It is established theoretically that an ordered state with continuous symmetry is inherently unstable to arbitrarily small amounts of disorder 1,2. This principle is of central importance in a wide variety of condensed systems including superconducting vortices 3,4 , Ising spin models 5 and their dynamics 6 , and liquid crystals in porous media 7,8 , where some degree of disorder is ubiquitous, although its experimental observation has been elusive. On the basis of these ideas, it was predicted 9 that 3 He in high-porosity aerogel would become a superfluid glass. We report here our nuclear magnetic resonance measurements on 3 He in aerogel demonstrating destruction of long-range orientational order of the intrinsic superfluid orbital angular momentum, confirming the existence of a superfluid glass. In contrast, 3 He-A generated by warming from superfluid 3 He-B has perfect long-range orientational order providing a mechanism for switching off this effect. Close to the absolute zero of temperature, liquid 3 He condenses into a p-wave superfluid of Cooper pairs resulting in two phases with fundamentally different symmetry: the isotropic B-phase and an anisotropic A-phase. In zero magnetic field, 3 He-A appears in a small corner of the pressure versus temperature phase diagram shown in Fig. 1d. Its anisotropy, a paradigm for more recently discovered unconventional superconductors 10 , is characterized by the orientation of its order parameter defined by orbital angular momentum and spin induced by magnetic field,l andŝ. The spin is necessarily aligned with an applied magnetic field, H; however, the orbital angular momentum has continuous rotational symmetry. That symmetry can be broken, for example, at a wall or interface to whichl must be perpendicular, thereby defining a preferred direction on a macroscopic scale. Volovik proposed 9 that this long-range orientational coherence of angular momentum would be destroyed by random microscopic disorder that can be realized if the 3 He is imbibed in highly porous silica aerogel as shown in our simulation Fig. 1a,b. This sensitivity to small amounts of disorder on a microscopic scale was discussed by Larkin 1 and Imry and Ma 2 for a broad range of physical phenomena 3-8 and we refer to this as the LIM effect. If this proposal is correct then in the LIM state the order parameter structure of the superfluid will be completely hidden, a behaviour of potential significance for understanding exotic superconductors such as URu 2 Si 2 (ref. 11). We use nuclear magnetic resonance (NMR) to look for the LIM state of superfluid 3 He-A, directly interrogating the orientation of l by measuring the Leggett shift 12 of the NMR spectrum, ω A. In pure 3 He this frequency shift is proportional to the nuclear dipole energy, F D ∝ −(l •d) 2 , whered is a spin-space vector constrained to be perpendicular toŝ while minimizing F D. This shift is strongly temperature dependent, but for an orbital glass it should be very small, or ideally zero (Supplementary Information) as we report here.
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