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Soviet Journal of Low Temperature Physics

Photoinduced macroscopic quantum tunneling in superconducting systems

A. A. Golub

Published Jun 1, 1985• 0 citations
Publisher

Abstract

The problem of macroscopic quantum coherence in superconducting systems is studied theoretically. A two-level model of a SQUID with phonon-field coupling is considered. The probability of a transition, induced by a periodic perturbation, occurring between the lowest states of the two-well potential, describing the phase dependence of the energy in the SQUID, is calculated for a particular region of this coupling. Use is made of the conformity between this model and the resonance-level model. We also consider the strong-viscosity limit. It is shown that in this case the two-level model cannot be used to describe quantum interferometers.

DOI
10.1063/10.0031304

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The problem of macroscopic quantum coherence in superconducting systems is studied theoretically. A two-level model of a SQUID with phonon-field coupling is considered. The probability of a transition, induced by a periodic perturbation, occurring between the lowest states of the two-well potential, describing the phase dependence of the energy in the SQUID, is calculated for a particular region of this coupling. Use is made of the conformity between this model and the resonance-level model. We also consider the strong-viscosity limit. It is shown that in this case the two-level model cannot be used to describe quantum interferometers.
We consider the theoretical problem of resonant phenomena in the macroscopic quantum tunneling for an rf superconducting quantum interference device in the presence of an external irradiating field. The transition probability between different flux states is studied by varying the external parameters of the double-well potential describing the system in a way that the pumping level in the left potential well is close to one of the levels in the right potential well. The dependence of the transition probability on the external drive of the system shows two resonance peaks, the former connected with the resonant tunneling and the latter with the resonant pumping. The relative position of the peaks depends on the pumping frequency $\ensuremath{\omega}$ and on the system parameters.
Recently there has been interest in macroscopic systems which can be described in terms of the quantum dynamics of the same collective variables which describe their classical behavior. In particular, there has been considerable interest in the following questions: (1) Is it possible to observe unambiguous evidence of the quantum-mechanical nature of a macroscopic collective coordinate? (2) In what way is the quantum mechanics of a macroscopic variable different from that of a microscopic variable or, in other words, what is the effect of dissipation on the dynamics of a quantum-mechanical system? Spectroscopic evidence of the quantization of energy levels can be found by measuring the system's response to an applied ac perturbation, exploiting the quantum-mechanical relation between energy and frequency. The specific system studied is a superconducting quantum interference device (SQUID). It is shown that a time-varying magnetic field through the superconducting loop in a rf SQUID can cause transitions between different fluxoid states. The role of dissipation is discussed in detail, and it is shown that in the case that dissipation is characterized by linear damping in the classical limit, the photon-absorption process depends critically on the ratio of the resistance of the weak link to the fundamental unit of resistance h/e2{e}^{2}e2. .AE
We present a theoretical study of the resonant quantum behavior for a macroscopic superconducting system interacting with an external microwave at proper frequency. Here we consider a system described by a double well potential, an rf-SQUID, in the extremely underdamped regime. Numerical simulations for resonant phenomena have been performed for this system, whose parameters belong to the range typically used in the experiments. The dependence of the transition probability W on the external drive of the system, φx, can show three resonance peaks, in a small microwave frequency range. One peak is connected with the anticrossing and the other two with the external microwave frequency ν. The relative position and the height of the two lateral peaks depend on the microwave frequency. This behavior is studied here for the first time.
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.
It is shown that a time-varying magnetic field through the superconducting loop in a rf SQUID can cause transitions between the fluxoid states. Experimental observation of these transitions should constitute evidence for the quantum mechanical character of the macroscopic variable, the total flux through the loop. In the case that dissipation is characterized by linear damping in the quasiclassical limit, the photon absorption process depends critically on the ratio of the resistance of the weak link to the fundamental unit of resistance he2\frac{h}{{e}^{2}}e2h​.
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.