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Amplification and cross-Kerr nonlinearity in waveguide quantum electrodynamics
摘要： We explore amplification and cross-Kerr nonlinearity by a three-level emitter (3LE) embedded in a waveguide and driven by two light beams. The coherent amplification and cross-Kerr nonlinearity were demonstrated in recent experiments, respectively, with a V and a ladder-type 3LE coupled to an open superconducting transmission line carrying two microwave fields. Here, we consider (cid:2), V, and ladder-type 3LE, and compare the efficiency of coherent and incoherent amplification as well as the magnitude of the cross-Kerr phase shift in all three emitters. We apply the Heisenberg-Langevin equations approach to investigate the scattering of a probe and a drive beam, both initially in coherent states. We particularly calculate the regime of the probe and drive powers when the 3LE acts most efficiently as a coherent amplifier and derive the second-order coherence of amplified probe photons. Finally, we apply the Kramers-Kronig relations to correlate the amplitude and phase response of the probe beam, which are used in finding the coherent amplification and the cross-Kerr phase shift in these systems.
关键词： waveguide quantum electrodynamics,three-level emitter,cross-Kerr nonlinearity,amplification,Heisenberg-Langevin equations,Kramers-Kronig relations
更新于2025-09-23 15:21:01
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Single-photon limit of dispersive readout of a qubit with a photodetector
摘要： We study the dispersive readout of a qubit in the ultimate limit of a single-photon probe. The use of a single-photon probe avoids the errors due to nonorthogonality of coherent states. A photodetector is used in the scheme we consider. The dynamics of the system is studied using the Heisenberg-Langevin equations. We treat the counter-rotating terms in the Hamiltonian perturbatively, which leads to the Bloch-Siegert shift in the resonator frequency. It is shown how the shift can improve the readout. The theory of photon transport through the qubit and the resonator it couples to is provided while taking the effect of the counter-rotating terms into account. To calculate the readout contrast, we use two approaches. The first one neglects the qubit relaxation and allows us to derive a compact expression for the contrast. Also, we obtain simple estimates for the system parameters to maximize the contrast. The second approach accounts for the qubit relaxation, which allows us to further improve the contrast. We demonstrate that for a readout time of 1 μs, a contrast of more than 75% can be achieved for an ideal detector and single-photon source.
关键词： Heisenberg-Langevin equations,qubit,dispersive readout,photon transport,Bloch-Siegert shift,readout contrast,photodetector,single-photon probe
更新于2025-09-23 15:21:01