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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
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Ultrafast 3D Bloch-Siegert B1+-mapping using variational modeling
摘要： Purpose: Highly accelerated B1-mapping based on the Bloch–Siegert shift to allow 3D acquisitions even within a brief period of a single breath-hold. Theory and Methods: The B1 dependent Bloch–Siegert phase shift is measured within a highly subsampled 3D-volume and reconstructed using a two-step variational approach, exploiting the different spatial distribution of morphology and B1-field. By appropriate variable substitution the basic non-convex optimization problem is transformed in a sequential solution of two convex optimization problems with a total generalized variation (TGV) regularization for the morphology part and a smoothness constraint for the B1-field. The method is evaluated on 3D in vivo data with retro- and prospective subsampling. The reconstructed B1-maps are compared to a zero-padded low resolution reconstruction and a fully sampled reference. Results: The reconstructed B1-field maps are in high accordance to the reference for all measurements with a mean error below 1% and a maximum of about 4% for acceleration factors up to 100. The minimal error for different sampling patterns was achieved by sampling a dense region in k-space center with acquisition times of around 10–12 s for 3D-acquisitions. Conclusions: The proposed variational approach enables highly accelerated 3D acquisitions of Bloch–Siegert data and thus full liver coverage in a single breath hold.
关键词： fast imaging,Bloch–Siegert shift,single breath hold acquisition,B1-mapping,total generalized variation
更新于2025-09-09 09:28:46