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Quasiparticle beams in superfluid3He-B at very low temperatures
PHYSICA
Physica B 194--196(1994) 789-790 North-Holland
Quasiparticle
Beams in Superfluid 3He-B at Very Low Temperatures
M. P. Enrico, S. N. Fisher, A. M. Gufinault, G. R. Pickett and K. Torizuka School of Physics and Materials, Lancaster University, Lancaster LA1 4YB, U.I~. We have been interested in developing source-experiment-detector type quasiparticle beam experiments in superfluid SHe for some time. Recently we have developed a new source and detector based on the quasiparticle equivalent of the blackbody radiator. We have already used these devices for a few simple experiments b u t m a n y more are possible, for example the direct observation of quasiparticle transmission across an A-B interface. The radiators are so sensitive that we can easily see the h e a t leak entering the liquid from the epoxy walls and also note that the leak from copper walls is more than 100 times smaller than from the epoxy.
The B-phase of superfluid 3He is described by an isotropic energy gap. This gives rise to an exponential temperature dependence of the number density of quasiparticle excitations. At the lowest accessible temperatures of 0.1T¢ the fraction of unpaired particles is about 10-6 of the whole and their m e a n free paths are of order kilometres. The ultradilute excitation gas is an ideal medium in which to perform experiments with quasiparticle beams. This allows us to study those transport phenomena of superfluid 3He-B that are entirely dominated by the excitations. Apart from the three essential components of a b e a m source, an experiment and a detector, two important criteria m u s t be m e t in order for an experiment of this nature to be successful. First, the temperature m u s t be low enough to ensure that the beams can propagate without significant loss due to scattering with background excitations. Secondly, the thermal contact between the helium and the copper refrigerant m u s t be sufficient to ensure a good beam resolution in spite of the power injected into the cell to produce the beam. In order to meet these criteria, the experimental cell is constructed in a nested configuration [1]. The inner cell contains the refrigerant and a small (H1 cc) free volume containing the actual experiment. The refrigerant takes the form of seventy or so copper plates with sintered silver
on both sides. As a result, approximately one in three quasipartides are absorbed on collision with the refrigerant. Quasipartide b e a m s can be produced using blackbody radiators. These consist of two vibrating wire resonators enclosed in a box with a small hole in one side as shown in figure 1. One of the vibrating wires is used as a heater which when driven increases the quasiparticle density within the radiator, causing a beam ofquasiparticles to emerge from the hole. The b e a m has a thermal distribution governed
Figure 1. A blackbody radiator.
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E0974-L
790 by the temperature T inside the radiator. The quasiparticle density and the temperature inside the radiator can be inferred from the measured damping A f2 of the second vibrating wire.
particle beam incident on the radiator hole. So far we have used two materials to construct the blackbody radiators and the inner cell walls. These are epoxy (Stycast-soakedpaper) and copper. It is believed that the epoxy walls never cool much below 10mK. The residual heat leak from the epoxy walls into the helium in the inner cell is found to be --~lpWcm -2. This places a significant restriction on the sensitivity of the radiator when used as a detector. The residual heat leak from copper walls was found to be too small to measure in a radiator with a 0.3mm diameter hole (the effect of the heat leak was indistinguishable from the intrinsic damping of the vibrating wire). We estimate an upper limit to the heat leak of lOfWcm -2.
Neglecting the intrinsic damping of the resonators, A f2 is related to the total power entering the radiator by [2] (~ = CAf2Tf~T, where C is a constant proportional to the area of the radiator hole and contains unknown geometrical factors relating to the vibrating wire. ET=A+kT is the m e a n quasiparticle energy. The calibration of the blackbody radiator amounts to measuring the constant C. This is done by measuring the damping A f2 as a function of the power Q~v applied to the heater wire. The effect of the heat leak from the walls of the radiator can be eliminated by subtracting from Af2TJET the value of the same quantity measured when no power is applied to the heater wire. This yields the width p a r a m e t e r W such that C2~p=CW. A typical calibration is shown in figure 2 for two pressures. The width p a r a m e t e r is found to be linear over more than six orders of magnitude in the applied power. This confirms that the excitation gas inside the radiator attains thermal equilibrium. Armed with this calibration, a m e a s u r e m e n t of W gives the power entering the radiator hole from either an internal source or from an external quasiI
I
I
I
I
I
I
I
I
I
I
t
I~
I, lo 0
C) P = 0 b a r j • P = 11.3 b a r , , ~ ~
References
15 2
16 4 _
164
oO
,r 15 s
-
r 16 2
r f i i J I f I 151 10 0 101 102 10 3
Applied power, Rap (pW) Figure 2. Calibration for the radiator.
To date, we have made use of the blackbody radiators as detectors in two important applications. We have measured the divergence of a beam of quasiparticles produced by a vibrating wire moving at supercritical velocities [2] and the Andreev reflection of a beam of quasiparticles from a superflow gradient (see [3] and the accompanying article). A future application is in measuring the Andreev reflection o f a quasiparticle beam incident on the A-B phase boundary. As shown in figure 2 the radiator is able to resolve a power dissipation of order lfW. Its sensitivity m a y be increased by several orders of magnitude by a corresponding decrease in the size of the radiator hole. This gives a wide scope for future application in the m e a s u r e m e n t of ultralow power dissipation.
1. D. I. Bradley, A. M. Gu6nault, V. Keith, C. J. Kennedy, I. E. Miller, S. G. Mussett, G. R. Pickett and W. P. Pratt, Jr., J. Low Temp. Phys. 57, (1984) 359. 2. S. N. Fisher, A. M. Gu6nault, C. J. Kennedy and G. R. Pickett, Phys. Rev. Lett. 69, (1992) 1073. 3. M. P. Enrico, S. N. Fisher, A. M. Gu6nault, G. R. Pickett and K. Torizuka, Phys. Rev. Lett. 70, (1993) 1846.
Physica B 194--196(1994) 789-790 North-Holland
Quasiparticle
Beams in Superfluid 3He-B at Very Low Temperatures
M. P. Enrico, S. N. Fisher, A. M. Gufinault, G. R. Pickett and K. Torizuka School of Physics and Materials, Lancaster University, Lancaster LA1 4YB, U.I~. We have been interested in developing source-experiment-detector type quasiparticle beam experiments in superfluid SHe for some time. Recently we have developed a new source and detector based on the quasiparticle equivalent of the blackbody radiator. We have already used these devices for a few simple experiments b u t m a n y more are possible, for example the direct observation of quasiparticle transmission across an A-B interface. The radiators are so sensitive that we can easily see the h e a t leak entering the liquid from the epoxy walls and also note that the leak from copper walls is more than 100 times smaller than from the epoxy.
The B-phase of superfluid 3He is described by an isotropic energy gap. This gives rise to an exponential temperature dependence of the number density of quasiparticle excitations. At the lowest accessible temperatures of 0.1T¢ the fraction of unpaired particles is about 10-6 of the whole and their m e a n free paths are of order kilometres. The ultradilute excitation gas is an ideal medium in which to perform experiments with quasiparticle beams. This allows us to study those transport phenomena of superfluid 3He-B that are entirely dominated by the excitations. Apart from the three essential components of a b e a m source, an experiment and a detector, two important criteria m u s t be m e t in order for an experiment of this nature to be successful. First, the temperature m u s t be low enough to ensure that the beams can propagate without significant loss due to scattering with background excitations. Secondly, the thermal contact between the helium and the copper refrigerant m u s t be sufficient to ensure a good beam resolution in spite of the power injected into the cell to produce the beam. In order to meet these criteria, the experimental cell is constructed in a nested configuration [1]. The inner cell contains the refrigerant and a small (H1 cc) free volume containing the actual experiment. The refrigerant takes the form of seventy or so copper plates with sintered silver
on both sides. As a result, approximately one in three quasipartides are absorbed on collision with the refrigerant. Quasipartide b e a m s can be produced using blackbody radiators. These consist of two vibrating wire resonators enclosed in a box with a small hole in one side as shown in figure 1. One of the vibrating wires is used as a heater which when driven increases the quasiparticle density within the radiator, causing a beam ofquasiparticles to emerge from the hole. The b e a m has a thermal distribution governed
Figure 1. A blackbody radiator.
0921-4526/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved SSDI 0921-4526(93)E0974-L
790 by the temperature T inside the radiator. The quasiparticle density and the temperature inside the radiator can be inferred from the measured damping A f2 of the second vibrating wire.
particle beam incident on the radiator hole. So far we have used two materials to construct the blackbody radiators and the inner cell walls. These are epoxy (Stycast-soakedpaper) and copper. It is believed that the epoxy walls never cool much below 10mK. The residual heat leak from the epoxy walls into the helium in the inner cell is found to be --~lpWcm -2. This places a significant restriction on the sensitivity of the radiator when used as a detector. The residual heat leak from copper walls was found to be too small to measure in a radiator with a 0.3mm diameter hole (the effect of the heat leak was indistinguishable from the intrinsic damping of the vibrating wire). We estimate an upper limit to the heat leak of lOfWcm -2.
Neglecting the intrinsic damping of the resonators, A f2 is related to the total power entering the radiator by [2] (~ = CAf2Tf~T, where C is a constant proportional to the area of the radiator hole and contains unknown geometrical factors relating to the vibrating wire. ET=A+kT is the m e a n quasiparticle energy. The calibration of the blackbody radiator amounts to measuring the constant C. This is done by measuring the damping A f2 as a function of the power Q~v applied to the heater wire. The effect of the heat leak from the walls of the radiator can be eliminated by subtracting from Af2TJET the value of the same quantity measured when no power is applied to the heater wire. This yields the width p a r a m e t e r W such that C2~p=CW. A typical calibration is shown in figure 2 for two pressures. The width p a r a m e t e r is found to be linear over more than six orders of magnitude in the applied power. This confirms that the excitation gas inside the radiator attains thermal equilibrium. Armed with this calibration, a m e a s u r e m e n t of W gives the power entering the radiator hole from either an internal source or from an external quasiI
I
I
I
I
I
I
I
I
I
I
t
I~
I, lo 0
C) P = 0 b a r j • P = 11.3 b a r , , ~ ~
References
15 2
16 4 _
164
oO
,r 15 s
-
r 16 2
r f i i J I f I 151 10 0 101 102 10 3
Applied power, Rap (pW) Figure 2. Calibration for the radiator.
To date, we have made use of the blackbody radiators as detectors in two important applications. We have measured the divergence of a beam of quasiparticles produced by a vibrating wire moving at supercritical velocities [2] and the Andreev reflection of a beam of quasiparticles from a superflow gradient (see [3] and the accompanying article). A future application is in measuring the Andreev reflection o f a quasiparticle beam incident on the A-B phase boundary. As shown in figure 2 the radiator is able to resolve a power dissipation of order lfW. Its sensitivity m a y be increased by several orders of magnitude by a corresponding decrease in the size of the radiator hole. This gives a wide scope for future application in the m e a s u r e m e n t of ultralow power dissipation.
1. D. I. Bradley, A. M. Gu6nault, V. Keith, C. J. Kennedy, I. E. Miller, S. G. Mussett, G. R. Pickett and W. P. Pratt, Jr., J. Low Temp. Phys. 57, (1984) 359. 2. S. N. Fisher, A. M. Gu6nault, C. J. Kennedy and G. R. Pickett, Phys. Rev. Lett. 69, (1992) 1073. 3. M. P. Enrico, S. N. Fisher, A. M. Gu6nault, G. R. Pickett and K. Torizuka, Phys. Rev. Lett. 70, (1993) 1846.