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arXiv:1511.06280 · Physical review. B./Physical review. B

Correlated Cooper pair transport and microwave photon emission in the dynamical Coulomb blockade

Juha Leppäkangas, M. Fogelström, Michael Marthaler, Göran Johansson

Published Jan 11, 2016• 30 citations
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Abstract

Using a perturbation expansion to the fourth order in a junction critical current, the authors study the generation of nonclassical microwave radiation by inelastic Cooper pair tunneling in a small voltage-biased Josephson junction connected to a superconducting transmission line. The second order in the tunneling current only allows consideration of independent events. Pushing the calculation to the fourth order allows capture of the temporal correlations in the charge transport and their connection to the ones in the emitted electromagnetic radiation.

DOI
10.1103/physrevb.93.014506

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Using a perturbation expansion to the fourth order in a junction critical current, the authors study the generation of nonclassical microwave radiation by inelastic Cooper pair tunneling in a small voltage-biased Josephson junction connected to a superconducting transmission line. The second order in the tunneling current only allows consideration of independent events. Pushing the calculation to the fourth order allows capture of the temporal correlations in the charge transport and their connection to the ones in the emitted electromagnetic radiation.
We study microwave radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. An input-output formalism for the radiation field is established, using a perturbation expansion in the junction's critical current. Using output field operators solved up to the second order, we estimate the spectral density and the second-order coherence of the emitted field. For typical transmission line impedances and at frequencies below the main emission peak at the Josephson frequency, radiation occurs predominantly due to two-photon emission. This emission is characterized by a high degree of photon bunching if detected symmetrically around half of the Josephson frequency. Strong phase fluctuations in the transmission line make related nonclassical phase-dependent amplitude correlations short lived, and there is no steady-state two-mode squeezing. However, the radiation is shown to violate the classical Cauchy-Schwarz inequality of intensity cross-correlations, demonstrating the nonclassicality of the photon pair production in this region.
We study microwave radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. An input-output formalism for the radiation field is established, using a perturbation expansion in the junction's critical current. Using output field operators solved up to the second order, we estimate the spectral density and the second-order coherence of the emitted field. For typical transmission line impedances and at frequencies below the main emission peak at the Josephson frequency, radiation occurs predominantly due to two-photon emission. This emission is characterized by a high degree of photon bunching if detected symmetrically around half of the Josephson frequency. Strong phase fluctuations in the transmission line make related nonclassical phase-dependent amplitude correlations short lived, and there is no steady-state two-mode squeezing. However, the radiation is shown to violate the classical Cauchy-Schwarz inequality of intensity cross-correlations, demonstrating the nonclassicality of the photon pair production in this region.
We explore the photonic (bright) side of the dynamical Coulomb blockade (DCB) by measuring the radiation emitted by a dc voltage-biased Josephson junction embedded in a microwave resonator. In this regime Cooper pair tunneling is inelastic and associated with the transfer of an energy 2eV into the resonator modes. We have measured simultaneously the Cooper pair current and the photon emission rate at the resonance frequency of the resonator. Our results show two regimes, in which each tunneling Cooper pair emits either one or two photons into the resonator. The spectral properties of the emitted radiation are accounted for by an extension to DCB theory.
We study scattering of propagating microwave fields by a DC-voltage-biased Josephson junction. At sub-gap voltages, a small Josephson junction works merely as a non-linear boundary that can absorb, amplify, and diversely convert propagating microwaves. We find that in the leading-order perturbation theory of the Josephson coupling energy, the spectral density and quadrature fluctuations of scattered thermal and coherent radiation can be described in terms of the well-known P(E)P(E)P(E) function. Applying this, we show how thermal and coherent radiation can be absorbed and amplified in a circuit with a resonance frequency. We also show when a coherent input can create a two-mode squeezed output. In addition, we evaluate scattering amplitudes between arbitrary photon-number (Fock) states, describing individual photon multiplication and absorption processes occuring at the junction.
We investigate electromagnetic radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. At frequencies below the well-known emission peak at the Josephson frequency (2eV/h), extra radiation is triggered by quantum fluctuations in the transmission line. For weak tunneling couplings and typical Ohmic transmission lines, the corresponding photon-flux spectrum is symmetric around half the Josephson frequency, indicating that the photons are predominately created in pairs. By establishing an input-output formalism for the microwave field in the transmission line, we give further evidence for this nonclassical photon pair production, demonstrating that it violates the classical Cauchy-Schwarz inequality for two-mode flux cross correlations. In connection to recent experiments, we also consider a stepped transmission line, where resonances increase the signal-to-noise ratio.
We demonstrate theoretically that charge transport across a Josephson junction, voltage-biased through a resistive environment, produces antibunched photons. We develop a continuous-mode description of the emitted radiation field in a semi-infinite transmission line terminated by the Josephson junction. Within a perturbative treatment in powers of the tunneling coupling across the Josephson junction, we capture effects originating in charging dynamics of consecutively tunneling Cooper pairs. We find that within a feasible experimental setup the Coulomb blockade provided by high zero-frequency impedance can be used to create antibunched photons at a very high rate and in a very versatile frequency window ranging from a few GHz to a THz.