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arXiv:2307.08743 · Physical Review Letters

Shapiro Steps in Driven Atomic Josephson Junctions

Vijay Pal Singh, Juan Polo, Ludwig Mathey, Luigi Amico A

Published Aug 26, 2024• 19 citations
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Abstract

We study driven atomic Josephson junctions realized by coupling two two-dimensional atomic clouds with a tunneling barrier. By moving the barrier at a constant velocity, dc and ac Josephson regimes are characterized by a zero and nonzero atomic density difference across the junction, respectively. Here, we monitor the dynamics resulting in the system when, in addition to the above constant velocity protocol, the position of the barrier is periodically driven. We demonstrate that the time-averaged particle imbalance features a plateau behavior that is the analog of Shapiro steps observed in driven superconducting Josephson junctions. The underlying dynamics reveals an intriguing interplay of the vortex and phonon excitations, where Shapiro steps are induced via suppression of vortex growth. We study the system with a classical-field dynamics method, and benchmark our findings with a driven circuit dynamics.

DOI
10.1103/physrevlett.133.093401

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We study driven atomic Josephson junctions realized by coupling two two-dimensional atomic clouds with a tunneling barrier. By moving the barrier at a constant velocity, dc and ac Josephson regimes are characterized by a zero and nonzero atomic density difference across the junction, respectively. Here, we monitor the dynamics resulting in the system when, in addition to the above constant velocity protocol, the position of the barrier is periodically driven. We demonstrate that the time-averaged particle imbalance features a plateau behavior that is the analog of Shapiro steps observed in driven superconducting Josephson junctions. The underlying dynamics reveals an intriguing interplay of the vortex and phonon excitations, where Shapiro steps are induced via suppression of vortex growth. We study the system with a classical-field dynamics method, and benchmark our findings with a driven circuit dynamics.
The current-voltage characteristic of a driven superconducting Josephson junction displays discrete steps. This phenomenon, called the Shapiro steps, forms today's voltage standard. In this work, we report the observation of Shapiro steps in a driven Josephson junction in a gas of ultracold atoms. We demonstrate that the steps exhibit universal features and provide insight into the microscopic dissipative dynamics that we directly observe in the experiment. We find that the steps are directly connected to phonon emission and nucleation of solitonic excitations, whose dynamics we follow in space and time. The experimental results are underpinned by extensive numerical simulations based on classical-field dynamics and may enable metrological and fundamental advances.
We propose an ac-driven atomic Josephson junction as a clean and tunable source of three dimensional (3D) solitary waves in quantum fluids. Depending on the height of the junction barrier, the emitted excitations appear as vortex rings at low velocity or vorticity-free rarefaction pulses near the sound velocity, thus spanning the complete Jones-Roberts family of solitons. The Shapiro-step phenomenon renders the emission deterministic: on the first, second, third Shapiro steps, the junction ejects one, two, and three solitary excitations per drive cycle. This enables controlled generation of single- and multi-excitation configurations, allowing detailed studies of the full crossover between vortex rings and rarefaction pulses and their interaction dynamics. In particular, deterministic multi-ring emission provides insights into leapfrogging dynamics of two and three coaxial rings and their decay via boundary-assisted, sound-mediated processes. This ac-driven protocol establishes a compact and reproducible platform for generating, classifying, and controlling 3D solitonic excitations, paving the way for precision studies of nonlinear vortex dynamics, dissipation, and quantum turbulence in trapped superfluids.
We propose an experiment that would demonstrate the dc and ac Josephson effects in two weakly linked Bose-Einstein condensates. We consider a time-dependent barrier, moving adiabatically across the trapping potential. The phase dynamics are governed by a "driven-pendulum" equation, as in current-driven superconducting Josephson junctions. At a critical velocity of the barrier (proportional to the critical tunneling current), there is a sharp transition between the dc and ac regimes. The signature is a sudden jump of a large fraction of the relative condensate population. Analytical results are compared with a numerical integration of the Gross-Pitaevskii equation, in an experimentally realistic situation.
Driven many-body systems exhibit diverse and complex dynamical behaviors. Here, we report the observation of Shapiro steps in periodically driven Josephson junctions between strongly interacting Fermi superfluids of ultracold atoms. The height and the width of the observed quantized plateaus in the current-potential characteristics mirror the external drive frequency and the junction nonlinear response. Direct measurements of the current-phase relationship showcase how Shapiro steps arise from the synchronization between the relative phase of the two reservoirs and the external drive. Such a mechanism is further supported by the detection of periodic phase-slippage processes, in the form of vortex-antivortex pairs. Our results are corroborated by a circuital model and numerical simulations. Our work may open prospects for studying emergent nonequilibrium dynamics in quantum many-body systems under external drives.
We analyze the emergence of Shapiro resonances in tunnel-coupled Bose–Einstein condensates, realizing a bosonic Josephson junction. Our analysis is based on an experimentally relevant implementation using magnetic double-well potentials on an atomchip. In this configuration, the potential bias (implementing the junction voltage) and the potential barrier (realizing the Josephson link) are intrinsically coupled. We show that the dynamically driven system exhibits significantly enhanced Shapiro resonances which will facilitate experimental observation. To describe the system's response to the dynamic drive, we compare a single-mode Gross–Pitaevskii (GP) description, an improved two-mode (TM) model and the self-consistent multi-configurational time-dependent Hartree equations for bosons (MCTDHB) method. We show that in the case of significant atom–atom interactions, the spatial dynamics of the involved modes has to be taken into account and only the MCTDHB method allows reliable predictions.
We analyze the effect of the barrier motion on the Bose-Hubbard Hamiltonian of a ring-shaped Bose-Einstein condensate interrupted by a pair of Josephson junctions, a configuration which is the cold-atom analog of the well-known dc superconducting quantum interference device (SQUID). Such an effect is also shown to modify the Heisenberg equation of motion of the boson field operator in the two-mode approximation, where a hysteretic contribution that could affect the dynamics for accelerated or overlapping barriers is identified. By studying the energy landscape as a function of order and control parameters, we determine the diagram with the location of the dc and ac Josephson regimes, along with the critical points that are shown to depend on the junction's position. We analyze the dc to ac Josephson transition for adiabatic barrier trajectories that lead to a final uniform velocity, or which perform symmetric velocity paths. We show that such symmetric trajectories may induce, when reaching the critical point, highly hysteretic oscillating return paths within the dc regime, similar to the underdamped hysteresis loops arising from the action of a resistive flow in the ac regime. We also consider nonequilibrium initial conditions resulting from a finite phase difference on either side of the junctions, along with the critical features of such a parameter. An excellent agreement between the Gross-Pitaevskii simulations and the two-mode results is found in all cases.