Superconducting electrical circuits can be used to study the physics of cavity quantum electrodynamics (QED) in new regimes, therefore realizing circuit QED. For quantum information processing and quantum optics, an interesting regime of circuit QED is the dispersive regime, where the detuning between the qubit transition frequency and the resonator frequency is much larger than the interaction strength. In this paper, we investigate how non-linear corrections to the dispersive regime affect the measurement process. We find that in the presence of pure qubit dephasing, photon population of the resonator used for the measurement of the qubit act as an effective heat bath, inducing incoherent relaxation and excitation of the qubit. Measurement thus induces both dephasing and mixing of the qubit, something that can reduce the quantum non-demolition aspect of the readout. Using quantum trajectory theory, we show that this heat bath can induce quantum jumps in the qubit state and reduce the achievable signal-to-noise ratio of a homodyne measurement of the voltage.
We develop a time-dependent Schrieffer-Wolff-Lindblad perturbation theory to study effective interactions for driven open quantum systems. The starting point of our analysis is a given Lindblad equation, based on which we obtain an effective (averaged) map that describes the renormalization of both the Hamiltonian and collapse operators due to the drive. As a case study, we apply this method to the dispersive readout of a transmon qubit and derive an effective disperive map that describes measurement-induced dephasing and Stark shift for the transmon. The effective map we derive is completely …
We present and demonstrate a general three-step method for extracting the quantum efficiency of dispersive qubit readout in circuit QED. We use active depletion of post-measurement photons and optimal integration weight functions on two quadratures to maximize the signal-to-noise ratio of the non-steady-state homodyne measurement. We derive analytically and demonstrate experimentally that the method robustly extracts the quantum efficiency for arbitrary readout conditions in the linear regime. We use the proven method to optimally bias a Josephson traveling-wave parametric amplifier and to qua…
Quantum parameter estimation via dispersive measurement in circuit QED
研究了电路量子电动力学中的量子参数估计问题。基于Metropolis Hastings（MH）算法和Markov chain Monte Carlo（MCMC）积分，提出了一种新的由未知参数估计的随机主方程计算Fisher信息的算法。这里，Fisher信息以对数似然函数的形式表示，并进一步由MCMC积分近似。数值结果表明，Fisher信息的单次演化可以逼近量子费舍尔信息.在短时间内的系综演化中也观察到了同样的现象。这些结果证明了该算法的有效性。
In superconducting circuit architectures for quantum computing, microwave resonators are often used both to isolate qubits from the electromagnetic environment and to facilitate qubit state readout. We analyze the full counting statistics of photons emitted from such driven readout resonators both in and beyond the dispersive approximation. We calculate the overlap between emitted-photon distributions for the two qubit states and explore strategies for its minimization with the purpose of increasing fidelity of intensity-sensitive readout techniques. In the dispersive approximation and at negl…
Qubit-photon interactions in a cavity: Measurement induced dephasing and number splitting
我们从理论上研究了电路QED结构中超导量子比特的测量诱导退相，并将结果与Schuster { \it et al.}的实验结果进行了比较，[Phys. Rev. Lett. 94，123602（2005）]。量子位与谐振器的强耦合导致量子位跃迁频率的显著ac-Stark偏移。结果，填充谐振器的光子数的量子波动导致量子比特的退相。我们发现量子比特谱的预测线形和实验结果之间有很好的一致性。此外，在强色散极限下，每个光子的斯塔克位移与腔衰减速率和量子比特线宽相比很大，我们预测量子比特光谱将分裂成多个峰，每个峰对应于腔中不同数量的光子。
Discrete time crystals (DTC) have been demonstrated experimentally in several different quantum systems in the past few years. Spin couplings and cavity losses have been shown to play crucial roles for realizing DTC order in open many-body systems out of equilibrium. Recently, it has been proposed that eternal and transient DTC can be present with an open Floquet setup in the thermodynamic limit and in the deep quantum regime with few qubits, respectively. In this work, we consider the effects of spin damping and spin dephasing on the DTC order in spin-optomechanical and open cavity systems in…
In the cavity-QED architecture, photon number fluctuations from residual cavity photons cause qubit dephasing due to the AC Stark effect. These unwanted photons originate from a variety of sources, such as thermal radiation, leftover measurement photons, and crosstalk. Using a capacitively-shunted flux qubit coupled to a transmission line cavity, we demonstrate a method that identifies and distinguishes coherent and thermal photons based on noise-spectral reconstruction from time-domain spin-locking relaxometry. Using these measurements, we attribute the limiting dephasing source in our system…
Full-Wave Green's-Function Modeling of Collective Single-Photon Emission in Non-Markovian Open-System QED with Finite-Bandwidth Compensation of Dispersive Interactions
Pohang University of Science and Technology（韩国科学技术院）；Purdue University（普渡大学）
Hybrid devices based on the superconducting qubits have emerged as a promising platform for controlling the quantum states of macroscopic resonators. The nonlinearity added by a qubit can be a valuable resource for such control. Here we study a hybrid system consisting of a mechanical resonator longitudinally coupled to a transmon qubit. The qubit readout can be done by coupling to a readout mode like in c-QED setup. The coupling between the mechanical resonator and transmon qubit can be implemented by modulation of the SQUID inductance. In such a tri-partite system, we analyze the steady-stat…
We develop a theoretical framework to describe the scattering of photons against a two-level quantum emitter with arbitrary correlated dephasing noise. This is particularly relevant to waveguide-QED setups with solid-state emitters, such as superconducting qubits or quantum dots, which couple to complex dephasing environments in addition to the propagating photons along the waveguide. Combining input-output theory and stochastic methods, we predict the effect of correlated dephasing in single-photon transmission experiments with weak coherent inputs. We discuss homodyne detection and photon co…
Discrete time-translation symmetry breaking can be observed in periodically-driven systems oscillating at a fraction of the frequency of the driving force. However, with the exception of the parametric instability in period-doubling, multi-periodic driving does not lead to an instability threshold. In this paper, we point out that quantum vacuum fluctuations can be generically employed to induce period multiplication. In particular, we discuss the period-tripled states in circuit QED and propose a microwave setup. We show that for weak dissipation or strong driving, the system exhibits a non-e…
We study the emission spectrum of a qubit under deep strong driving in the high-frequency dispersive regime when the driving frequency and strength exceed significantly the qubit transition frequency. Closed-form expressions for the steady-state first-order field correlation function and the multiphoton emission spectrum are obtained. The spectrum comprises a series of narrow delta-like lines that stem from coherent processes and Lorenzian peaks that result from the incoherent scattering of photons. The oscillating dependence of the widths of the emission lines on the driving strength is predi…
