Müller, Wu, Mohan, Eyvazov, Wu and Dumke (New J. Phys. 10, 073006, 2008) proposed a Mach–Zehnder-type guided atom interferometer on a high-temperature-superconducting atom chip: a two-wire magnetic guide whose central third conductor is a closed superconducting loop carrying a persistent current, forming two opposing Y-junctions that split and recombine ultracold 87^{87}Rb without external current feeds. The proposal explicitly left its load-bearing assumptions experimentally untested: whether matter waves guided through the static magnetic Y-junctions are split and recombined phase-coherently, without uncontrolled phase noise or transverse-mode excitation; and whether the current-corrugation-induced fragmentation of trapped clouds that limits normal-conducting chips is suppressed near superconducting wires at the micrometre working distances. Subsequent work has established superconducting atom chips as a trapping platform (Bose–Einstein condensates, persistent-current traps, second-scale hyperfine coherence, atom-based sensing of quantized flux and critical-state currents) and has demonstrated coherent on-chip interferometry by other routes (radio-frequency-dressed double wells, meaning time-averaged adiabatic potentials synthesized by RF fields, and optical waveguides), but no superconducting-chip guided interferometer, no phase-coherent splitting at a static magnetic Y-junction, and no direct measurement of fragmentation suppression near superconducting wires have been reported. The problem therefore remains open.

Background

An atom chip is a microfabricated device in which current-carrying wires, combined with homogeneous bias magnetic fields, generate magnetic microtraps and waveguides for ultracold neutral atoms. For atoms in a weak-field-seeking state — a Zeeman substate whose energy increases with magnetic-field strength, so that the atoms are drawn to field minima — such as 87^{87}Rb ∣F=2,mF=2⟩|F=2,m_F=2\rangle, a field minimum above the chip surface can serve as a matter-wave guide; two parallel wires carrying opposite currents, plus perpendicular bias fields BbiasXB_{biasX} and BbiasZB_{biasZ}, produce such a guide with intrinsically symmetric transverse confinement. Adding a third wire whose current opposes that of its neighbour splits the guide into two arms in the shape of a Y-junction, the magnetic analogue of an optical fiber coupler, an idea brought forward around 2000 together with nanofabricated wire splitters for thermal atomic beams (Cassettari et al., Appl. Phys. B 70, 721, 2000). Two opposing Y-junctions joined by two arms form a guided Mach–Zehnder interferometer, attractive for compact inertial sensing because the Sagnac phase — the rotation-induced phase shift of an interferometer — grows with the enclosed area.

Normal-conducting chips face two obstacles to this programme. First, every wire must be fed by an external current source, which breaks the closed topology needed for two opposing Y-junctions in a planar layout. Second, at atom–wire distances below about 100 μm100\,\mu\mathrm{m}, imperfections of the wires — edge roughness and bulk inhomogeneities that deviate the current flow from its intended path — corrugate the longitudinal potential and fragment Bose–Einstein condensates (BECs) and thermal clouds (Leanhardt et al., Phys. Rev. Lett. 90, 100404, 2003; Estève et al., Phys. Rev. A 70, 043629, 2004); later work showed that the current deviations in disordered normal-metal films are organized in long-lived channels (Aigner et al., Science 319, 1226, 2008).

The 2008 proposal of Müller et al. (New J. Phys. 10, 073006, 2008; arXiv:0806.1789) addresses both obstacles with a high-temperature superconducting (YBCO) chip. The central third wire of the splitter is realized as a closed lemon-shaped loop that sustains a persistent current (a dissipationless supercurrent that flows indefinitely in a superconducting ring), so no external feed is needed and two opposing Y-junctions close into a Mach–Zehnder topology with an enclosed area of about 0.17 mm20.17\,\mathrm{mm}^2, giving a Sagnac phase of roughly 33 mrad33\,\mathrm{mrad} per earth rotation rate for 87^{87}Rb. Because the current flows without resistance, scattering at conductivity inhomogeneities — a dominant corrugation source in optimized normal wires — is expected to be suppressed, and the epitaxially grown YBCO film showed exceptionally smooth surfaces (edge structures of about 200 nm200\,\mathrm{nm}, surface rms roughness 2.3 nm2.3\,\mathrm{nm}), motivating the prediction of substantially reduced fragmentation at the planned working distance of about 5 μm5\,\mu\mathrm{m}. A type-II superconductor can be driven from the Meissner state (complete magnetic-field expulsion) to the mixed, or Shubnikov, state (magnetic flux penetrates as pinned vortices), and the critical current density — the maximum current density the superconductor can carry without losing superconductivity — Jc≈13(1) MA/cm2J_c \approx 13(1)\,\mathrm{MA/cm^2} at 4.2 K4.2\,\mathrm{K}, estimated in the source from the measured temperature dependence, would allow much tighter traps at higher currents. Operation requires writing and tuning the persistent current via a controlled temperature and offset-field sequence, and a stability of the bias field BbiasZB_{biasZ} better than 1 μT1\,\mu\mathrm{T} to keep the relative loop-current stability at the percent level. At the time, only the chip, its material characterization, and finite-element simulations of the guiding potential existed; all matter-wave questions were open.

Problem Statement

Realize and experimentally validate the guided Mach–Zehnder atom interferometer on a superconducting atom chip proposed by Müller et al. (New J. Phys. 10, 073006, 2008), in which a closed superconducting loop carrying a persistent current forms the central conductor of two opposing two-wire Y-junctions that split and recombine a guided ultracold 87^{87}Rb cloud (thermal cloud or Bose–Einstein condensate). The problem has one overarching objective — demonstrating interferometric operation of this superconducting-chip geometry — supported by two load-bearing scientific questions and an enabling requirement that serves that same objective: (1) Coherent splitting: show that atoms guided through the first Y-junction are divided and, after recombination at the second Y-junction, exhibit matter-wave interference, quantifying the splitting efficiency, the excitation of transverse modes, and the loss of fringe contrast with hold time and arm separation, so that uncontrolled phase noise is bounded. (2) Fragmentation: directly measure the longitudinal potential corrugation experienced by ultracold atoms at micrometre-scale distances from the superconducting wires (through density-modulation or fragmentation spectra of trapped or guided clouds) and test whether it is substantially suppressed relative to normal-conducting chips, as the source predicts. Enabling requirement within the same objective, as specified by the source: reproducible preparation and tuning of the persistent current in the closed loop by controlled temperature and offset-field sequences, with bias-field BbiasZB_{biasZ} stability at the ∼1 μT\sim 1\,\mu\mathrm{T} level. The source additionally mentions, as optional future directions rather than requirements for demonstrating interferometer operation, running the guide at higher wire currents and bias fields and tuning the superconducting state from the Meissner to the Shubnikov (vortex) phase, where the critical current density is reduced under applied offsets and trapped-flux inhomogeneities appear.

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