Nonlocal quantum coherence between normal probes placed on a superconductor is predicted to occur through two microscopic processes. In crossed Andreev reflection (a) the electrons forming a Cooper pair in the superconductor break up, with each electron entering a different probe.

Coherent Nonlocal Effects in Superconducting NanostructuresPaul Cadden-Zimansky, Jian Wei and Venkat Chandrasekhar

Department of Physics and Astronomy, Northwestern University, Evanston, IL

Crossed Andreev Reflection & Elastic Cotunneling Nonlocal Signals

Nonlocal Coherence Experiment. Observation of Nonlocal Phase Coherence Coexistence of Normal Current and Supercurrent

In elastic cotunneling (b) the spatially extended Cooper pair mediates a long-range tunneling of electrons from one probe to another. These two processes should only occur if the normal metal probe separation is on the order of and can be observed when electrons are injected from one probe into the superconductor and a nonlocal voltage is monitored on the second probe.

Injecting a current from a gold normal metal lead (I+) into an aluminum superconductor (I-) the nonlocal voltages on spatially separated normal probes (V1-6) are measured relative to the superconductor potential (V-). Just below the 0.6 K superconducting transition, peaks in the nonlocal resistance are observed due to single electron excitations in the superconductor (charge imbalance). These excitations are frozen out at the lowest temperature revealing a remnant nonlocal resistance that decays rapidly as the distance to each nonlocal probe is increased. The decay length of this low-temperature, zero-bias resistance is several hundred nanometers, comparable to the superconducting coherence length.

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Motivation

Microscopic objects that have become quantum mechanically entangled exhibit novel behavior that violates many of our classical intuitions. The exploitation of entangled quantum objects is at the heart of a number of recently developed subfields in physics – quantum computation, quantum cryptography, quantum information, etc. Perhaps the simplest entangled object is two electrons of opposite spin bound in a singlet state.

As this length scale is now easily accessible to modern nanolithographic techniques, we ask the question: is it possible to use the Cooper pairs in a superconductor to quantum mechanically couple two normal metal (N) probes placed on it? In particular, can the quantum phase of electrons in one probe be coherently communicated to the other, without any current being passed between the probes?

This entanglement occurs in many materials which are cooled to low enough temperatures to become superconductors (S). In this phase transition singlet Cooper pairs of electrons are naturally created. Though the constituent electrons of these pairs form a single quantum object, they are spatially separated by a coherence length which can extend several hundred nanometers.

To demonstrate that a nonlocal signal between two probes can communicate information about the quantum phase of the electrons, a phase-dependent current I() from one probe into the superconductor needs to be established. The nonlocal voltage VN can then be monitored as the phase is tuned on a second probe located less than a superconducting coherence length from the first. To create the current, one of the normal probes is embedded in a hybrid normal metal-superconducting loop known as an Andreev interferometer. The phase of electrons around this loop are tuned by threading a magnetic flux through it. As this phase is altered, shifting quantum interference effects are observed, such as symmetric, periodic oscillations in the resistance of the interferometer. These oscillations are periodic in the o=h/2e superconducting quantum of flux. By creating a nonequilibrium distribution of electrons in the normal arm of the interferometer, such as by sending a small DC current into its center along with an AC measurement current, one can produce the phase-tunable I() current. The voltages generated by this current are monitored on probes at the top and bottom corners of the loop as well as the nonlocal probes just off it.

Phase coherent signals are observed both at the corners of the loop and also nonlocally. The amplitude of the nonlocal signals are reduced sixfold from those measured on the corners, consistent with rapid decay over the superconducting coherence length.

The fact that the oscillations at the top and bottom of the loop are of opposite polarities despite the symmetry of the device about its horizontal axis indicates that the sign of the voltages are determined by a flux-induced supercurrent that circulates around the interferometer loop.

One paradox regarding the supercurrent traveling around the hybrid loop is that the loop still has a finite resistance. This paradox can be resolved by showing that a normal metal can simultaneously support a resistive normal current and a resistanceless supercurrent.

Measurements of an SNS wire are made with two different sets of probes. Superconducting probes are used to measure the resistance of the whole wire while normal probes are used to measure a part of the normal section at its center. At low enough temperatures a supercurrent across the whole wire shows no resistance while the normal part is still resistive.

The apparent drop in the normal part resistance when the supercurrent is established is due to the fact that the measurement current injected at point A now has two paths to exit the wire at point B: the usual path along the normal wire and a second path that uses the resistanceless channel from one superconductor to the other.

Cadden-Zimansky et al., Physical Review Letters (2006)

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