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arXiv:quant-ph/0611255

Resonance phenomena in Macroscopic Quantum Tunneling: the small viscosity limit

Yu. N. Ovchinnikov, S. Rombetto, B. Ruggiero, Valentina Corato, P. Silvestrini

Published Nov 25, 2006• 0 citations
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Abstract

We present a new theoretical approach to describe the quantum behavior of a macroscopic system interacting with an external irradiation field, close to the resonant condition. Here we consider the extremely underdamped regime for a system described by a double well potential. The theory includes both: transitions from one well to the other and relaxation processes. We simulate resonant phenomena in a rf-SQUID, whose parameters lie in the range typically used in the experiments. The dependence of the transition probability W on the external drive of the system $ϕ_x$ shows three resonance peaks. One peak is connected with the resonant tunneling and the two others with the resonant pumping. The relative position of the two peaks correlated to the resonant pumping depends on the pumping frequency $ν$ and on the system parameters. The preliminary measurements on our devices show a low dissipation level and assure that they are good candidates in order to realize new experiments on the resonant phenomena in the presence of an external microwave irradiation of proper frequency.

DOI
10.48550/arxiv.quant-ph/0611255

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We present a new theoretical approach to describe the quantum behavior of a macroscopic system interacting with an external irradiation field, close to the resonant condition. Here we consider the extremely underdamped regime for a system described by a double well potential. The theory includes both: transitions from one well to the other and relaxation processes. We simulate resonant phenomena in a rf-SQUID, whose parameters lie in the range typically used in the experiments. The dependence of the transition probability W on the external drive of the system ϕxϕ_xϕx​ shows three resonance peaks. One peak is connected with the resonant tunneling and the two others with the resonant pumping. The relative position of the two peaks correlated to the resonant pumping depends on the pumping frequency ννν and on the system parameters. The preliminary measurements on our devices show a low dissipation level and assure that they are good candidates in order to realize new experiments on the resonant phenomena in the presence of an external microwave irradiation of proper frequency.
We present a new theoretical approach to describe the quantum behavior of a macroscopic system interacting with an external irradiation field, close to the resonant condition. Here we consider the extremely underdamped regime for a system described by a double well potential. The theory includes both: transitions from one well to the other and relaxation processes. We simulate resonant phenomena in a rf-SQUID, whose parameters lie in the range typically used in the experiments. The dependence of the transition probability W on the external drive of the system ϕx\phi_xϕx​ shows three resonance peaks. One peak is connected with the resonant tunneling and the two others with the resonant pumping. The relative position of the two peaks correlated to the resonant pumping depends on the pumping frequency ν\nuν and on the system parameters. The preliminary measurements on our devices show a low dissipation level and assure that they are good candidates in order to realize new experiments on the resonant phenomena in the presence of an external microwave irradiation of proper frequency.
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 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.
We study the resonant quantum behaviour of a macroscopic superconducting system interacting with an external field. First we consider the resonant tunneling assisted by microwave frequency in the moderate underdamped quantum regime. Then we consider the resonant process in the extreme underdamped limit. In both regimes we have investigated a small frequency range, where resonant phenomena take place. The transition probability W from the left to the right potential well has been numerically calculated for an rf-SQUID as function of the external flux φx for both regimes. Results indicate that, in a proper frequency and φx range, the transition probability W can present two or three resonant peaks, depending on the damping regime.
We have developed a quantitative theory of resonant tunneling of magnetic flux between discrete macroscopically distinct quantum states in superconducting quantum interference device systems. The theory is based on the standard density-matrix approach. Its elements include the discussion of the two different relaxation mechanisms that exist for the double-well potential, and description of the ``photon-assisted'' tunneling driven by external rf radiation. It is shown that in the case of coherent flux dynamics, rf radiation should lead to splitting of the peaks of resonant flux tunneling, indicating that the resonant tunneling is a convenient tool for studying macroscopic quantum coherence of flux.