Mutual phase-locking in Josephson junction arrays

Jain, Amit; Likharev, K. K.; Lukens, J. E.; Sauvageau, J. E.

doi:10.1016/0370-1573(84)90002-4

Cited by 302 publications

(208 citation statements)

References 65 publications

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“…The concept can be readily extended to systems with an intrinsic quantum mechanical origin such as nanomechanical resonators [7,8], optomechanical arrays [9], and Josephson junctions [10,11]. When the number of coupled oscillators is large, it has been demonstrated that the onset of classical synchronization is analogous to a thermodynamic phase transition [12] and exhibits similar scaling behavior [13].…”

mentioning

confidence: 99%

Synchronization of Two Ensembles of Atoms

Xu¹,

Tieri²,

Fine³

et al. 2014

Phys. Rev. Lett.

206

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We propose a system for observing the correlated phase dynamics of two mesoscopic ensembles of atoms through their collective coupling to an optical cavity. We find a dynamical quantum phase transition induced by pump noise and cavity output-coupling. The spectral properties of the superradiant light emitted from the cavity show that at a critical pump rate the system undergoes a transition from the independent behavior of two disparate oscillators to the phase-locking that is the signature of quantum synchronization. PACS numbers: 05.45.Xt, 42.50.Lc, 37.30.+i, 64.60.Ht Synchronization is an emergent phenomenon that describes coupled objects spontaneously phase-locking to a common frequency in spite of differences in their natural frequencies [1]. It was famously observed by Huygens, the seventeenth century clock maker, in the antiphase synchronization of two maritime pendulum clocks [2]. Dynamical synchronization is now recognized as ubiquitous behavior occurring in a broad range of physical, chemical, biological, and mechanical engineering systems [1,3,4].Theoretical treatments of this phenomenon are often based on the study of phase models [5,6], and as such have been applied to an abundant variety of classical systems, including the collective blinking of fireflies, the beating of heart cells, and audience clapping. The concept can be readily extended to systems with an intrinsic quantum mechanical origin such as nanomechanical resonators [7,8], optomechanical arrays [9], and Josephson junctions [10,11]. When the number of coupled oscillators is large, it has been demonstrated that the onset of classical synchronization is analogous to a thermodynamic phase transition [12] and exhibits similar scaling behavior [13].Recently, there has been increasing interest in exploring manifestations in the quantum realm. Small systems have been considered, e.g., one qubit [14] and two qubits [15] coupled to a quantum dissipative driven oscillator, two dissipative spins [16], two coupled cavities [17], and two micromechanical oscillators [18,19]. Connections between quantum entanglement and synchronization have been revealed in continuous variable systems [19]. It has been shown that quantum synchronization may be achieved between two canonically conjugate variables [20]. Since the phenomenon is inherently non-equilibrium, all of these systems share the common property of competition between coherent and incoherent driving and dissipative forces.In this paper, we propose a modern-day realization of the original Huygens experiment [2]. We consider the synchronization of two active atomic clocks coupled to a common single-mode optical cavity. It has been predicted that in the regime of steady-state superradiance [21-24] a neutral atom lattice clock could produce an ultracoherent optical field with a quality factor (ratio of frequency to linewidth) that approaches 10 18 . We show that two such clocks may exhibit a dynamical phase transition [26][27][28][29] from two disparate oscillators to quantum phase-locked dynamics. ...

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mentioning

confidence: 99%

Synchronization of Two Ensembles of Atoms

Xu¹,

Tieri²,

Fine³

et al. 2014

Phys. Rev. Lett.

206

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“…Arrays of overdamped junctions have seemed most promising for coherent emission, since junctions of this type have, at any given applied current, only a single voltage state, and thus have none of the multistability and chaotic behavior which could inhibit coherent emission. However in practice, it has proved very difficult to achieve an efficient a. c. to d. c. conversion in such systems; thus far the highest conversion efficiency is only about 1% [13][14][15] . The low efficiency may result from the high degree of neutral stability which has been shown to exist in such overdamped arrays in the absence of an applied magnetic field 16 .…”

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confidence: 99%

Dynamics of a Josephson array in a resonant cavity

Almaas

Stroud

2002

Phys. Rev. B

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We derive dynamical equations for a Josephson array coupled to a resonant cavity by applying the Heisenberg equations of motion to a model Hamiltonian described by us earlier [Phys. Rev. B 63, 144522 (2001); Phys. Rev. B 64, 179902 (E)]. By means of a canonical transformation, we also show that, in the absence of an applied current and dissipation, our model reduces to one described by Shnirman et al [Phys. Rev. Lett. 79, 2371(1997] for coupled qubits, and that it corresponds to a capacitive coupling between the array and the cavity mode. From extensive numerical solutions of the model in one dimension, we find that the array locks into a coherent, periodic state above a critical number of active junctions, that the current-voltage characteristics of the array have self-induced resonant steps (SIRS's), that when Na active junctions are synchronized on a SIRS, the energy emitted into the resonant cavity is quadratic in Na, and that when a fixed number of junctions is biased on a SIRS, the energy is linear in the input power. All these results are in agreement with recent experiments. By choosing the initial conditions carefully, we can drive the array into any of a variety of different integer SIRS's. We tentatively identify terms in the equations of motion which give rise to both the SIRS's and the coherence threshold. We also find higher-order integer SIRS's and fractional SIRS's in some simulations. We conclude that a resonant cavity can produce threshold behavior and SIRS's even in a one-dimensional array with appropriate experimental parameters, and that the experimental data, including the coherent emission, can be understood from classical equations of motion.

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“…More recently, a peak of Josephson radiation was observed in Ref. [21] in indium junctions at the frequency 9 GHz with the width 36 MHz. In Ref.…”

Section: Experimental Observation Of the Fractional Ac Josephson Effectmentioning

confidence: 86%

Theoretical prediction of the fractional ac Josephson effect in p- and d-wave superconductors

Kwon¹,

Sengupta²,

Yakovenko³

2003

Braz. J. Phys.

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For certain orientations of Josephson junctions between two p x -wave or two d-wave superconductors, the subgap Andreev states produce a 4π-periodic relation between the Josephson current I and the phase difference φ: I ∝ sin(φ/2). Consequently, the ac Josephson current has the fractional frequency eV / , where V is the dc voltage. In the tunneling limit, the Josephson current is proportional to the first power (not square) of the electron tunneling amplitude. Thus, the Josephson current is carried by single electrons, rather than by Cooper pairs.

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Mutual phase-locking in Josephson junction arrays

Cited by 302 publications

References 65 publications

Synchronization of Two Ensembles of Atoms

Synchronization of Two Ensembles of Atoms

Dynamics of a Josephson array in a resonant cavity

Theoretical prediction of the fractional ac Josephson effect in p- and d-wave superconductors

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