letters to nature ferometer is rotated at angular velocity I is modulated by an interferometer should evolve according to the equation3: interference term0 =(》 中=- [2ms P(t)dt (3) (2) oh wherep is the density of the liquid and P is the pressure differential where A is the area vector of the loop and K3=h/(2m)is the He across the ends of the device.So if the interferometer behaves as a quantum of circulation.Thus the effective critical current is pre- single Josephson weak link,a static pressure Po applied across the dicted to be modulated with a period determined by the rotation interferometer will cause the quantum phase to increase linearly flux through the interferometer,analogous to the manner in which in time,leading to mass current oscillations at a Josephson magnetic flux modulates the critical current of a d.c.SQUID. frequency: The interference occurs because the phase of the superfluid wavefunction receives equal and opposite shifts in the two arms 2P0 = (4) of the interferometer.The phase shift arising from the rotation flux hp is identical in form to that in other neutral-matter quantum As described in Fig.1 legend,the deflection of the flexible rotation interferometers3,as well as in the optical Sagnac membrane reveals both the pressure across the interferometer and interferometer2 if the photon effective mass is taken to be hole2. the mass current through it.We have developed a feedback method The goal ofour experiment is to demonstrate two ideas.(1)That that permits us to drive the system at constant pressure by applying the superfluid interferometer is indeed characterized as a single a time-varying voltage to the membrane.We select a pressure for weak link with a well defined critical current I,and (2)that by which the Josephson frequency lies near 270 Hz,a spectral region changing the orientation of the plane of the loop with respect to the away from parasitic acoustic noise lines in the displacement Earth's rotation vector,the current I'can be modulated according to transducer. the interference term in equation(2).I:should exhibit periodicity Figure 2 shows a Fourier transform of the mass current through of(2-A)/K3. the interferometer that results from the constant-pressure drive A geometrically more accurate sketch of our interferometer being applied for about 6 seconds.A sharp peak at 273Hz is is shown in Fig.1b.The quantum phase difference across the clearly visible.This corresponds to the Josephson oscillation.This =sinΦ Weak links x⑨ Electrode SQUID Membrane sense coil Figure 1 Two views of our superfluid quantum interferometer.a,Schematic diagram of trapped persistent curent which is partially shunted into the input coi of a d.c.SQUD if the basic interferometer loop.As shown in the Methods section,the total current through the membrane moves?.Knowledge of the deflection of the membrane,(),reveals the the two sides of the loop (is predicted to depend on the total phase difference across the pressure head across the interferometer.The rate of change of the deflection reveals the loop,,as given by equation (1)with replaced by (given by equation (2).b,The mass current through the interferometer.The noise in the displacement sensor is interferometer geometry used in this experiment.Although the two weak links are moved 2x10-5mHz-We use a feedback system that applies a voltage to the electrode closer together,the topology is unchanged and/is still given by equation(2).The such that the pressure across the interferometer is fixed at some predetemined value, nominal 'loop'area,A,is ~6 cm2,and the tube cross-sectional diameter is ~0.3 cm. typically near 1.5 mPa.Temperature is monitored with two thermometers,one using Pressure differences can be applied to the flexible metallized membrane(and hence platinum nuclear magnetic resonance and a second using lanthanum cerium magnesium across the two weak links)by applying voltages between it and the adjacent rigid nitrate (LCMN).The experiment is performed at zero ambient pressure. electrode.The membrane is coated with a superconducting film.The sense coil contains a 56 然©2001 Macmillan Magazines Ltd NATURE|VOL 412|5 JULY 2001 www.nature.comletters to nature 56 NATURE | VOL 412 | 5 JULY 2001 | www.nature.com ferometer is rotated at angular velocity Q, I p c is modulated by an interference term10 I p c ˆ 2Ic cos p 2Q×A k3           …2† where A is the area vector of the loop and k3 [ h=…2m3† is the 3 He quantum of circulation. Thus the effective critical current is pre￾dicted to be modulated with a period determined by the rotation ¯ux through the interferometer, analogous to the manner in which magnetic ¯ux modulates the critical current of a d.c. SQUID. The interference occurs because the phase of the super¯uid wavefunction receives equal and opposite shifts in the two arms of the interferometer. The phase shift arising from the rotation ¯ux is identical in form to that in other neutral-matter quantum rotation interferometers3,11, as well as in the optical Sagnac interferometer12 if the photon effective mass is taken to be ~q=c 2 . The goal of our experiment is to demonstrate two ideas. (1) That the super¯uid interferometer is indeed characterized as a single weak link with a well de®ned critical current I p c , and (2) that by changing the orientation of the plane of the loop with respect to the Earth's rotation vector, the current I p c can be modulated according to the interference term in equation (2). I p c should exhibit periodicity of …2Q×A†=k3. A geometrically more accurate sketch of our interferometer is shown in Fig. 1b. The quantum phase difference across the interferometer should evolve according to the equation13: © ˆ 2 # 2m3 r~ P…t†dt …3† where r is the density of the liquid and P is the pressure differential across the ends of the device. So if the interferometer behaves as a single Josephson weak link, a static pressure P0 applied across the interferometer will cause the quantum phase to increase linearly in time, leading to mass current oscillations at a Josephson frequency8 : qj ˆ 2m3 ~r P0 …4† As described in Fig. 1 legend, the de¯ection of the ¯exible membrane reveals both the pressure across the interferometer and the mass current through it. We have developed a feedback method that permits us to drive the system at constant pressure by applying a time-varying voltage to the membrane. We select a pressure for which the Josephson frequency lies near 270 Hz, a spectral region away from parasitic acoustic noise lines in the displacement transducer. Figure 2 shows a Fourier transform of the mass current through the interferometer that results from the constant-pressure drive being applied for about 6 seconds. A sharp peak at 273 Hz is clearly visible. This corresponds to the Josephson oscillation. This Electrode SQUID sense coil Membrane x(t) A a b Weak links ⇒ I = Icsin A b a c d I2 = Icsinφ2 * I1 = Icsinφ1 It Ω Φ Φ Ω It Φ Figure 1 Two views of our super¯uid quantum interferometer. a, Schematic diagram of the basic interferometer loop. As shown in the Methods section, the total current through the two sides of the loop (It ) is predicted to depend on the total phase difference across the loop, ©, as given by equation (1) with Ic replaced by I p c (given by equation (2)). b, The interferometer geometry used in this experiment. Although the two weak links are moved closer together, the topology is unchanged and I p c is still given by equation (2). The nominal `loop' area, A, is ,6 cm2 , and the tube cross-sectional diameter is ,0.3 cm. Pressure differences can be applied to the ¯exible metallized membrane (and hence across the two weak links) by applying voltages between it and the adjacent rigid electrode. The membrane is coated with a superconducting ®lm. The sense coil contains a trapped persistent current which is partially shunted into the input coil of a d.c. SQUID if the membrane moves26. Knowledge of the de¯ection of the membrane, x(t ), reveals the pressure head across the interferometer. The rate of change of the de¯ection reveals the mass current through the interferometer. The noise in the displacement sensor is 2 3 10 2 15 m Hz 2 1=2 . We use a feedback system that applies a voltage to the electrode such that the pressure across the interferometer is ®xed at some predetermined value, typically near 1.5 mPa. Temperature is monitored with two thermometers, one using platinum nuclear magnetic resonance and a second using lanthanum cerium magnesium nitrate (LCMN). The experiment is performed at zero ambient pressure. © 2001 Macmillan Magazines Ltd