Superfluid ${}^4\mathrm{He}$ interferometer operating near $2\mathrm{K}$

We report the observation of quantum interference in superfluid ${}^4\mathrm{He}$. The interferometer, an analog of a dc-superconducting quantum interference device (SQUID), employs a recently reported phenomenon wherein superfluid ${}^4\mathrm{He}$ exhibits Josephson frequency oscillations in an array of submicron apertures. An interference pattern is generated by reorienting the loop of the superfluid “SQUID” with respect to the Earth’s rotation vector, thereby varying the rotation flux in the loop. The experiment is performed at $2\mathrm{K}$, a temperature 2000 times higher than previously achieved with superfluid ${}^3\mathrm{He}$. We find that the interference exists not only when the aperture array current-phase relation is a sinusoidal function characteristic of the Josephson effect, but also at lower temperatures where it is linear and oscillations occur by phase slips. The modest requirements for the interferometer ($2\mathrm{K}$ cryogenics and fabrication of apertures at the level of $100\mathrm{nm}$) and its potential resolution suggest that, when engineering challenges such as vibration isolation are met, superfluid ${}^4\mathrm{He}$ interferometers could become important scientific probes.

Figure 1

Superfluid ${}^4\mathrm{He}$ interferometer schematic and equivalent circuit. (a) A sketch of the ${}^4\mathrm{He}$ interferometer. The x’s indicate the position of the two aperture arrays. The unshaded regions are filled with superfluid ${}^4\mathrm{He}$. The upper chamber is closed on the top by a flexible metalized diaphragm which serves both as a microphone to detect the Josephson oscillations and also as a pressure pump to maintain chemical potential differences across the arrays. Pressure is created by application of an electrostatic force between the diaphragm and electrode. The resistor R is a heater which can contribute to the chemical potential difference. Above the electrode is a superconducting pancake coil (not shown) which is part of a SQUID-based sensor (Ref. 11) used to detect the motion of the diaphragm. The interferometer is inside a can (outer shaded border) with the superfluid ${}^4\mathrm{He}$ inside pressurized to roughly half an atmosphere. The can is immersed in a conventional dewar filled with helium whose temperature T is feedback regulated (Ref. 12) with a stability of $\sim 50\mathrm{nK}$ just below its superfluid transition temperature ${\mathrm{T}}_{\lambda }=2.17\mathrm{K}$. Since the can is pressurized, the value of ${\mathrm{T}}_{\lambda }$ for the liquid inside it is slightly lower than that of the bath—this makes it easier to stabilize T very close to the ${\mathrm{T}}_{\lambda }$ of the can. A sketch of the equivalent interferometer topology, emphasizing the analogy with the dc-SQUID, is shown in (b).

Figure 2

Modulation of the amplitude of Josephson frequency oscillations as a function of rotation flux in a superfluid ${}^4\mathrm{He}$ matter-wave interferometer. The Earth is the source of rotation flux. The flux magnitude is varied by reorienting the interferometer with respect to the North-South axis of the Earth. The measured data is shown by the symbols. The solid lines are fits of the data to Eq. (4), strikingly showing that the measured data follows the predicted expression throughout the temperature range investigated. From top to bottom, the modulation curves were taken at temperatures $T_{\lambda }-T=12$, 7.0, 4.0, 3.0, 2.0, 1.5, 0.9, 0.6, 0.4, and $0.3\mathrm{mK}$.