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arXiv:cond-mat/0612548 · Physical Review B

Quantum cavity modes in spatially extended Josephson systems

M. V. Fistul, Alexey Vladimirovich Ustinov

Published Jun 12, 2007• 9 citations
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Abstract

We report a theoretical study of the macroscopic quantum dynamics in spatially extended Josephson systems. We focus on a Josephson tunnel junction of finite length placed in an externally applied magnetic field. In such a system, electromagnetic waves in the junction are excited in the form of cavity modes manifested by Fiske resonances, which are easily observed experimentally. We show that in the quantum regime, various characteristics of the junction such as its critical current ${I}_{c}$, width of the critical current distribution $\ensuremath{\sigma}$, escape rate $\ensuremath{\Gamma}$ from the superconducting state to a resistive one, and the time-dependent probability $P(t)$ of the escape are influenced by the number of photons excited in the junction cavity. Therefore, these characteristics can be used as a tool to measure the quantum states of photons in the junction, e.g., quantum fluctuations, coherent and squeezed states, entangled Fock states, etc.

DOI
10.1103/physrevb.75.214506

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We report a theoretical study of the macroscopic quantum dynamics in spatially extended Josephson systems. We focus on a Josephson tunnel junction of finite length placed in an externally applied magnetic field. In such a system, electromagnetic waves in the junction are excited in the form of cavity modes manifested by Fiske resonances, which are easily observed experimentally. We show that in the quantum regime, various characteristics of the junction such as its critical current Ic{I}_{c}Ic​, width of the critical current distribution \ensuremathσ\ensuremath{\sigma}\ensuremathσ, escape rate \ensuremathΓ\ensuremath{\Gamma}\ensuremathΓ from the superconducting state to a resistive one, and the time-dependent probability P(t)P(t)P(t) of the escape are influenced by the number of photons excited in the junction cavity. Therefore, these characteristics can be used as a tool to measure the quantum states of photons in the junction, e.g., quantum fluctuations, coherent and squeezed states, entangled Fock states, etc.
An extended Josephson junction consists of two superconducting electrodes separated by an insulator and is therefore also a microwave cavity. The superconducting phase difference across the junction determines the amplitude as well as the spatial distribution of the supercurrent. Both external magnetic fields and resonant intracavity fields produce a spatial modification of the superconducting phase along the junction. The interplay between these two effects leads to interference in the critical current of the junction and allows us to continuously tune the coupling strength between the first cavity mode and the Josephson phase from 1 to $\ensuremath{-}0.68$. This enables static and dynamic control of the junction in the ultrastrong-coupling regime.
We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on a Josephson phase escape for switching from the superconducting (the zero-voltage) state to a resistive one. Above the crossover temperature Tcr{T}_{cr}Tcr​ the thermal fluctuations of the Josephson phase induce such a switching, and as T<TcrT<{T}_{cr}T<Tcr​ the regime of the MQT occurs. In the absence of two-level systems (TLSs) a magnetic field applied parallel to the junction plane results in a smooth reduction of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$, where $\mathrm{\ensuremath{\Phi}}$ is an applied magnetic flux. As the TLSs are present in Josephson junctions we obtain a resonant enhancement of the MQT. This phenomenon manifests itself by a narrow peak in the dependence of ${T}_{cr}(\mathrm{\ensuremath{\Phi}})$ occurring in the intermediate range of $\mathrm{\ensuremath{\Phi}}$, i.e., $0<\mathrm{\ensuremath{\Phi}}<{\ensuremath{\phi}}_{0}$ (${\ensuremath{\phi}}_{0}$ is the magnetic flux quantum). We explain this effect quantitatively by a strong resonant suppression of the potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.
We report a theoretical study of the macroscopic quantum tunneling (MQT) in small Josephson junctions containing randomly distributed two-level systems. We focus on the magnetic field dependent crossover temperature TcrT_{cr}Tcr​ between the thermal fluctuation and quantum regimes of switching from the superconducting (the zero-voltage) state to a resistive one. In the absence of two-levels systems the crossover temperature shows a smooth decrease with an applied magnetic field characterized by an external flux ΦΦΦ. Beyond that we predict a narrow peak in the dependence of Tcr(Φ)T_{cr}(Φ)Tcr​(Φ) occurring in the intermediate range of ΦΦΦ. The effect becomes more pronounced as the junction size increases. We explain this effect quantitatively by a strong resonant suppression of a potential barrier for the Josephson phase escape that is due to the coherent quantum Rabi oscillations in two-level systems present in the junction.
We analyze the quantum dynamics of a superconducting cavity coupled to a voltage-biased Josephson junction. The cavity is strongly excited at resonances where the voltage energy lost by a Cooper pair traversing the circuit is a multiple of the cavity photon energy. We find that the resonances are accompanied by substantial squeezing of the quantum fluctuations of the cavity over a broad range of parameters and are able to identify regimes where the fluctuations in the system take on universal values.
de Broglie wave interferometers have been constructed, successfully utilizing extended superconducting links of tin to couple coherently the quantum phases of two Josephson junctions. The current transmitted by these devices was periodic in the enclosed flux (periodicity (.9 ± .3) h/2e) demonstrating unambiguously coherence of the superconducting order parameter over 1.33 meters. We may define a Josephson junction as one for which the quantum mechanical coupling energy is insufficient to overcome the disruptive effects of noise. Consequently, the relative phase of the coupled superconductors is not stabilized and the zero Josephson current fluctuates, (bandwidth ~ 2eVnoise/h) averaging to zero. Two such junctions have been coupled to an electromagnetic cavity formed by the superconducting arms of a quantum interferometer (junction separation 1. 33 meters). With an applied steady voltage such that the Josephson current excites a normal mode of the cavity, a coherent radiation field is built up. This coherent radiation feeds back to the junctions forcing time coherence on the phase precession, resulting in a dynamic stabilization of the junctions. Under these conditions a series of constant voltage has been observed in the I-V characteristic of one interferometer. The Josephson frequency associated with these steps is shown to be characteristic of the electromagnetic resonant modes of the cavity. Frequency modulation analysis, combined with a detailed analysis of the cavity-junction combination, predicts such maxima in the tunneling of pairs when a selection rule, (m + n) even, is obeyed. Here m/2 is the number of flux quanta (h/2e) linking the interferometer and n is the order of the cavity resonance excited. Experimental confirmation of the detailed predictions of the analysis is presented.
Conventional tunnel Josephson junctions form the basic building blocks of superconducting electronics. Their operation is based on comparatively simple dynamics where the superconducting phases across the junctions is the only dynamical degree of freedom. The goal of the project on which this thesis is based, is to understand the physics and develop a consistent theoretical description of the quantum dynamics of unconventional Josephson structures: spin active junctions, junctions containing low energy quasiparticles, and junctions composed of ddd-wave superconductors. Spin active Josephson junctions involve the additional degree of freedom of quasiparticle spin. Here we theoretically investigate the spin-structure of the current carrying interface bound states - Andreev Bound States (ABS), and induced ground state spin polarization of a short (shorter than the superconducting coherence length) nanowire junction containing a localized magnetic moment. We show that temporal variation of the superconducting phase difference and magnetic moment induce rotations in spin polarized and unpolarized subspaces respectively, which is manifested by temporal oscillation of the Josephson current.The interlevel transitions obey a selection rule that forbids manipulations in a certain region ofexternal parameters and results from specific properties of Andreev bound states in magnetic contacts where, in a certain regime of phase bias and strength of magnetic scatterer, ABS belong to different eigenstates of the combined charge and parity inversion symmetry operator.A general framework is developed to include low energy quasiparticle states into the dynamics of Josephson junctions. Such states exist in e.g. constriction type junctions with high transparency channels or resonant states, as well as in junctions of unconventional superconductors. The existence of such states prevent the separation of energy scales which in conventional tunnel junctions freezes out the quasiparticle degrees of freedom. We show that the resonant interaction with such low energy states rather than the Josephson potential defines the nonlinear Josephson dynamics at small amplitudes.The framework is applied to high temperature Josephson junctions, whose unconventional order parameter admits ABS with energies in the middle of the superconducting gap - Mid Gap States (MGS). In addition to the non-linear dynamics induced by the MGS, we identify a reentrance effect in the transition between thermal activation and macroscopic quantum tunneling associated with the MGS, and connect this phenomenon to experimental observations.