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arXiv:1201.2990 · Physical Review B

Quantum efficiency of a microwave photon detector based on a current-biased Josephson junction

Amrit Poudel, Robert McDermott, Maxim Vavilov

Published Nov 6, 2012• 59 citations
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Abstract

We analyze the quantum efficiency of a microwave photon detector based on a current-biased Josephson junction. We consider the Jaynes-Cummings Hamiltonian to describe coupling between the photon field and the junction. We then take into account the coupling of the junction and the resonator to the environment. We solve the equation of motion of the density matrix of the resonator-junction system to compute the quantum efficiency of the detector as a function of detection time, bias current, and energy relaxation time. Our results indicate that junctions with modest coherence properties can provide efficient detection of single microwave photons, with quantum efficiency in excess of $80%$.

DOI
10.1103/physrevb.86.174506

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We analyze the quantum efficiency of a microwave photon detector based on a current-biased Josephson junction. We consider the Jaynes-Cummings Hamiltonian to describe coupling between the photon field and the junction. We then take into account the coupling of the junction and the resonator to the environment. We solve the equation of motion of the density matrix of the resonator-junction system to compute the quantum efficiency of the detector as a function of detection time, bias current, and energy relaxation time. Our results indicate that junctions with modest coherence properties can provide efficient detection of single microwave photons, with quantum efficiency in excess of 8080%80.
We use a semiclassical formalism to optimize a microwave single-photon detector based on switching events of a current-biased Josephson junction coupled to a resonator. To detect very rare events, the average time between dark counts ${\ensuremath{\tau}}_{\mathrm{dark}}$ should be maximized taking into account that the switching time ${\ensuremath{\tau}}_{\mathrm{sw}}$ should be sufficiently small. We demonstrate that these times can be tuned in a wide range by changing the junction parameters, and ${\ensuremath{\tau}}_{\mathrm{dark}}/{\ensuremath{\tau}}_{\mathrm{sw}}\ensuremath{\sim}{10}^{9}$ can be achieved. Therefore, a junction-resonator arrangement can be used to detect extremely low photon fluxes (e.g., for searching for galactic axions).
Single-photon detection is an energy quantum limit detection (EQLD) of extremely weak electromagnetic waves. Given that the sensitivity of the conventional electromagnetic induction microwave receiver working at room temperature is very limited, as a result of the significantly strong thermal noise, here we analyze the possibility of approaching the EQLD of the weak microwave signal by using a current-biased Josephson junction (CBJJ) detector. By numerically simulating the dynamics for the phase particle of the CBJJ, we propose an approach to describe the discriminability between the probabilistically escaped events of the phase particle with and without the microwave current driving, by measuring the minimum dKC{d}_{\mathrm{KC}}dKC​ index. Our predictions indicate that the experimentally demonstrated CBJJ detector possesses the ability to resolve about a dozen photons. Furthermore, with the minimum detectable signal strength and the saturation threshold, we discuss how to determine the dynamic range of the proposed CBJJ detector. The feasibility of using the proposed CBJJ detector to achieve the EQLD in a microwave band is also discussed.
Detection of light dark matter, such as axion-like particles, puts stringent requirements on the efficiency and dark-count rates of microwave-photon detectors. The possibility of operating a current-biased Josephson junction as a single-microwave photon-detector was investigated through numerical simulations, and through an initial characterization of two Al junctions fabricated by shadow mask evaporation, done in a dilution refrigerator by measuring escape currents at different temperatures, from 40 mK up to the Al transition temperature. The escape dynamics of the junctions were reproduced in the simulation, including the dissipative effects. Inhibition of thermal activation was observed, leaving the macroscopic quantum tunneling as the dominant effect well beyond the crossover temperature.
A Lagrangian formalism is used to derive the Hamiltonian for a λ\lambdaλ/4 resonator shunted by a current-biased Josephson junction. The eigenstates and the quantum dynamics of the system are analyzed numerically, and we show that the system can function as an efficient detector of weak incident microwave fields.