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arXiv:0811.3909 · Physical Review Letters

Microwave Photon Detector in Circuit QED

Guillermo Romero, Juan José García‐Ripoll, E. Solano

Published Apr 29, 2009• 165 citations
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Abstract

In this Letter we design a metamaterial composed of discrete superconducting elements that implements a high-efficiency microwave photon detector. Our design consists of a microwave guide coupled to an array of metastable quantum circuits, whose internal states are irreversibly changed due to the absorption of photons. This proposal can be widely applied to different physical systems and can be generalized to implement a microwave photon counter.

DOI
10.1103/physrevlett.102.173602

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In this Letter we design a metamaterial composed of discrete superconducting elements that implements a high-efficiency microwave photon detector. Our design consists of a microwave guide coupled to an array of metastable quantum circuits, whose internal states are irreversibly changed due to the absorption of photons. This proposal can be widely applied to different physical systems and can be generalized to implement a microwave photon counter.
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 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.
The strong interaction of superconducting integrated circuits with microwave photons forms the basis of circuit quantum electrodynamics (cQED), an attractive paradigm for scalable quantum computing and a test bed for quantum optics in the strong coupling regime [1–6]. While singlephoton detectors are an important component of the standard quantum optics toolbox [7], they have not played a role in cQED, as there are no microwave photon counters currently available. In the search for a microwave component that will emulate the nonlinearity of traditional optical photon counters, it is natural to consider the Josephson junction—a nonlinear, nondissipative superconducting circuit element with tunable microwave-frequency transitions. There has been recent interest in the development of on-chip detectors to probe the microwave radiation emitted by mesoscopic quantum circuits [8–14], including proposals to utilize Josephson circuits as photon counters in the context of cQED [8,9]. This study represents the first experimental measurement of the coincidence counting statistics of microwave photons. We exploit microwaveinduced transitions between discrete energy levels in a Josephson junction to realize an efficient, versatile microwave detector. Moreover, we use a parallelized detector circuit to probe the counting statistics of both coherent and thermal microwave sources. Acircuitdiagramofthesingle-channeldetectorisshown in Fig. 1(a). The Josephson junction is current biased near thecriticalcurrent I0.Thejunctionpotentialenergyisgiven by Uð� Þ¼� I
In order to apply all ideas from quantum optics to the field of quantum circuits, one of the missing ingredients is a high-efficiency single-photon detector. In this work we propose a design for such a device which successfully reaches 100% efficiency with only one absorber. Our photon detector consists of a three-level system (a phase qubit) coupled to a semi-infinite one-dimensional waveguide (a microwave transmission line) which performs highly efficient photodetection in a simplified manner as compared to previous proposals. Using the tools of quantum optics we extensively study the scattering properties of realistic wave packets against this device, thereby computing the efficiency of the detector. We find that the detector has many operating modes, can detect detuned photons, is robust against design imperfections, and can be made broadband by using more than one absorbing element in the design. Many of these ideas could be translated to other single-mode photonic or plasmonic waveguides interacting with three-level atoms or quantum dots.
Superconducting circuits have recently become a major contender for the implementation of quantum computers owing to their compatibility with existing microchip fabrication technologies. Their utility stems largely from their ability to be coupled with resonant cavities for the purposes of trapping and relaying microwave radiation. Because of this feature, scientists are able to transmit quantum information from a variety of qubits. Though quantum-limited amplifiers exist, unfortunately there currently exists no microwave photon counter capable of single shot quantum detection. Hence, we use superconducting circuits with Josephson junctions to design a microwave photon detector based on a modified phase qubit that exhibits a bandwidth of 4GHz, and a detection fidelity of 98%. We use metastable barrier transition (driven by incident photons) to create an avalanche effect analogous to current photo-diodes. Linear coupling of the junction flux with the radiation permits photodetection from an arbitrary quantum source in the GHz range. We show the device to be robust to changes in drive frequency, temporal photon width, and resonator quality factor, and we optimize our device with respect to these parameters. We show the device to be stable over the necessary time scales, and yet sensitive enough to accurately measure photons on demand.
We propose a viable design of a microwave two-photon threshold detector. In essence, the considered scheme is an extension of the existing single-photon detector—a Josephson photomultiplier (JPM)—an absorbing microwave detector based on a capacitively shunted rf superconducting quantum interference device (SQUID). To implement a two-photon threshold detector, we utilize a dimer of resonators—two lumped-element resonators interacting via an asymmetric dc SQUID, with one of the resonators capacitively coupled to the JPM. By specific tuning of the resonator frequencies and the external flux through the dc SQUID coupler, we engineer a nonperturbative two-photon coupling between the resonators. This coupling results in the coherent conversion of a photon pair from one resonator into a single photon in another resonator, enabling selective response to quantum states with at least two photons. We also consider an extended coupler design that allows on-demand switching of two-photon coupling. In addition, we propose the modified JPM design to improve its performance. Our calculations demonstrate that, for realistic circuit parameters, we can achieve more than 99 % fidelity of photon pair detection in less than 50 ns. The considered scheme may serve as a building block for the implementation of efficient photon-number-resolving detectors in circuit QED architecture.
Various types of single-photon counters operating in infrared, ultraviolet, and optical wavelength ranges are successfully used to study electromagnetic fields, analyze radiation sources, and solve problems in quantum informatics. However, their operating principles become ineffective at millimeter band, S-band, and ultra-high frequency bands of wavelengths due to the decrease in quantum energy by 4–5 orders of magnitude. Josephson circuits with discrete Hamiltonians and qubits are a good foundation for the construction of single-photon counters at these frequencies. This paper presents a frequency-tuned microwave photon counter based on a single-junction superconducting quantum interferometer and flux qutrit. The control pulse converts the interferometer into a two-level system for resonance absorption of photons. Decay of the photon-induced excited state changes the magnetic flux in the interferometer, which is measured by a SQUID magnetometer. Schemes for recording the magnetic flux using a DC SQUID or ideal parametric detector, based on a qutrit with high-frequency excitation, are discussed. It is shown that the counter consisting of an interferometer with a Josephson junction and a parametric detector demonstrates high performance and is capable of detecting single photons in a microwave band.