Abstract
Inelastic Cooper pair tunneling across a voltage-biased Josephson junction in series with one or more microwave cavities can generate photons via resonant processes in which the energy lost by the Cooper pair matches that of the photon(s) produced. We generalize previous theoretical treatments of such systems to analyze cases where two or more different photon generation processes are resonant simultaneously. We also explore in detail a specific case where the generation of a single photon in one cavity mode is simultaneously resonant with the generation of two photons in a second mode. We find that the coexistence of the two resonances leads to effective couplings between the modes which in turn generate entanglement.
Highlights
Circuits in which voltage biased Josephson junctions (JJ) are combined with microwave cavities provide an ideal platform for exploring a wide range of microwave photonics
All of the voltage energy associated with tunneling Cooper pairs must be transferred into photons and the properties of JJ-cavity systems can be tuned over a wide range either in-situ or by design,1–6
Such resonances can be selected by tuning the voltage and are modelled theoretically using a rotating wave approximation (RWA) which leads to a convenient time-independent Hamiltonian for the system 9,10,12,19
Summary
Circuits in which voltage biased Josephson junctions (JJ) are combined with microwave cavities provide an ideal platform for exploring a wide range of microwave photonics. All of the voltage energy associated with tunneling Cooper pairs must be transferred into photons and the properties of JJ-cavity systems can be tuned over a wide range either in-situ or by design,. Energy exchange between charge carriers and microwaves in JJ-cavity systems is concentrated at resonances where the energy lost by a given Cooper-pair is commensurate with that of the photons in one or more microwave mode(s) 1–3. Such resonances can be selected by tuning the voltage and are modelled theoretically using a rotating wave approximation (RWA) which leads to a convenient time-independent Hamiltonian for the system 9,10,12,19.
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