Wormholes are fascinating cosmological objects that can connect two distant regions of the universe. Because of their intriguing nature, constructing a wormhole in a lab seems a formidable task. A theoretical proposal by Greenleaf et al. presented a strategy to build a wormhole for electromagnetic waves. Based on metamaterials, it could allow electromagnetic wave propagation between two points in space through an invisible tunnel. However, an actual realization has not been possible until now. Here we construct and experimentally demonstrate a magnetostatic wormhole. Using magnetic metamaterials and metasurfaces, our wormhole transfers the magnetic field from one point in space to another through a path that is magnetically undetectable. We experimentally show that the magnetic field from a source at one end of the wormhole appears at the other end as an isolated magnetic monopolar field, creating the illusion of a magnetic field propagating through a tunnel outside the 3D space. Practical applications of the results can be envisaged, including medical techniques based on magnetism.
(a) The field of a magnetic source (right) is appearing as an isolated magnetic monopole when passing through the magnetostatic wormhole; the whole spherical device is magnetically undetectable. (b) The wormhole is composed of (from left to right) an outer spherical ferromagnetic metasurface, a spherical superconducting layer, and an inner spirally wound ferromagnetic sheet.
(a) 3D scheme of the experimental setup. (b) A detailed description of the central plane, including the lines at which probes T (red) and C (green) measure the transferred and cloaked (or distorted) fields, respectively. The uniform applied field is created by the two Helmholtz coils. (d) In this case, the z-component of magnetic field is measured by probe C as a function x and for different distances, z, to the wormhole. (e) Measurements at z = 5 are shown in detail. (c) Analogous measurements are done for a non-uniform applied field, created by exciting only one of the coils, and results are shown in (f). Red lines are for only the ferromagnetic layer, green for only the superconducting one and blue for the complete device. Black lines represent the measured applied field for each case.Although we have constructed a spherical wormhole, similar results can be obtained for the shape of an elongated ellipsoid that could extend to long distances in one direction. These ideas may be applied in devices requiring the local application of magnetic fields in a particular magnetic background that should not be distorted. One particularly relevant application along this line could be in magnetic resonance imaging. Using the ideas in this work, one could foresee ways to apply a magnetic field locally to a patient, without distorting the homogenous magnetic field in the region3,31. They could be useful, for example, in medical operations using simultaneous MRI imaging3.
Measurements of the horizontal component of magnetic field measured by probe T as a function of distance in (a) linear, and (b) double-logarithmic scales. Field shows a dependence with distance d roughly as ∼1/d1.5, very different from a dipolar dependence ∼1/d3.
Two final comments on the validity and exactness of our wormhole. First, both ends of the wormhole have been considered only in an approximate way. Because of the finite openings in the spherical shell, the cloaking properties will not be perfect near these regions. The field distortion at the ends could be reduced by refining the design. Second, our results have been experimentally confirmed only for dc fields. However, both ferromagnets and superconductors have been shown to maintain their properties for low frequencies electromagnetic waves in Refs. 32 and 33, so the wormhole could also be effective at low ac frequencies.
To sum up, we have demonstrated that the ideas in Ref. 3 of effectively changing the topology of space can be realized with magnetic fields, not only as an abstract paradigm11, but by constructing an actual 3D spatial wormhole and measuring its properties. Our wormhole appears roughly as a sphere in most regions of the electromagnetic spectrum, including visible light. However, with respect to magnetic fields, the object allows the passage of field lines through its interior while being magnetically invisible. The situation is analogous as having the magnetic field propagating through a handlebody attached to the R3 space3. In this way, the magnetic field of a dipole entering in one end of the wormhole appears as a monopolar-like field at the other end. These ideas can be useful in practical situations where magnetic fields have to be transferred without distorting a given field distribution, as in magnetic resonance imaging.