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New Journal of Physics

Theory of deterministic down-conversion of single photons occurring at an impedance-matched Λ system

Kazuki Koshino, K. Inomata, Tsuyoshi Yamamoto, Yasunobu Nakamura

Published Nov 15, 2013• 15 citations
Publisher

Abstract

We theoretically investigate the optical response of a Λ system interacting with a semi-infinite waveguide field. In particular, we focus on the case of an impedance-matched Λ system, in which the two decay rates from the top level are identical. We derive the analytical formulae to evaluate the amplitude and the power spectrum of the output field, and present numerical results assuming an implementation by a circuit quantum electrodynamics system. For a low input power (single-photon regime), input photons are down-converted deterministically by inducing the Raman transition in the Λ system. In contrast, for a high input power (multi-photon regime), the conversion efficiency decreases because of the saturation of the Λ system.

DOI
10.1088/1367-2630/15/11/115010

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We theoretically investigate the optical response of a Λ system interacting with a semi-infinite waveguide field. In particular, we focus on the case of an impedance-matched Λ system, in which the two decay rates from the top level are identical. We derive the analytical formulae to evaluate the amplitude and the power spectrum of the output field, and present numerical results assuming an implementation by a circuit quantum electrodynamics system. For a low input power (single-photon regime), input photons are down-converted deterministically by inducing the Raman transition in the Λ system. In contrast, for a high input power (multi-photon regime), the conversion efficiency decreases because of the saturation of the Λ system.
By driving a dispersively coupled qubit-resonator system, we realize an "impedance-matched" Λ system that has two identical radiative decay rates from the top level and interacts with a semi-infinite waveguide. It has been predicted that a photon input from the waveguide deterministically induces a Raman transition in the system and switches its electronic state. We confirm this through microwave response to a continuous probe field, observing near-perfect (99.7%) extinction of the reflection and highly efficient (74%) frequency down-conversion. These proof-of-principle results lead to deterministic quantum gates between material qubits and microwave photons and open the possibility for scalable quantum networks interconnected with waveguide photons.
In one-dimensional optical setups, light-matter interaction is drastically enhanced by the interference between the incident and scattered fields. Particularly, in the impedance-matched Λ-type three-level systems, a single photon deterministically induces the Raman transition and switches the electronic state of the system. Here, we show that such a Λ system can be implemented by using dressed states of a driven superconducting qubit and a resonator. The input microwave photons are perfectly absorbed and are down-converted into other frequency modes in the same waveguide. The proposed setup is applicable to the detection of single microwave photons and the swapping of the photon and matter qubits.
By properly driving a qubit-resonator system in the strong dispersive regime, we implement an ``impedance-matched'' $\ensuremath{\Lambda}$ system in the dressed states, where a resonant single photon deterministically induces a Raman transition and excites the qubit. Combining this effect and a fast dispersive readout of the qubit, we realize a detector of itinerant microwave photons. We theoretically analyze the single-photon response of the $\ensuremath{\Lambda}$ system and evaluate its performance as a detector. We achieve a high detection efficiency without relying on precise temporal control of the input pulse shape and under a conservative estimate of the system parameters. The detector can also be reset quickly by applying microwave pulses, which allows a short dead time and a high repetition rate.
We theoretically investigate single-photon polarization conversion via scattering by an atom with Λ configuration coupled to a semi-infinite waveguide and discuss the two cases in which the Λ system is non-degenerated and degenerated. By applying the hard-wall boundary condition of the semi-infinite waveguide, it is found that single-photon polarization conversion can be realized with unit probability for both cases under the ideal condition. Together with the polarization conversion, the frequency conversion of a single photon can also be realized with unit probability in the ideal case if the Λ system is not degenerated.
Single-photon detection is a requisite technique in quantum-optics experiments in both the optical and the microwave domains. However, the energy of microwave quanta are four to five orders of magnitude less than their optical counterpart, making the efficient detection of single microwave photons extremely challenging. Here we demonstrate the detection of a single microwave photon propagating through a waveguide. The detector is implemented with an impedance-matched artificial Λ system comprising the dressed states of a driven superconducting qubit coupled to a microwave resonator. Each signal photon deterministically induces a Raman transition in the Λ system and excites the qubit. The subsequent dispersive readout of the qubit produces a discrete 'click'. We attain a high single-photon-detection efficiency of 0.66±0.06 with a low dark-count probability of 0.014±0.001 and a reset time of ∼400 ns. This detector can be exploited for various applications in quantum sensing, quantum communication and quantum information processing.
The up-conversion dynamics of two photons in a three-level system is investigated theoretically. The analysis is based on a rigorous formalism that incorporates the multimode nature of the photon field, enabling quantitative handling of the spatial profiles of the photon pulses. We have derived an analytic formula that connects the wavefunction of two input photons to that of an up-converted output photon. The up-conversion efficiency and the output pulse profile are numerically calculated using this formula.