Bloch band dynamics of a Josephson junction in an inductive environment

Weißl, Thomas; Rastelli, Gianluca; Matei, Iulian; Pop, I.; Buisson, Olivier; Hekking, F. W. J.; Guichard, Wiebke

doi:10.1103/physrevb.91.014507

Cited by 36 publications

(38 citation statements)

References 35 publications

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“…This is correct for relatively short chains, with N < 2C/C 0 . Yet for longer chains, these modes appear and their effect on the phase-slip amplitude is non-negligible 19,20 . Indeed, in the thermodynamic limit, it is the interplay between the modes and the phase-slips that leads to the superconductor-insulator transition.…”

Section: Introductionmentioning

confidence: 99%

Kerr coefficients of plasma resonances in Josephson junction chains

et al. 2015

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We present an experimental and theoretical analysis of the self-and cross-Kerr effect of extended plasma resonances in Josephson junction chains. We calculate the Kerr coefficients by deriving and diagonalizing the Hamiltonian of a linear circuit model for the chain and then adding the Josephson non-linearity as a perturbation. The calculated Kerr-coefficients are compared with the measurement data of a chain of 200 junctions. The Kerr effect manifests itself as a frequency shift that depends linearly on the number of photons in a resonant mode. By changing the input power on a low signal level, we are able to measure this shift. The photon number is calibrated using the self-Kerr shift calculated from the sample parameters. We then compare the measured cross-Kerr shift with the theoretical prediction, using the calibrated photon number.

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Section: Introductionmentioning

confidence: 99%

Kerr coefficients of plasma resonances in Josephson junction chains

et al. 2015

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“…The results presented in this paper are relevant for recent experiments on Josephson junction chains [43] and nanowires [47,50]. In these works, typical phase-slip energies U 0 are in the range of 1-10 GHz, whereas the environmental inductances L are 50-500 nH.…”

Section: Discussionmentioning

confidence: 71%

“…The larger L, the smaller E L , and the larger the ratio U 0 /E L , thus favoring a well-defined charge state of the QPSJ. Recent experiments on nanowires [47,50] and chains of Josephson junctions [43] typically achieve U 0 /E L ratios that are of the order of 10 −2 -10 −1 . We will analyze the microwave response of a QPSJ in this regime in detail and study in particular the resolution and accuracy of the dual Shapiro steps.…”

Section: Introductionmentioning

confidence: 99%

“…The Josephson junction has an exact dual counterpart, the so-called quantum phase-slip junction (QPSJ) [29][30][31][32][33][34][35][36][37][38]. Physical realizations of QPSJ that have been discussed in the literature are a single Josephson junction with a finite capacitance [29][30][31][32][37][38][39] or a linear chain of such Josephson junctions [38,[40][41][42][43], and a narrow superconducting nanowire [44][45][46][47][48][49][50]. With respect to an ordinary JJ, the role of the phase and the charge in a QPSJ is interchanged.…”

Section: Introductionmentioning

confidence: 99%

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Quantum phase-slip junction under microwave irradiation

2015

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We consider the dynamics of a quantum phase-slip junction (QPSJ), a dual Josephson junction, connected to a microwave source with frequency ω mw . With respect to an ordinary Josephson junction, a QPSJ can sustain dual Shapiro steps, consisting of well-defined current plateaus at multiple integers of eω mw /π in the current-voltage (I -V ) characteristic. The experimental observation of these plateaus has been elusive up to now. We argue that thermal as well as quantum fluctuations can smear the I -V characteristic considerably. In order to understand these effects, we study a current-biased QPSJ under microwave irradiation and connected to an inductive and resistive environment. We find that the effect of the fluctuations is governed by the resistance of the environment and by the ratio of the phase-slip energy and the inductive energy. Our results are of interest for experiments aiming at the observation of dual Shapiro steps in QPSJ devices for the definition of a new quantum current standard.

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“…Typically, because both the fine structure constant and atomic dipoles are small, matter-light coupling is weak, allowing treatment by simple and controlled methodologies, such as the rotating wave approximation (RWA), Born-Markov schemes, and Fock space truncation [1]. However, recent artificial systems such as superconducting waveguides [2][3][4][5][6][7], especially the ones using Josephson junction elements to boost the circuit impedance [8][9][10][11][12], constitute metamaterials where charge density fluctuations mimic an optical-like medium in which the coupling to matter (namely superconducting qubits) can be ultra strong. In this situation, a plethora of interesting phenomena, such as wide-band frequency conversion [13], large nonlinearities [14], and non-trivial many-body vacua [13,15], have been theoretically predicted.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a qubit in a high-impedance transmission line from a bath perspective

2016

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We investigate the quantum dynamics of a generic model of light-matter interaction in the context of high impedance waveguides, focusing on the behavior of the photonic states generated in the waveguide. The model treated consists simply of a two-level system coupled to a bosonic bath (the ohmic spin-boson model). Quantum quenches as well as scattering of an incident coherent pulse are studied using two complementary methods. First, we develop an approximate ansatz for the electromagnetic waves based on a single multimode coherent state wavefunction; formally, this approach combines in a single framework ideas from adiabatic renormalization, the Born-Markov approximation, and input-output theory. Second, we present numerically exact results for scattering of a weak intensity pulse by using Numerical Renormalization Group (NRG) calculations. NRG provides a benchmark for any linear response property throughout the ultra-strong coupling regime. We find that in a sudden quantum quench, the coherent state approach produces physical artifacts, such as improper relaxation to the steady state. These previously unnoticed problems are related to the simplified form of the ansatz that generates spurious correlations within the bath. In the scattering problem, NRG is used to find the transmission and reflection of a single photon, as well as the inelastic scattering of that single photon. Simple analytical formulas are established and tested against the NRG data that predict quantitatively the transport coefficients for up to moderate environmental impedance. These formulas resolve pending issues regarding the presence of inelastic losses in the spin-boson model near absorption resonances, and could be used for comparison to experiments in Josephson waveguide quantum electrodynamics (QED). Finally, the scattering results using the coherent state wavefunction approach are compared favorably to the NRG results for very weak incident intensity. We end our study by presenting results at higher power where the response of the system is nonlinear.

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Bloch band dynamics of a Josephson junction in an inductive environment

Cited by 36 publications

References 35 publications

Kerr coefficients of plasma resonances in Josephson junction chains

Kerr coefficients of plasma resonances in Josephson junction chains

Quantum phase-slip junction under microwave irradiation

Dynamics of a qubit in a high-impedance transmission line from a bath perspective

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