Physica B 284}288 (2000) 287}288
Rotation measurements with a super#uid He gyrometer
Yury Mukharsky *, Olivier Avenel , ED ric Varoquaux
CEA-DRECAM, Service de Physique de l+E! tat Condense& , Centre d+E! tudes de Saclay, 91191 Gif-sur-Yvette Cedex, France
CNRS-Laboratoire de Physique des Solides, BaL t. 510, Universite& Paris-Sud, 91405 Orsay, France
Abstract
We report the "rst precision rotation measurements with a super#uid He gyrometer. This device operates in the
Josephson non-hysteretic regime. Its practical sensitivity could ultimately compare with those of ring lasers and atom
interferometers. 2000 Elsevier Science B.V. All rights reserved.
Keywords: He super#uid; Josephson e!ect; Rotation measurements
The sensitivity of super#uid gyrometers is limited in
He by intrinsic critical velocity #uctuations and one
cannot be very optimistic about their future [1,2]. For
the same device operated in super#uid He there is no
such limitation as long as phase slips do not occur (i.e. in
the Josephson regime) and we "nd that the basic operation is also much simpler.
Our gyrometer is a miniature Helmholtz resonator
with a single micro-ori"ce (0.18 lm;2.8 lm) and, in
parallel, a 5.9 cm rotation pick-up loop made of a twoturn coil of 0.4 mm i.d. capillary. The plane of the loop of
oriented area A is a local vertical plane. The circulation
trapped in this loop by the Earth rotation "eld,
i "2X ) A, is varied by changing the orientation of the
V
=
cryostat about the vertical axis. This reorientation changes the phase bias across the ori"ce and also changes the
resonance frequency when the current}phase relationship departs from linearity [3].
A typical curve of the resonance frequency versus trapped circulation normalized to the quantum of circulation
i is represented in Fig. 1. Maximum rotation sensitivity
is obtained when the gyrometer is biased in a region of
maximum slope. This slope is governed, in particular, by
the parallel path inductance and by the temperature. It
can be made arbitrarily large by tuning the device close
to the point where its response becomes hysteretic.
* Corresponding author.
E-mail address: [email protected] (Yu. Mukharsky)
At a "xed cryostat orientation, corresponding to
the operating point indicated by the arrow in Fig. 1, the
resonance frequency was tracked by monitoring the
phase di!erence between a small excitation at constant
frequency and the response signal of the resonator. The
time evolution of the deviation of the phase from its
average value is represented in the inset of Fig. 2 for an
observation period of 9 h.
The power spectrum of this error signal is plotted in
Fig. 2. The normalization of the power spectrum is
chosen so that rotations are referred to the axis perpendicular to the plane of the pick-up loop. The down-turn
at high frequency in Fig. 2 is due to electronic "ltering.
This "gure represents the useful sensitivity of the
gyrometer, 14;10\ (rad/s)/(Hz, an improvement of
nearly three orders of magnitude over the He gyrometer.
As was the case with super#uid He, we usually observe, when cooling through ¹ , a non-zero circulation
bias not accounted for by the Earth rotation. This bias
has been subtracted from the data shown in Fig. 1. In
He, the bias was easily changed by tapping gently on the
cryostat. Somewhat surprisingly, super#uid He is far
less sensitive to mechanical disturbances. However, sudden changes of the bias have been recorded occasionally
with no apparent cause. Also, at times, the system has
been observed to switch to a di!erent current}phase
relationship [3], again with no apparent cause. This
somewhat erratic behavior is under investigation. It is in
particular thought that stabilizing the texture of the
n vector in the cell should prevent changes from a current}phase determination to another.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 6 1 9 - 8
288
Yu. Mukharsky et al. / Physica B 284}288 (2000) 287}288
Fig. 1. Resonance frequency versus trapped circulation at 0.2
bar and 0.614¹ in super#uid He}B. The Q factor of the
resonator is appoximately 100. The horizontal line represents
the large signal resonance frequency [3].
We believe that the present sensitivity is essentially
limited by rotational noise in the cryostat environment.
The He temperature was stabilized with an LCMN
thermometer to within 1 lK for periods of several days.
Temperature drifts in the cold parts of the experimental
set-up do not seem to be a problem in these measurements. Temperature drifts at room temperature a!ect the
air legs on which the cryostat is suspended, causing small
rotations of the whole set-up.
These experiments are preliminary and much room is
left for improvement. A gain by two orders of magnitude
can reasonably be expected. Such a gain would make this
device as sensitive as state of the art ring lasers and atom
interferometers which can presently resolve 13 and
8;10\ (rad/s)/(Hz, respectively [4].
Fig. 2. Smoothed power spectrum of the drift signal of the
gyrometer biased at the operating point shown in Fig. 1 recorded over a 9 h period. The cut-o! at high frequencies is due to
electronic "ltering. The inset displays the actual drift versus
time. The vertical axis on the right shows the corresponding
reading dX of the gyrometer in units of X "X ) A/A, the e!ect
#
=
of the Earth rotation at the latitude of Saclay.
References
[1] O. Avenel, P. Hakonen, E. Varoquaux, J. Low Temp. Phys.
110 (1997) 709, and references therein.
[2] Yu. Mukharsky, O. Avenel, E. Varoquaux, J. Low Temp.
Phys. 113 (1998) 915.
[3] O. Avenel, Yu. Mukharsky, E. Varoquaux, in these Proceedings (LT-22), Physica B 284}288 (2000).
[4] G.E. Stedman, M.A. Kasevich, APS March Meeting, Atlanta, USA, 1999.