Breaking the Superfluid Speed Limit in a Fermionic Condensate
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LETTERS PUBLISHED ONLINE: 18 JULY 2016 | DOI: 10.1038/NPHYS3813 Breaking the superfluid speed limit in a fermionic condensate D. I. Bradley, S. N. Fisher†, A. M. Guénault, R. P. Haley*, C. R. Lawson, G. R. Pickett, R. Schanen, M. Skyba, V. Tsepelin and D. E. Zmeev Coherent condensates appear as emergent phenomena in many a 1–8 systems . They share the characteristic feature of an energy Inner cell gap separating the lowest excitations from the condensate Cu refrigerant ground state. This implies that a scattering object, moving through the system with high enough velocity for the excitation Outer cell spectrum in the scatterer frame to become gapless, can create (muted colours) excitations at no energy cost, initiating the breakdown of the condensate1,9–13—the well-known Landau velocity9. Whereas, 3 Vibrating wire for the neutral fermionic superfluid He-B in the T 0 limit, thermometer flow around an oscillating body displays a very clearD critical velocity for the onset of dissipation12,13, here we show that for Detection coils uniform linear motion there is no discontinuity whatsoever in the dissipation as the Landau critical velocity is passed and Moving wire exceeded. Given the importance of the Landau velocity for our B (73 mT) understanding of superfluidity, this result is unexpected, with Quartz tuning fork implications for dissipative eects of moving objects in all thermometer coherent condensate systems. The Landau critical velocity marks the minimum velocity at which an object moving through a condensate can generate b excitations with zero energy cost9. In the frame of the object, moving at velocity v relative to the fluid, excitations of momentum p are shifted, by Galilean transformation, from energy E to (E − v·p). Superfluid 3He-B has a BCS dispersion curve1 with energy minima, D ∆ E at momenta pF. Therefore, excitation generation should Vibrating wire begin as soon as one energy minimum reaches zero, that is, when thermometer ∆= the velocity reaches the Landau critical value, vL ≈ pF. We can investigate v in condensates in two limiting regimes, L Detection coils that is, for the motion of microscopic objects (for example, ions) or for that of macroscopic objects. For ions, the critical velocity has Moving wire been observed in superfluid 4He at the expected value of ≈46 m s−1 at 25 bar (ref. 10) (at lower pressures vortex nucleation sets in at Quartz tuning fork lower velocities and the critical velocity is difficult to measure), and thermometer confirmed in superfluid 3He-B at 18 bar as being consistent with the expected ≈67 mm s−1 value11. For macroscopic objects, the onset of 4 | The experimental cell. extra dissipation at vL in superfluid He cannot be observed since Figure 1 a, View of the nested demagnetization damping from vorticity becomes prohibitive at much lower veloci- cooling cell (outer cell muted). The adiabatic demagnetization refrigerant ties. However, while macroscopic objects can be readily accelerated comprises high-purity copper plates coated in sintered silver for thermal at the lowest temperatures to the much lower critical velocities in contact and immersed in the superfluid 3He sample filling the cell that is superfluid 3He, the experimental picture is not so straightforward. cooled to ≈140 µK. b, The moving-wire ‘goalpost’ (crossbar width 9 mm) is In superfluid 3He, oscillating macroscopic objects do indeed driven perpendicular to its plane through the 3He and can move over a 12 = show a sudden increase in damping , but at a velocity of only ≈vL 3, horizontal distance of 6 mm before touching the inner cell wall. Its arising from the emission of quasiparticle excitations from the position is sensed by detection coils in the outer cell. The temperature, or pumping of surface excitations driven by the reciprocating motion13. thermal quasiparticle density, is monitored by vibrating wire and quartz Although this mechanism does not involve bulk pair-breaking, it tuning fork resonators. We calibrate the position of the wire by moving it has created the impression that a Landau critical velocity has indeed until it is stopped by the cell wall in each direction (see Methods) providing been confirmed in 3He, which is not the case. the two fixed points needed to determine the absolute position. The What should we expect for uniform motion? The textbook pre- temperature rise caused by the dissipation is monitored by the vibrating diction suggests that at vL all details of the process become irrelevant. wire and quartz tuning fork thermometers. Department of Physics, Lancaster University, Lancaster LA1 4YB, UK. †Deceased. *e-mail: [email protected] NATURE PHYSICS | VOL 12 | NOVEMBER 2016 | www.nature.com/naturephysics 1017 © ƐƎƏƖɥMacmillan Publishers LimitedƦɥ/13ɥ.$ɥ/1(-%#1ɥ341#. All rights reservedƥ LETTERS NATURE PHYSICS DOI: 10.1038/NPHYS3813 a 100 a.c. sweep 2 Velocity = 15.4 mm s−1 (150−177 μK) ‘Naive’ expectation 80 for the d.c. dissipation 60 One-third Landau velocity, ν ∼ −1 Landau velocity, L, 27 mm s 1 ν /3, ∼9 mm s−1 Force (nN) 40 L Position (mm) Thermal quasiparticle dissipation 20 0 0 0 10 20 30 40 50 60 050100 150 Velocity (mm s−1) Time (ms) b 60 160 Surface quasiparticle d.c. stroke escape during acceleration 40 (150−157μK) and deceleration 158 Force (nN) 20 K) δT = 6.20 μK μ 156 0 0 10 20 30 40 50 60 Velocity (mm s−1) Temperature ( 154 Figure 3 | The damping force as a function of velocity for oscillatory (a.c.) motion compared with steady (d.c.) motion. ∆= 152 The Landau velocity, pF, is marked and the region above the Landau velocity tinted red for clarity. 012a, The measured dissipation for oscillatory (a.c.) motion shows a very = Time (s) sudden rise when the peak velocity reaches vL 3. The small dissipation arising from the residual thermal gas of quasiparticles is also indicated. On Figure 2 | The sustained d.c. velocity method and measurement. The the basis of the observations for ionic motion in both superfluid 3He and upper panel shows the very accurate linear strokeof the moving wire, 4He, we might naively expect the dissipation for steady motion to rise sustained over a distance of 2 mm, with blue bands indicating the periods rapidly above the Landau velocity, as indicated10–12. b, However, our of initial acceleration and of final deceleration. The lower panel shows the measurements for the steady (d.c.) motion at a similar temperature show associated temperature response, with the period of the linear motion only a slow rise (arising from the same escape of local excitations that shown by the red band. The line shape is consistent with a burst of leads to the dissipation in the oscillatory motion, see text), but no sudden dissipation during the initial acceleration and a second during the final increase in the damping force, even as the Landau critical velocity of deceleration (see Methods). (In principle, we could infer the drag force vL D∆=pF is passed (ringed). We see this behaviour independently of from the feedback current needed to maintain the uniform motion of the temperature up to the highest velocities and temperatures at which we can wire. Unfortunately, the wire inertia dominates, and any contribution from measure, that is, ≈2.5vL and 190 µK. (The cell gradually warms while the the liquid is negligible.) data are taken as indicated by the temperature ranges in the figure. This is a small eect for the d.c. data of b, but the large dissipation of the higher Condensate breakdown becomes inevitable; the constituent Cooper velocity a.c. data of a causes a significant temperature rise.) pairs separate; and the properties rapidly approach those of the normal liquid. Under our experimental conditions, this should be Figure3 shows the velocity dependence of the damping force on spectacular, since the damping force in the normal fluid is some five the moving wire for both a.c. and d.c. motion at around 150 µK. orders of magnitude higher than that of the superfluid. Despite this The oscillatory motion shows the expected rapid rise starting at = expectation that at vL the dissipation should suddenly increase to approximately vL 3. However, the d.c. results are strikingly different, = very high values, here we show that in fact no discontinuity at all is showing only a very slow rise, again starting at ≈vL 3, but with no = observed in the damping as vL is exceeded. discontinuity whatsoever on passing either vL 3 or vL. The measurements are made in 3He-B at zero pressure, between A hint to the processes involved comes from the oscillatory 140 and 190 µK (in the quasiparticle ballistic limit) in the cooling behaviour, for which we have a reasonable understanding. We use a cell shown in Fig.1 (see Methods). The macroscopic `moving object' simple model13 where we assume a gas of quasiparticle states in the is a wire formed into a rectangular shape. We can move the wire region of depressed gap near the wire surface. The precise nature over a range of velocities in two ways: with a single stroke of steady of these states is complex since the order parameter near the wall uniform velocity; or by oscillation at 66 Hz, the mechanical resonant has directional structure depending on the scattering nature of the frequency. For oscillatory motion the damping force as a function surface. The states may have Majorana and Andreev bound-state of velocity is directly measured from the resonance. For steady properties15. However, in the plane of the surface we assume these motion we infer the damping from the thermal response, as shown states are mobile and have a gapless dispersion curve.