surface owing to the low viscosity. The surface precesses in the coordinate system rotating with the cryostat; this can be seen as lateral motion of the reflected beam in the camera. When the sample is warmed above the critical temperature Tc, the SHe-liquid becomes very viscous and begins to move with the walls of the cell. The surface stays at rest in the rotating coordinate system and the precession stops. This can be seen clearly in the image. The shape of the surface of a classical fluid or of a superfluid with the equilibrium number of vortices is determined, under rotation, by the relation z( r) = .(2 2 r 2 / 2 g ,
(1)
where I2 is the angular velocity. The surface thus acts as a parabolic mirror for the reflected light. At a certain speed the reflection from the surface is focused to a single point. This was calculated to happen, using the geometry of our system, at £2 = 2.1 + 0.1 rad/s. We measured this focusing effect in the normal state and in the superfluid down to the minimum temperature of T / T c ~ 0.75. In both cases the focusing happened at the angular velocity ,(2 = 2.25 + 0.10 rad/s (Fig. 2). Therefore, the superflttid had the same surface profile as the normal liquid. This means that the equilibrium number of vortices was present, because a superfluid can only rotate like a solid body when vortices are generated in the liquid. We also saw optically the fountain effect in a thin layer of 3He-B. A superleak was not needed because
the viscous normal component was immobile on the bottom of the cell. We warmed the illuminated area using a long light pulse and saw interference fringes shrinking towards their center. This meant that the thickness of the fiquid was increasing. The explanation is that the superfluid component moved to the illuminated area, thereby trying to reduce the temperature d~fference. Typically, this increase was about 10 gm during a few seconds, which is about 300 times more than the effect of thermal expansion [5]. This movement stopped, when the sample warmed above the critical temperature, and the surface started to relax back indicating a decrease in its thickness. This work was supported by the Academy of Finland.
REFERENCES 1. P.L. Marston and W. M. Fairbank, Phys. Rev. Lett. 39, 1208 (1977). 2. K.-P. Miiller and D. Haarer, Phys. Rev. Lett. 66, 2344 (1991). 3. A.J. Manninen, H. Alles, A. V Babkin, and J. P. Pekola, Physica B 178 (1992 p. ? 2. 4. A.J. Manninen, J. P. Pekola, G M. K a, J. P. Ruutu, A. V. Babkin, H. Alles, and O. V'. Lounasmaa, Phys. Rev. Lett. 69, 2392 (1992). 5. G.W. Swift and R. E. Packard, J. Low Temp. Phys. 43, 517 (1981).
Physica B 194-196 (1994) 757-758 North-Holland
Optical observations on 3He-B superfluid J. P. O. Ruutu, H. Alles, A. V. Babkin, G. M. Kira,* A. J. Manninen, J. P. Pekola,* and O. V. Lounasmaa Low Temperature Laboratory, Heisinki University of Technology, 02150 Espoo, Finland
Optical observations on the free surface of superfluid 3He-B have been made usin~ an interferometer. The change in viscosity was seen at the superfluid transition, and the fountain effect in He-B was observed directly. The equilibrium average density of vortices was ascertained by looking at the reflection of light from the free surface of the rotating superfluid. Heat leaks due to illumination were investigated. Our results will be illustrated by a video film showing the similarities and differences between the superfluid and the normal liquid.
Before our experiments it had not been possible to reach temperatures low enough to study superfluid 3He optically [1,2].The main problem was thermal radiation through conventionally used windows that connected the sample cell optically to room temperature. We have removed this difficulty by employing fibers instead of windows and by selecting carefully the optical components [3]. Using the new techniques, we built an interferometer (Fig. 1) inside our rotating nuclear demagnetization cryostat ROTA 2 for studying the shape of the free surface of superfluid 3He [4]. A He-Nelaser LA produces a light beam through a singlemode optical fiber F inside the vacuum jacket VJ of the cryostat. Lens BE expands the parallel beam to a diameter of 2 mm. The light is then guided through a beam splitter BS, mirrors M1 and M2, and a pair of lenses L1 and L2 to the optical cell OC. Main part of the beam passes through upper window UW and reference window RW of the cell and is reflected by mirror M3 out of the coldest part of the cryostat. Only about 0.01% of the illuminating beam is reflected from the surface of liquid helium HE and about 1% from the antireflection-coated RW. These beams interfere with each other while they return up to BS and pass through it. The image beam is next guided through the fiber bundle FB, which consists of 30000 single optical fibers. Finally, the image is reflected by mirror M4 and it then passes through window W and lens L3 to a CCD-camera that is connected to a video recorder and a computer. The power of the beam is on the order of 60 gW in the sample cell. Continuous illumination causes a heat leak of 2 gW into the nuclear stage, i.e., 3% of the light is absorbed. The main heat load comes
probably from secondary reflections and scattered light, because the measured heat absorption of the fused silica windows in the optical cell is only about 0.15%. For this reason the sample is illuminated typically using 50 ms pulses every 5 seconds, so the average heat load is about 20 nW. ~
kl
1 -
-,-
I,w
-
1
- , 7 - - 2 - - - - ' - - - - -
Fig. 1. The interferometer. For explanations, see text. Lateral motion of the image allowed us to detect the superfluid transition. We rotated the slightly tilted cryostat and monitored the light beam reflected from the liquid surface. When the 3He-liquid is in the superfluid state, gravity determines the ori-
* Present address: Department of Physics, University of Jyv~iskyla,P.O. Box 35, 40351 Jyv~iskyl~i,Finland. 0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved S S D I 0921-4526(93)E0958-J
158
~2 = 2.1 rad/s (a)
ii
f2
0 rad/s
....
f2 = 2.0 rad/s
f2 =2.3 rad/s
f2
2.6 radls
(b)
Figure 2. Focusing of light reflected from the surface of (a) normal liquid and (b) superfluid 3He. The interference pattern can be seen shrinking to its minimum at about 2.3 rad/s. entation of the surface owing to the low viscosity. The surface precesses in the coordinate system rotating with the cryostat; this can be seen as lateral motion of the reflected beam in the camera. When the sample is warmed above the critical temperature Tc, the SHe-liquid becomes very viscous and begins to move with the walls of the cell. The surface stays at rest in the rotating coordinate system and the precession stops. This can be seen clearly in the image. The shape of the surface of a classical fluid or of a superfluid with the equilibrium number of vortices is determined, under rotation, by the relation z( r) = .(2 2 r 2 / 2 g ,
(1)
where I2 is the angular velocity. The surface thus acts as a parabolic mirror for the reflected light. At a certain speed the reflection from the surface is focused to a single point. This was calculated to happen, using the geometry of our system, at £2 = 2.1 + 0.1 rad/s. We measured this focusing effect in the normal state and in the superfluid down to the minimum temperature of T / T c ~ 0.75. In both cases the focusing happened at the angular velocity ,(2 = 2.25 + 0.10 rad/s (Fig. 2). Therefore, the superflttid had the same surface profile as the normal liquid. This means that the equilibrium number of vortices was present, because a superfluid can only rotate like a solid body when vortices are generated in the liquid. We also saw optically the fountain effect in a thin layer of 3He-B. A superleak was not needed because
the viscous normal component was immobile on the bottom of the cell. We warmed the illuminated area using a long light pulse and saw interference fringes shrinking towards their center. This meant that the thickness of the fiquid was increasing. The explanation is that the superfluid component moved to the illuminated area, thereby trying to reduce the temperature d~fference. Typically, this increase was about 10 gm during a few seconds, which is about 300 times more than the effect of thermal expansion [5]. This movement stopped, when the sample warmed above the critical temperature, and the surface started to relax back indicating a decrease in its thickness. This work was supported by the Academy of Finland.
REFERENCES 1. P.L. Marston and W. M. Fairbank, Phys. Rev. Lett. 39, 1208 (1977). 2. K.-P. Miiller and D. Haarer, Phys. Rev. Lett. 66, 2344 (1991). 3. A.J. Manninen, H. Alles, A. V Babkin, and J. P. Pekola, Physica B 178 (1992 p. ? 2. 4. A.J. Manninen, J. P. Pekola, G M. K a, J. P. Ruutu, A. V. Babkin, H. Alles, and O. V'. Lounasmaa, Phys. Rev. Lett. 69, 2392 (1992). 5. G.W. Swift and R. E. Packard, J. Low Temp. Phys. 43, 517 (1981).