Photodetection of propagating quantum microwaves in circuit QED

We develop the theory of a metamaterial composed of an array of discrete quantum absorbers inside a one-dimensional waveguide that implements a high-efficiency microwave photon detector. A basic design consists of a few metastable superconducting nanocircuits spread inside and coupled to a one-dimensional waveguide in a circuit QED setup. The arrival of a {\it propagating} quantum microwave field induces an irreversible change in the population of the internal levels of the absorbers, due to a selective absorption of photon excitations. This design is studied using a formal but simple quantum field theory, which allows us to evaluate the single-photon absorption efficiency for one and many absorber setups. As an example, we consider a particular design that combines a coplanar coaxial waveguide with superconducting phase qubits, a natural but not exclusive playground for experimental implementations. This work and a possible experimental realization may stimulate the possible arrival of “all-optical” quantum information processing with propagating quantum microwaves, where a microwave photodetector could play a key role.

💡 Research Summary

The paper presents a comprehensive theoretical framework for a high‑efficiency microwave photon detector based on a metamaterial consisting of discrete quantum absorbers embedded in a one‑dimensional waveguide, a configuration that is naturally suited to circuit‑QED platforms. The authors begin by highlighting the lack of practical single‑photon detectors in the microwave regime, which limits the development of propagating‑microwave quantum information processing. To address this, they propose a detector architecture in which a small number of metastable superconducting circuits—referred to as quantum absorbers—are distributed along a transmission line. Each absorber possesses a ground state |g⟩, an excited state |e⟩ that couples resonantly to the traveling microwave mode, and a long‑lived “measurement” state |m⟩. When a propagating photon is absorbed, the system is promoted from |g⟩ to |e⟩; a rapid, irreversible transition |e⟩→|m⟩ (characterized by rate γ) then records the event by permanently changing the internal population of the absorber.

The dynamics are described by a Jaynes‑Cummings‑type Hamiltonian for the waveguide‑absorber coupling together with a Lindblad master equation that incorporates the non‑unitary |e⟩→|m⟩ decay. Using input‑output theory, the authors first analyze a single absorber. They find that the reflection coefficient vanishes only under an impedance‑matching condition κ = γ/2, where κ is the waveguide‑absorber coupling rate. Even at this optimum, the absorption probability is limited to η≈0.5 because half of the incident energy is transmitted past the absorber.

To overcome this limitation, the paper investigates arrays of N absorbers spaced by half the photon wavelength (λ/2). In this configuration, reflected waves from successive absorbers interfere destructively, effectively canceling the overall back‑scattering. By concatenating the individual scattering matrices, the total transmission matrix yields a reflection amplitude that scales as (1‑η)^N, leading to an overall detection efficiency η_N≈1−(1−η)^N. Numerical evaluation shows that with as few as three to five absorbers, the efficiency exceeds 90 %, while the detector bandwidth remains on the order of a few hundred megahertz, set by the coupling strength and inter‑absorber spacing.

For a concrete implementation, the authors consider a coplanar coaxial waveguide coupled to superconducting phase qubits. Phase qubits provide tunable transition frequencies in the 5–10 GHz range and can be engineered to have a fast, irreversible decay to a read‑out state, typically within tens of nanoseconds. Realistic circuit parameters—capacitance coupling C_c≈10 fF, decay rate γ≈10 MHz, and waveguide loss α≈0.001 dB cm⁻¹—are used in finite‑difference time‑domain simulations. The results confirm that a three‑qubit array spaced by λ/2 yields a detection efficiency of ≈92 % and a usable bandwidth of ≈300 MHz. Moreover, operating at dilution‑refrigerator temperatures (<20 mK) suppresses thermal photon occupation to <10⁻⁵, ensuring an extremely low dark‑count rate.

The paper also discusses practical considerations such as fabrication tolerances, the impact of dephasing and additional loss channels, and read‑out strategies for the measurement state |m⟩ (e.g., dispersive readout via a separate resonator). The authors argue that the required lithographic precision and control electronics are already standard in superconducting quantum circuits, making experimental realization feasible in the near term.

In the concluding section, the authors outline future directions: extending the design to multi‑frequency or broadband operation by varying absorber frequencies, integrating photon‑re‑emission capabilities to realize quantum memories, and optimizing large‑scale detector arrays for quantum networks. Overall, the work establishes a clear pathway toward an “all‑optical” microwave quantum information processing platform where a reliable, high‑efficiency photon detector plays a central role.