We employ a functional integral technique to calculate the macroscopic quantum tunneling rate at zero temperature of a current-biased Josephson junction weakly coupled to a resonator. We allow for the effects of environmental dissipation on both the junction and the resonator via baths of harmonic oscillators, and we consider both cases of weak and strong junction damping. The resonator can be, in principle, any quantum harmonic oscillator that couples to the junction bilinearly in either the coordinate or the velocity. The Josephson phase difference $\ensuremath{\phi}$ is the tunneling variable in this system, and the low-lying bound states in the junction's potential energy well are weakly metastable due to tunneling through a finite-width energy barrier. There has been some interest in using such biased junctions as qubits with the resonator providing multiqubit coupling. The main result of this work is that coupling to the resonator has a suppressive effect on the junction's tunneling: the stronger the coupling strength between the junction and resonator, the greater the reduction of the tunneling rate. Including damping to the junction also suppresses tunneling, a well-known result, but damping of the resonator actually reduces the magnitude of suppression; i.e., damping the resonator partially counteracts the suppression provided directly by the junction-resonator coupling. Details of the junction-resonator coupling yield interesting variations on this theme that may be useful for qubit design. For example, the coupling ${U}_{\mathit{int}}$ between a current-biased junction and an AlN dilatational resonator should depend on the angular frequency of the resonator ${\ensuremath{\omega}}_{R}$ in a power-law fashion [A. N. Cleland and M. R. Geller, Phys. Rev. Lett. 93, 070501 (2004)], specifically ${U}_{\mathit{int}}\ensuremath{\propto}{({\ensuremath{\omega}}_{R})}^{n}$, where $n=1∕2$ . We find that for any value of $n$ in the range $0<n<1$ the junction's tunneling rate exhibits a nonmonotonic dependence on ${\ensuremath{\omega}}_{R}$, and for $n=1∕2$ , the tunneling rate is maximally suppressed for ${\ensuremath{\omega}}_{R}∕{\ensuremath{\omega}}_{J}\ensuremath{\approx}1$, where ${\ensuremath{\omega}}_{J}$ is the bias current-dependent plasma frequency of the junction.We employ a functional integral technique to calculate the macroscopic quantum tunneling rate at zero temperature of a current-biased Josephson junction weakly coupled to a resonator. We allow for the effects of environmental dissipation on both the junction and the resonator via baths of harmonic oscillators, and we consider both cases of weak and strong junction damping. The resonator can be, in principle, any quantum harmonic oscillator that couples to the junction bilinearly in either the coordinate or the velocity. The Josephson phase difference $\ensuremath{\phi}$ is the tunneling variable in this system, and the low-lying bound states in the junction's potential energy well are weakly metastable due to tunneling through a finite-width energy barrier. There has been some interest in using such biased junctions as qubits with the resonator providing multiqubit coupling. The main result of this work is that coupling to the resonator has a suppressive effect on the junction's tunneling: the stronger the coupling strength between the junction and resonator, the greater the reduction of the tunneling rate. Including damping to the junction also suppresses tunneling, a well-known result, but damping of the resonator actually reduces the magnitude of suppression; i.e., damping the resonator partially counteracts the suppression provided directly by the junction-resonator coupling. Details of the junction-resonator coupling yield interesting variations on this theme that may be useful for qubit design. For example, the coupling ${U}_{\mathit{int}}$ between a current-biased junction and an AlN dilatational resonator should depend on the angular frequency of the resonator ${\ensuremath{\omega}}_{R}$ in a power-law fashion [A. N. Cleland and M. R. Geller, Phys. Rev. Lett. 93, 070501 (2004)], specifically ${U}_{\mathit{int}}\ensuremath{\propto}{({\ensuremath{\omega}}_{R})}^{n}$, where $n=1∕2$. We find that for any value of $n$ in the range $0<n<1$ the junction's tunneling rate exhibits a nonmonotonic dependence on ${\ensuremath{\omega}}_{R}$, and for $n=1∕2$, the tunneling rate is maximally suppressed for ${\ensuremath{\omega}}_{R}∕{\ensuremath{\omega}}_{J}\ensuremath{\approx}1$, where ${\ensuremath{\omega}}_{J}$ is the bias current-dependent plasma frequency of the junction.

Physical Review BDec 13, 20076 citations

Diode Effects in Current-Biased Josephson Junctions

Jacob F. Steiner, Larissa Melischek, Martina Trahms +2 more

Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. Here, we develop a theory for diodelike effects in the switching and retrapping currents of weakly damped Josephson junctions. We find that while the diodelike behavior of switching currents is rooted in asymmetric current-phase relations, nonreciprocal retrapping currents originate in asymmetric quasiparticle currents. These different origins also imply distinctly different symmetry requirements. We illustrate our results by a microscopic model for junctions involving a single magnetic atom. Our theory provides significant guidance in identifying the microscopic origin of nonreciprocities in Josephson junctions.Current-biased Josephson junctions exhibit hysteretic transitions between dissipative and superconducting states as characterized by switching and retrapping currents. Here, we develop a theory for diodelike effects in the switching and retrapping currents of weakly damped Josephson junctions. We find that while the diodelike behavior of switching currents is rooted in asymmetric current-phase relations, nonreciprocal retrapping currents originate in asymmetric quasiparticle currents. These different origins also imply distinctly different symmetry requirements. We illustrate our results by a microscopic model for junctions involving a single magnetic atom. Our theory provides significant guidance in identifying the microscopic origin of nonreciprocities in Josephson junctions.

arXiv:2212.06866Physical Review LettersApr 27, 202357 citations

Study of Phase Dynamics in Moderately Damped Josephson Junctions

D. Massarotti, Luigi Longobardi, D. Stornaiuolo +5 more

Journal of Superconductivity and Novel MagnetismDec 29, 20122 citations

Characterization of Moderately Damped Low Tc Josephsonjunctions through Measurements of Switching Current Distributions

D. Massarotti, Luigi Longobardi, G. Rotoli +6 more

We report on measurements of the switching current probability both in the thermal and quantum regime on moderately damped NbN/MgO/NbN Josephson junctions with very low critical current density (’ 2A/cm2). We observed three distinct regimes: below 90 mK the width of the switching distributions is constant within the experimental error, while from 90 mK to 1.6 K the width increases with temperature, this change of behavior signaling the standard transition from macroscopic quantum tunneling (MQT) to thermal activation (TA) regime respectively. Above 1.6 K we find effects of anti-correlation between the bath temperature and thermal fluctuations since the width of the histograms starts to collapse, and indications of a transition to a third regime called Phase Diffusion (PD) are evident, such as the change of the switching distributions symmetry. Experimental data have been analyzed through numerical fitting of the switching probability and Monte Carlo simulations, and we found a good agreement with theoretical expectations based on multiple re-trapping processes, which strongly depend on the junction damping. The parameters which completely characterize the dynamics of such moderately damped Josephson junctions have been also extracted.We report on measurements of the switching current probability both in the thermal and quantum regime on moderately damped NbN/MgO/NbN Josephson junctions with very low critical current density (’ 2A/cm2). We observed three distinct regimes: below 90 mK the width of the switching distributions is constant within the experimental error, while from 90 mK to 1.6 K the width increases with temperature, this change of behavior signaling the standard transition from macroscopic quantum tunneling (MQT) to thermal activation (TA) regime respectively. Above 1.6 K we find effects of anti-correlation between the bath temperature and thermal fluctuations since the width of the histograms starts to collapse, and indications of a transition to a third regime called Phase Diffusion (PD) are evident, such as the change of the switching distributions symmetry. Experimental data have been analyzed through numerical fitting of the switching probability and Monte Carlo simulations, and we found a good agreement with theoretical expectations based on multiple re-trapping processes, which strongly depend on the junction damping. The parameters which completely characterize the dynamics of such moderately damped Josephson junctions have been also extracted.

Physics ProcediaJan 1, 20121 citation

Coherent transient effects in Josephson junctions

R. Bonifacio, Daniel N. Rogovin, Marlan O. Scully

Optics CommunicationsMay 1, 19778 citations

{U}_{\mathit{int}}

between a current-biased junction and an AlN dilatational resonator should depend on the angular frequency of the resonator ${\ensuremath{\omega}}_{R}$ in a power-law fashion [A. N. Cleland and M. R. Geller, Phys. Rev. Lett. 93, 070501 (2004)], specifically ${U}_{\mathit{int}}\ensuremath{\propto}{({\ensuremath{\omega}}_{R})}^{n}$, where

n=1∕2

. We find that for any value of

n

in the range

0<n<1

the junction's tunneling rate exhibits a nonmonotonic dependence on ${\ensuremath{\omega}}_{R}$, and for

n=1∕2

, the tunneling rate is maximally suppressed for ${\ensuremath{\omega}}_{R}∕{\ensuremath{\omega}}_{J}\ensuremath{\approx}1$, where ${\ensuremath{\omega}}_{J}$ is the bias current-dependent plasma frequency of the junction.