Research ArticlePHYSICS

Nonequilibrium optical control of dynamical states in superconducting nanowire circuits

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Science Advances  30 Mar 2018:
Vol. 4, no. 3, eaao0043
DOI: 10.1126/sciadv.aao0043
  • Fig. 1 Schematic representation of the experiment.

    (A) Schematic representation of the evolution of the averaged superfluid density 〈ρs 〉, the order parameter ψ = |ψ|eiθ, and the average resistance 〈R 〉 upon photoswitching between different phase-slip configurations. Absorption of the pulse leads to the transient reduction of the order parameter, eventually resulting in a state with more PSCs and a higher resistance. (B) SEM image of the MoN nanowire. Pt contacts are shown in green. Blue and yellow false colors schematically indicate superconducting and normal regions of the sample, representing putative PSCs. White marker length is 5 μm.

  • Fig. 2 Optical switching to the stable and quasi-stable states.

    (A) Current-voltage map of accessible dissipative states at 9.2 K. Gray line marks the states that are obtained in current cycling. Spheres show the states observed in the laser switching experiments at fixed values of the current: White, blue, and red symbols represent the initial, stable photoinduced, and quasi-stable photoinduced states, respectively. Note that the numbers do not correspond to the actual number of PSCs. (B) Time dependence of the laser fluence, which corresponds to the switching experiment in (C); 1100-nm, 50-fs-long laser pulses arrive every 2 s. (C) Switching between stable dynamical states at i = 0.3405 mA. (D) Example of switching into the quasi-stable state |2q〉 (i = 0.337 mA). For comparison, the later event of spontaneous decay of state |4q〉 into the stable state |2〉 obtained in the same experiment is shown. (E) Pointers mark the arrival of the laser pulses in the same experiment as in (D); the length of the pointers is proportional to the pulse energy. Switching to state |2q〉 occurs after nearly every pulse after a threshold pulse energy has been achieved. Experiments in (B) and (C) as well as (D) and (E) are conducted at fixed currents, which are highlighted in (A) by pink and yellow rectangles, respectively.

  • Fig. 3 Analysis of the accessibility of the hidden state.

    (A and B) Current cycling after photoexcitation of the hidden state at high and low temperatures, respectively (red lines). Current cycling of the initial state |4〉 is shown by blue solid lines. Edge points at which the transition occurs are marked by open symbols. In (A), the Embedded Image state is accessible with both current and optical stimulus. In (B), the Embedded Image state does not exist at the high-current edge point of state |4〉 and thus can only be accessed by photoexcitation. (C) Current-temperature map of the stability regions of the Embedded Image and |4〉 states from experiments in (A) and (B) at a number of temperatures. The high-current instability edges of the Embedded Image and |4〉 states are shown in red and blue solid lines, respectively. The Embedded Image state is accessible through the instability if the transition occurs above 9.5 K, where the instability line of the initial state (blue) falls into the stability region of the Embedded Image state. The green arrow indicates the trajectory in the case of a temperature surge caused by the laser pulse. The dashed purple line indicates the trajectory required to achieve switching by adiabatic excitation from the same initial state.

  • Fig. 4 Predicted real-time dynamics of the order parameter through a photoinduced transition to a hidden dynamically stable state.

    (A) The order parameter amplitude |ψ| is plotted as a function of time and coordinate along the nanowire. The timing of the laser pulse is indicated. (B) Average voltage 〈V〉 as the current is ramped up and down in both states to test stability, similar to the experiments in Fig. 3. Voltage is calculated in units of Embedded Image.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/3/eaao0043/DC1

    note S1. Calculation of the initial electronic temperature evolution.

    note S2. TDGL modeling. Case of quasi-equilibrium cooling.

    note S3. Phase trajectories of the order parameter in the initial and hidden states. Role of the synchronization between laser pulses and the phase-slip process.

    note S4. Decay of the quasi-stable state.

    fig. S1. Estimated electronic temperature evolution across the nanowire.

    fig. S2. Spatiotemporal evolution of the order parameter amplitude in the case of the quasi-equilibrium cooling (time is horizontal and changes continuously from left to right, from top to bottom).

    fig. S3. Cut of the phase trajectory of the order parameter at the center of the nanowire in the |ψ| − E (order parameter amplitude − electric field) phase space.

    fig S4. Distribution of the lifetimes of the quasi-stable state |2q〉.

    References (3739)

  • Supplementary Materials

    This PDF file includes:

    • note S1. Calculation of the initial electronic temperature evolution.
    • note S2. TDGL modeling. Case of quasi-equilibrium cooling.
    • note S3. Phase trajectories of the order parameter in the initial and hidden states. Role of the synchronization between laser pulses and the phase-slip process.
    • note S4. Decay of the quasi-stable state.
    • fig. S1. Estimated electronic temperature evolution across the nanowire.
    • fig. S2. Spatiotemporal evolution of the order parameter amplitude in the case of the quasi-equilibrium cooling (time is horizontal and changes continuously from left to right, from top to bottom).
    • fig. S3. Cut of the phase trajectory of the order parameter at the center of the nanowire in the |ψ| − E (order parameter amplitude − electric field) phase space.
    • fig S4. Distribution of the lifetimes of the quasi-stable state |2q〉.
    • References (37–39)

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