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arXiv:1707.06400 · Physical Review Letters

Reflective Amplification without Population Inversion from a Strongly Driven Superconducting Qubit

P. Y. Wen, Anton Frisk Kockum, Hou Ian, Jung-Chieh Chen, Franco Nori, I.-C. Hoi

Published Feb 6, 2018• 51 citations
arXivHTMLPDF

Abstract

Amplification of optical or microwave fields is often achieved by strongly driving a medium to induce population inversion such that a weak probe can be amplified through stimulated emission. Here we strongly couple a superconducting qubit, an artificial atom, to the field in a semi-infinite waveguide. When driving the qubit strongly on resonance such that a Mollow triplet appears, we observe a 7% amplitude gain for a weak probe at frequencies in between the triplet. This amplification is not due to population inversion, neither in the bare qubit basis nor in the dressed-state basis, but instead results from a four-photon process that converts energy from the strong drive to the weak probe. We find excellent agreement between the experimental results and numerical simulations without any free fitting parameters. Since our device consists of a single two-level artificial atom, the simplest possible quantum system, it can be viewed as the most fundamental version of a four-wave-mixing parametric amplifier.

DOI
10.1103/physrevlett.120.063603

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Amplification of optical or microwave fields is often achieved by strongly driving a medium to induce population inversion such that a weak probe can be amplified through stimulated emission. Here we strongly couple a superconducting qubit, an artificial atom, to the field in a semi-infinite waveguide. When driving the qubit strongly on resonance such that a Mollow triplet appears, we observe a 7% amplitude gain for a weak probe at frequencies in between the triplet. This amplification is not due to population inversion, neither in the bare qubit basis nor in the dressed-state basis, but instead results from a four-photon process that converts energy from the strong drive to the weak probe. We find excellent agreement between the experimental results and numerical simulations without any free fitting parameters. Since our device consists of a single two-level artificial atom, the simplest possible quantum system, it can be viewed as the most fundamental version of a four-wave-mixing parametric amplifier.
We demonstrate amplification of a microwave signal by a strongly driven two-level system in a coplanar waveguide resonator. The effect, similar to the dressed-state lasing known from quantum optics, is observed with a single quantum system formed by a persistent current (flux) qubit. The transmission through the resonator is enhanced when the Rabi frequency of the driven qubit is tuned into resonance with one of the resonator modes. Amplification as well as linewidth narrowing of a weak probe signal has been observed. The stimulated emission in the resonator has been studied by measuring the emission spectrum. We analyzed our system and found an excellent agreement between the experimental results and the theoretical predictions obtained in the dressed-state model.
Reaching the quantum limit for added noise in amplification processes is an important step toward many quantum technologies. Nearly quantum-limited traveling-wave parametric amplifiers with Josephson junction arrays have been developed and recently even become commercially available. However, the fundamental question of whether a single atom also can reach this quantum limit has not yet been answered in practice. Here, we investigate the amplification of a microwave probe signal by a superconducting artificial atom, a transmon, at the end of a semi-infinite transmission line, under a strong pump field. The end of the transmission line acts as a mirror for microwave fields. Due to the weak anharmonicity of the artificial atom, the strong pump field creates multi-photon excitations among the dressed states. Transitions between these dressed states, Rabi sidebands, give rise to either amplification or attenuation of the weak probe. We obtain a maximum power amplification of 1.402 ± 0.025, higher than in any previous experiment with a single artificial atom. We achieve near-quantum-limited added noise (0.157 ± 0.003 quanta; the quantum limit is 0.143 ± 0.006 quanta for this level of amplification), due to quantum coherence between Rabi sidebands, leading to constructive interference between emitted photons.
Abstract We investigate three types of amplification processes for light fields coupling to an atom near the end of a one-dimensional (1D) semi-infinite waveguide. We consider two setups where a drive creates population inversion in the bare or dressed basis of a three-level atom and one setup where the amplification is due to higher-order processes in a driven two-level atom. In all cases, the end of the waveguide acts as a mirror for the light. We find that this enhances the amplification in two ways compared to the same setups in an open waveguide. Firstly, the mirror forces all output from the atom to travel in one direction instead of being split up into two output channels. Secondly, interference due to the mirror enables tuning of the ratio of relaxation rates for different transitions in the atom to increase population inversion. We quantify the enhancement in amplification due to these factors and show that it can be demonstrated for standard parameters in experiments with superconducting quantum circuits.
Abstract This study conducts a theoretical investigation into the signal amplification arising from multiple Rabi sideband coherence within a waveguide quantum electrodynamics system. We utilize a semi-infinite waveguide to drive an anharmonic multi-level transmon with a strong coherent microwave field, examining the scattering behaviour by introducing a probe signal. Our findings show signal amplification under specific resonant conditions, presenting spectra that reveal finer details than previously documented in the literature. To elucidate the mechanisms behind this amplification, we develop a model that explicitly accounts for multiple dressed sidebands in the presence of a strong driving field. From this model, we derive the reflection amplitude of the probe signal. Notably, our results indicate that amplification can occur due to either population inversion or, in some instances, through the constructive interference of multiple sidebands even in the absence of population inversion. Additionally, we explore how qubit dephasing impacts the amplification process.
This study conducts a theoretical investigation into the signal amplification arising from multiple Rabi sideband coherence within a one-dimensional waveguide quantum electrodynamics system. We utilize a semi-infinite waveguide to drive an anharmonic multi-level transmon with a strong coherent microwave field, examining the scattering behavior by introducing a probe signal. Our findings reveal signal amplification under specific resonant conditions, presenting spectra that reveal finer details than previously documented in the literature. To elucidate the mechanisms behind this amplification, we develop a model that explicitly accounts for multiple dressed sidebands in the presence of a strong driving field. From this model, we derive the reflection amplitude of the probe signal. Notably, our results indicate that amplification can occur due to either population inversion or, in some instances, through the constructive interference of multiple sidebands even in the absence of population inversion. Additionally, we explore how qubit dephasing impacts the amplification process.
We study the response of a magnetic-field-driven superconducting qubit strongly coupled to a superconducting coplanar waveguide resonator. We observed a strong amplification/damping of a probing signal at different resonance points corresponding to a one and two-photon emission/absorption. The sign of the detuning between the qubit frequency and the probe determines whether amplification or damping is observed. The larger blue detuned driving leads to two-photon lasing while the larger red detuning cools the resonator. Our experimental results are in good agreement with the theoretical model of qubit lasing and cooling at the Rabi frequency.