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arXiv:2507.01188 · Physical Review Research

Fractional Shapiro steps in a cavity-coupled Josephson ring condensate

N. Pradhan, Rina Kanamoto, Mishkatul Bhattacharya, Pankaj Kumar Mishra

Published Nov 20, 2025• 2 citations
arXivHTMLPDF

Abstract

The Josephson effect presents a fundamental example of macroscopic quantum coherence as well as a crucial enabler for metrology (e.g., voltage standard), sensing (e.g., superconducting quantum interference device), and quantum information processing (Josephson qubits). Recently, there has been a major renewal of interest in the effect, following its observation in Bose, Fermi, and dipolar atomic condensates, in exciton-polariton condensates, and in momentum space. We present theoretically a nondestructive, , and real time protocol for observing the ac and dc Josephson effects including integer (recently observed in cold atoms) and fractional (hitherto unobserved in cold atoms) Shapiro steps, using a ring condensate coupled to an optical cavity. Our analysis presents a single-shot metrology standard that does not require measurement of atomic number and that challenges the conventional wisdom that quantum computations cannot be observed without being destroyed. Our results have implications for the fields of atomtronics, sensing, metrology, and quantum information processing.

DOI
10.1103/6vnd-vyr4

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The Josephson effect presents a fundamental example of macroscopic quantum coherence as well as a crucial enabler for metrology (e.g., voltage standard), sensing (e.g., superconducting quantum interference device), and quantum information processing (Josephson qubits). Recently, there has been a major renewal of interest in the effect, following its observation in Bose, Fermi, and dipolar atomic condensates, in exciton-polariton condensates, and in momentum space. We present theoretically a nondestructive, , and real time protocol for observing the ac and dc Josephson effects including integer (recently observed in cold atoms) and fractional (hitherto unobserved in cold atoms) Shapiro steps, using a ring condensate coupled to an optical cavity. Our analysis presents a single-shot metrology standard that does not require measurement of atomic number and that challenges the conventional wisdom that quantum computations cannot be observed without being destroyed. Our results have implications for the fields of atomtronics, sensing, metrology, and quantum information processing.
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.
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A Bose-Einstein condensate confined in ring shaped lattices interrupted by a weak link and pierced by an effective magnetic flux defines the atomic counterpart of the superconducting quantum interference device: the atomtronic quantum interference device (AQUID). In this paper, we report on the detection of current states in the system through a self-heterodyne protocol. Following the original proposal of the NIST and Paris groups, the ring-condensate many-body wave function interferes with a reference condensate expanding from the center of the ring. We focus on the rf AQUID which realizes effective qubit dynamics. Both the Bose-Hubbard and Gross-Pitaevskii dynamics are studied. For the Bose-Hubbard dynamics, we demonstrate that the self-heterodyne protocol can be applied, but higher-order correlations in the evolution of the interfering condensates are measured to readout of the current states of the system. We study how states with macroscopic quantum coherence can be told apart analyzing the noise in the time of flight of the ring condensate.
Nondemolition protocols use ancilla qubits to identify the fragile quantum state of a qubit without destroying its encoded information, thus playing a crucial role in nondestructive quantum measurements particularly relevant for quantum error correction. However, the multitude of ancilla preparations, information transfers, and ancilla measurements in these protocols create an intrinsic overhead for information processing. Here we consider an Andreev qubit defined in a quantum-dot Josephson junction and show that the macroscopic time-dependent oscillatory supercurrent arising from the quantum interference of the many-body eigenstates, can be used to probe the qubit itself-arbitrarily close to the nondestructive limit-under currently available experimental capabilities. This readout of arbitrary superposition states of Andreev qubits avoids ancillae altogether and significantly reduces experimental overhead as no repetitive qubit reinitialization is needed. Our prediction of an AC-like Josephson effect without an applied external voltage, which enables the nondestructive qubit readout, is a unique macroscopic manifestation of the microscopic dynamics of the Andreev quantum state. Our findings should have an unprecedented impact on advancing research and applications involving Andreev dots, thus positioning them as promising qubit contenders for quantum processing and technologies.
We review our theoretical advances in quantum tunneling of Bose-Einstein condensates in optical traps and in microcavities. By employing a real physical system, the frequencies of the pseudo Goldstone modes in different phases between two optical traps are studied respectively, which are the crucial feature of the non-Abelian Josephson effect. When the optical lattices are under gravity, we investigate the quantum tunneling in the “Wannier-Stark localization” regime and “Landau-Zener tunneling” regime. We finally get the total decay rate and the rate is valid over the entire range of temperatures. At high temperatures, we show how the decay rate reduces to the appropriate results for the classical thermal activation. At intermediate temperatures, the results of the total decay rate are consistent with the thermally assisted tunneling. At low temperatures, we obtain the pure quantum tunneling ultimately. And we study the alternating-current and direct-current (ac and dc) photonic Josephson effects in two weakly linked microcavities containing ultracold two-level atoms, which allows for direct observation of the effects. This enables new investigations of the effect of many-body physics in strongly coupled atom-cavity systems and provides a strategy for constructing novel interference devices of coherent photons. In addition, we propose the experimental protocols to observe these quantum tunneling of Bose-Einstein condensates.
Abstract Bloch oscillations in small Josephson junctions were predicted theoretically as the quantum dual to Josephson oscillations. A significant consequence of this prediction is the emergence of quantized current steps, so-called dual Shapiro steps, when synchronizing Bloch oscillations to an external microwave signal. These steps potentially enable a fundamental standard of current I, defined via the frequency f of the external signal and the elementary charge e, I = ± n × 2ef, where n is a natural number. Here, we realize this fundamental relation by synchronizing the Bloch oscillations in small Al/AlOx/Al Josephson junctions to sinusoidal drives with frequencies from 1 to 6 GHz and observe dual Shapiro steps up to I ≈ 3 nA. Inspired by today’s voltage standards and to further confirm the duality relation, we investigate a pulsed drive regime and observe an asymmetric pattern of dual Shapiro steps. This work confirms quantum duality effects in Josephson junctions and paves the way towards a range of applications in quantum metrology based on well-established fabrication techniques and straightforward circuit design.