Mahmoud Abdel-Aty
We propose a method for analyzing Berry phase for a multi-qubit system of superconducting charge qubits interacting with a microwave field. By suitably choosing the system parameters and precisely controlling the dynamics, novel connection found between the Berry phase and entanglement creations.
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With a counter-diabatic field supplemented to the reference control field, the `shortcut to adiabaticiy' (STA) protocol is implemented in a superconducting phase qubit. The Berry phase measured in a short time scale is in good agreement with the theoretical result acquired from an adiabatic loop. The trajectory of a qubit vector is extracted, verifying the Berry phase alternatively by the integrated solid angle. The classical noise is introduced to the amplitude or phase of the total control field. In the statistics of the Berry phase, the mean with either noise is almost equal to that without…
Geometric phases are well known in classical electromagnetism and quantum mechanics since the early works of Pantcharatnam and Berry. Their origin relies on the geometric nature of state spaces and has been studied in many different systems such as spins, polarized light and atomic physics. Recent works have explored their application in interferometry and quantum computation. Earlier works suggest how to observe these phases in single quantum systems adiabatically driven by external classical devices or sources, where, by classical, we mean any system whose state does not change considerably …
We revisit earlier studies on Berry phases suggested to appear in certain cavity QED settings. It has been especially argued that a non-trivial geometric phase is achievable even in the situation of no cavity photons. We, however, show that such results hinge on imposing the {\it rotating wave approximation} (RWA), while without the RWA no Berry phases occur in these schemes. A geometrical interpretation of our results is obtained by introducing semi-classical energy surfaces which in a simple way brings out the phase space dynamics. With the RWA, a conical intersection between the surfaces em…
The Berry phase (BP) in a quantized light field demonstrated more than a decade ago (Phys. Rev. Lett. 89, 220404) has attracted considerable attentions, since it plays an important role in the cavity quantum electrodynamics. However, it is argued in a recent paper ( Phys. Rev. Lett. 108, 033601) that such a BP is just due to the rotating wave approximation (RWA) and the relevant BP should vanish beyond this approximation. Based on a consistent analysis we conclude in this letter that the BP in a generic Rabi model actually exists, no matter whether the RWA is applied. The existence of BP is al…
We propose a scheme for generating entangled states for two superconducting quantum interference devices in a thermal cavity with the assistance of a microwave pulse.
We present a way to realize quantum information transfer with superconducting flux qubits coupled to a cavity. Because only resonant qubit-cavity interaction and resonant qubit-pulse interaction are applied, the information transfer can be performed much faster, when compared with the previous proposals. This proposal does not require adjustment of the qubit level spacings during the operation. Moreover, neither uniformity in the device parameters nor exact placement of qubits in the cavity is needed by this proposal.
We have created a quantum three-level ladder system with the cavity dispersive energy level in a superconducting circuit quantum electrodynamics system consisting of a transmon qubit and a cavity, and have directly observed the Autler-Townes splitting effect instead of representing it by the probability of the qubit being at each level. A coupler tone is applied on the transition between the second excited state of transmon and cavity dispersive level, while the cavity spectrum is probed. A doublet transmission and anormalous dispersion spectrum of the cavity level is clearly shown. The invers…
We present a scheme to achieve maximally entangled states, controlled phase-shift gate, and SWAP gate for two superconducting-quantum-interference-device (SQUID) qubits, by placing SQUIDs in a microwave cavity. We also show how to transfer quantum information from one SQUID qubit to another. In this scheme, no transfer of quantum information between the SQUIDs and the cavity is required, the cavity field is only virtually excited and thus the requirement on the quality factor of the cavity is greatly relaxed.
Motivated by the work [Phys. Rev. Lett. 89, 220404 (2002)] for detecting the vacuum-induced Berry phases with two-mode Jaynes-Cummings models (JCMs), we show here that, for a parameter-dependent single-mode JCM, certain atom-field states also acquire the photon-number-dependent Berry phases after the parameter slowly changed and eventually returned to its initial value. This geometric effect related to the field quantization still exists, even the filed is kept in its vacuum state. Specifically, a feasible Ramsey interference experiment with cavity quantum electrodynamics (QED) system is desig…
We present a measurement scheme for observing the Berry phase in a flux assisted Cooper pair pump - the Cooper pair sluice. In contrast to the recent experiments, in which the sluice was employed to generate accurate current through a resistance, we consider a device in a superconducting loop. This arrangement introduces a connection between the pumped current and the Berry phase accumulated during the adiabatic pumping cycles. From the adiabaticity criterion, we derive equations for the maximum pumped current and optimize the sluice accordingly. These results apply also to the high accuracy p…
We propose schemes to create cluster states and W states by many superconducting-quantum-interference-device (SQUID) qubits in cavities under the influence of the cavity decay. Our schemes do not require auxiliary qubits, and the excited levels are only virtually coupled throughout the scheme, which could much reduce the experimental challenge. We consider the cavity decay in our model and analytically demonstrate its detrimental influence on the prepared entangled states.
We present a novel approach for studying the dynamics of a superconducting qubit in a cavity. We succeed in linearizing the Hamiltonian through the application of an appropriate unitary transformation followed by a rotating wave approximation (RWA). For certain values of the parameters involved, we show that it is possible to obtain a a Jaynes-Cummings type Hamiltonian. As an example, we show the existence of super-revivals for the qubit inversion.
A scheme for implementing 2-qubit quantum controlled phase gate (QCPG) is proposed with two superconducting quantum interference devices (SQUIDs) in a cavity. The gate operations are realized within the two lower flux states of the SQUIDs by using a quantized cavity field and classical microwave pulses. Our scheme is achieved without any type of measurement, does not use the cavity mode as the data bus and only requires a very short resonant interaction of the SQUID-cavity system. As an application of the QCPG operation, we also propose a scheme for generating the cluster states of many SQUIDs…
Multiplexed Readout of Superconducting Qubits Using a 3D Re-entrant Cavity Filter
提出一种3D重入腔滤波器用于超导量子比特频率多路复用读出，其平面外电容耦合设计可扩展至大规模阵列，兼具大线宽带通与固有Purcell滤波功能，并在四量子比特器件上完成验证。
We propose how to realize a three-step controlled-phase gate of one superconducting qubit simultaneously controlling n qubits selected from N qubits in a cavity (1<n<N). The operation time of this gate is independent of the number n of qubits involved in the gate operation. This phase gate controlling at once n qubits is insensitive to the initial state of the cavity mode and can be used to produce an analogous CNOT gate simultaneously acting on n qubits.
Three-dimensional microwave waveguide cavities are essential tools for many cavity quantum electrodynamics experiments. However, the need to control quantum emitters with dc magnetic fields inside the cavity often limits such experiments to normal-conducting cavities with relatively low quality factors of about $10^4$. Similarly, controlling quantum emitters with dc electric fields in normal- and superconducting waveguide cavities has so far been difficult, because the insertion of dc electrodes has strongly limited the quality factor. Here, we present a method to apply dc electric fields with…
We propose an approach to realize an $n$-qubit controlled-$U$ gate with superconducting quantum interference devices (SQUIDs) in cavity QED. In this approach, the two lowest levels of a SQUID represent the two logical states of a qubit while a higher-energy intermediate level serves the gate manipulation. Our method operates essentially by creating a single photon through one of the control SQUIDs and then performing an arbitrary unitrary transformation on the target SQUID with the assistance of the cavity photon. In addition, we show that the method can be applied to implement an $n $% -qubit…
We propose a simple unconventional geometric scenario to achieve a kind of nontrivial multi-qubit operations with superconducting charge qubits placed in a microwave cavity. The proposed quantum operations are insensitive not only to the thermal state of cavity mode but also to certain random operation errors, and thus may lead to high-fidelity quantum information processing. Executing the designated quantum operations, a class of highly entangled cluster states may be generated efficiently in the present scalable solid-state system, enabling one to achieve one-way quantum computation.
We analyze a new scheme for quantum information processing, with superconducting charge qubits coupled through a cavity mode, in which quantum manipulations are insensitive to the state of the cavity. We illustrate how to physically implement universal quantum computation as well as multi-qubit entanglement based on unconventional geometric phase shifts in this scalable solid-state system. Some quantum error-correcting codes can also be easily constructed using the same technique. In view of the gate dependence on just global geometric features and the insensitivity to the state of cavity mode…
We theoretically study the transmission of a weak probe field under the influence of a strong pump field in a coupled nanomechanical resonator-superconducting microwave cavity system. Using the standard input-output theory, we find that both pulse delay (slow light effect) and advancement (fast light effect) of the probe field can appear in this coupled system provided that we choose the suitable detuning of the pump field from cavity resonance. The magnitude of the delay (advancement) can be tuned continuously by adjusting the power of the pump field. This technique demonstrates great potenti…
We present a way for implementing an n-qubit controlled-rotation gate with three-level superconducting qubit systems in cavity QED. The two logical states of a qubit are represented by the two lowest levels of each system while a higher-energy level is used for the gate implementation. The method operates essentially by preparing a $W$ state conditioned on the states of the control qubits, creating a single photon in the cavity mode, and then performing an arbitrary rotation on the states of the target qubit with assistance of the cavity photon. It is interesting to note that the basic operati…
he Jaynes-Cummings model (JCM) is an very important model for describing interaction between quantized electromagnetic fields and atoms in cavity quantum electrodynamics (QED). This model is generalized in many different direction since it predicts many novel quantum effects that can be verified by modern physics experimental technologies. In this paper, the Berry phase and entropy of the ground state for arbitrary photon number $n$ of a two-atom Jaynes-Cummings model with Kerr like medium are investigated. It is found that there are some correspondence between their images, especially the exi…
Superconducting cavity qubit with tens of milliseconds single-photon coherence time
本文提出一种新型超导腔量子比特，将相干时间提升至34毫秒，比此前结果提高一个数量级以上，并成功存储1024光子薛定谔猫态，展示了其在玻色量子纠错中的潜力。
A cavity-mediated reconfigurable coupling scheme for superconducting qubits
本文提出了一种基于谐振腔的可重构耦合方案，通过动态调整量子比特间的相互作用，实现高保真度的量子门操作，为超导量子处理器提供了增强的交互灵活性。
A superconducting qubit in the strong dispersive regime of a circuit quantum electrodynamics system is a powerful probe for microwave photons in a cavity mode. In this regime, a qubit spectrum is split into multiple peaks, with each peak corresponding to an individual photon number in the cavity (discrete ac Stark shift). Here, we measure the qubit spectrum in the cavity that is driven continuously with a squeezed vacuum field generated by a Josephson parametric amplifier. By fitting the qubit spectrum with a model which takes into account the finite qubit excitation power, the photon number d…
Circuit-QED has demonstrated very strong coupling between individual microwave photons trapped in a superconducting coplanar resonator and nearby superconducting qubits. In this work we show how, by designing a novel interconnect, one can strongly connect the superconducting resonator, via a magnetic interaction, to a small number (perhaps single), of electronic spins. By choosing the electronic spin to be within a Nitrogen Vacancy centre in diamond one can perform optical readout, polarization and control of this electron spin using microwave and radio frequency irradiation. More importantly,…
We report a superconducting artificial atom with an observed quantum coherence time of T2*=95us and energy relaxation time T1=70us. The system consists of a single Josephson junction transmon qubit embedded in an otherwise empty copper waveguide cavity whose lowest eigenmode is dispersively coupled to the qubit transition. We attribute the factor of four increase in the coherence quality factor relative to previous reports to device modifications aimed at reducing qubit dephasing from residual cavity photons. This simple device holds great promise as a robust and easily produced artificial qua…
We present a new optomechanical device where the motion of a micromechanical membrane couples to a microwave resonance of a three-dimensional superconducting cavity. With this architecture, we realize ultrastrong parametric coupling, where the coupling rate not only exceeds the dissipation rates in the system but also rivals the mechanical frequency itself. In this regime, the optomechanical interaction induces a frequency splitting between the hybridized normal modes that reaches 88% of the bare mechanical frequency, limited by the fundamental parametric instability. The coupling also exceeds…
It has been shown that there are not only transverse but also longitudinal couplings between microwave fields and a superconducting qubit with broken inversion symmetry of the potential energy. Using multiphoton processes induced by longitudinal coupling fields and frequency matching conditions, we design a universal algorithm to produce arbitrary superpositions of two-mode photon states of microwave fields in two separated transmission line resonators, which are coupled to a superconducting qubit. Based on our algorithm, we analyze the generation of evenly-populated states and NOON states. Co…
Qubit Noise Sensing via Induced Photon Loss in a Superconducting Cavity
本文提出利用超导谐振腔诱导的光子损失测量量子比特频率噪声，通过中电路测量和后选择分离诱导损失，验证了该方法在强驱动下的噪声表征能力。
Engineering One Axis Twisting via a Dissipative Berry Phase Using Strong Symmetries
该研究提出利用开放量子系统中的强对称性积累原子数依赖的 Berry 相，从而在共振原子–腔系统中通过单轴扭曲动力学生成自旋压缩纠缠态。
Reservoir-Engineered Refrigeration of a Superconducting Cavity with Double-Quantum-Dot Spin Qubits
利用双量子点自旋量子比特实现超导谐振腔的库仑工程制冷，通过门控制实现有效光子过程，验证了毫开尔文级冷却技术。
In this Letter, we demonstrate the generation of multimode entangled states of propagating microwaves. The entangled states are generated by parametrically pumping a multimode superconducting cavity. By combining different pump frequencies, applied simultaneously to the device, we can produce different entanglement structures in a programable fashion. The Gaussian output states are fully characterized by measuring the full covariance matrices of the modes. The covariance matrices are absolutely calibrated using an in situ microwave calibration source, a shot noise tunnel junction. Applying a v…
We propose and experimentally demonstrate a new method to generate arbitrary Fock-state superpositions in a superconducting quantum circuit, where a qubit is dispersively coupled to a microwave cavity mode without the need of fine-frequency tuning. Here the qubit is used to conditionally modulate the probability amplitudes of the Fock state components of a coherent state to those of the desired superposition state, instead of pumping photons one by one into the cavity as in previous schemes. Our method does not require the adjustment of the qubit frequency during the cavity state preparation, …
Berry Phase and Topology in Ultrastrongly Coupled Quantum Light-Matter Systems
本文提出一个理论框架，用于分析二维材料超强耦合到腔电磁场的量子几何与拓扑，并在深度强耦合区域发现向拓扑平凡相的再入转变，通过幺正映射与 Haldane 模型建立联系。
Important tasks in cavity quantum electrodynamics include the generation and control of quantum states of spatially-separated particles distributed in different cavities. An interesting question in this context is how to prepare entanglement among particles located in different cavities, which are important for large-scale quantum information processing. We here consider a multi-cavity system where cavities are coupled to a superconducting (SC) qubit and each cavity hosts many SC qubits. We show that all intra-cavity SC qubits plus the coupler SC qubit can be prepared in an entangled Greenberg…
Dephasing induced by residual thermal photons in the readout resonator is a leading factor limiting the coherence times of qubits in the circuit QED architecture. This residual thermal population, of the order of $10^{-1}$--$10^{-3}$, is suspected to arise from noise impinging on the resonator from its input and output ports. To address this problem, we designed and tested a new type of band-pass microwave attenuator that consists of a dissipative cavity well thermalized to the mixing chamber stage of a dilution refrigerator. By adding such a cavity attenuator inline with a 3D superconducting …
We show that optically active coupled quantum dots embedded in a superconducting microwave cavity can be used to realize a fast quantum interface between photonic and transmon qubits. Single photon absorption by a coupled quantum dot results in generation of a large electric dipole, which in turn ensures efficient coupling to the microwave cavity. Using cavity parameters achieved in prior experiments, we estimate that bi-directional microwave-optics conversion in nanosecond timescales with efficiencies approaching unity is experimentally feasible with current technology. We also outline a prot…
Frequency conversion between microwave and optical photons is a key enabling technology to create links between superconducting quantum processors and to realize distributed quantum networks. We propose a microwave-optical transduction platform based on long-coherence-time superconducting radio-frequency (SRF) cavities coupled to electro-optic optical cavities to mitigate the loss mechanisms that limit the attainment of high conversion efficiency. In the design, we optimize the microwave-optical field overlap and optical coupling losses, while achieving long microwave and optical photon lifeti…
We propose a scheme able to entangle at the steady state a nanomechanical resonator with a microwave cavity mode of a driven superconducting coplanar waveguide. The nanomechanical resonator is capacitively coupled with the central conductor of the waveguide and stationary entanglement is achievable up to temperatures of tens of milliKelvin.
We present a quantum open-system approach to analyze the nonunitary dynamics of a superconducting qubit when it evolves under the influence of external noise. We consider the presence of longitudinal and transverse environmental fluctuations affecting the system's dynamics and model these fluctuations by defining their correlation function in time. By using a Gaussian-like noise correlation, we can study low- and high-frequency noise contribution to decoherence and implement our results in the computation of geometric phases in open quantum systems. We numerically study when the accumulated ph…
We present a way to realize a 3-qubit quantum controlled-phase gate with superconducting qubit systems coupled to a cavity. This proposal does not require adjustment of the qubit level spacings or identical qubit-cavity coupling constants. Moreover, since only a resonant interaction is applied, the gate can be performed fast, within $\sim $ 10 nanosecond. This proposal is quite general, which can be applied to various types of superconducting qubits, atoms trapped in a cavity, or quantum dots coupled to a resonator.
We experimentally demonstrate the coupling at zero magnetic field of an isotopically pure erbium doped yttrium orthosilicate crystal ($^{167}$Er:YSO) to a three-dimensional superconducting cavity with a $Q$ factor of $10^5$. A tunable loop-gap resonator is used, and its resonance frequency is tuned to observe the hyperfine transitions of the erbium sample. The observed spectrum differs from what is predicted by the published spin Hamiltonian parameters. The narrow cavity linewidth also enables the observation of asymmetric line shapes for these hyperfine transitions. Such a broadly tunable sup…
We extend the approach of Ref. [Yu-xi Liu, L. F. Wei, and F. Nori, Europhys. Lett. 67, 941 (2004)] for preparing superposition states of a cavity field interacting with a superconducting charge qubit. We study effects of the nonlinearity on the creation of such states. We show that the main contribution of nonlinear effects is to shorten the time necessary to build the superposition.
We present a way for fast implementation of a two-qubit controlled phase gate with superconducting flux qubits coupled to a cavity. A distinct feature of this proposal is that since only qubit-cavity resonant interaction and qubit-pulse resonant interaction are used, the gate can be performed much faster when compared with the previous proposals. This proposal does not require adjustment of the qubit level spacings during the gate operation. In addition, neither uniformity in the qubit parameters nor exact placement of qubits in the cavity is needed by this proposal.
We present a scheme for the implementation of three qubit Grover's algorithm using four-level superconducting quantum interference devices (SQUIDs) coupled to a superconducting resonator. The scheme is based on resonant, off-resonant interaction of the cavity field with SQUIDs and the application of classical microwave pulses. We show that adjustment of SQUID level spacing during the gate operations, adiabatic passage, and second-order detuning are not required that leads to faster implementation. We also show that the marked state can be searched with high fidelity even in the presence of lev…
Leveraging the quantum information processing ability of superconducting circuits and long-distance distribution ability of optical photons promises the realization of complex and large-scale quantum networks. In such a scheme, a coherent and efficient quantum transducer between superconducting and photonic circuits is critical. However, such quantum transducer is still challenging since the use of intermediate excitations in current schemes introduces extra noise and limits bandwidth. Here we realize direct and coherent transduction between superconducting and photonic circuits based on tripl…
We study electron-spin-photon coupling in a single-spin double quantum dot embedded in a superconducting stripline cavity. With an external magnetic field, we show that either a spin-orbit interaction (for InAs) or an inhomogeneous magnetic field (for Si and GaAs) could produce a strong spin-photon coupling, with a coupling strength of the order of 1 MHz. With an isotopically purified Si double dot, which has a very long spin coherence time for the electron, it is possible to reach the strong-coupling limit between the spin and the cavity photon, as in cavity quantum electrodynamics. The coupl…
Nonlinear phenomena in superconducting resonator circuits are of great significance in the field of quantum technology. We observe thermal self-oscillations in a monolayer graphene flake coupled to Molybdenum-Rhenium superconducting resonator. The graphene flake forms a SINIS junction coupled to the resonator with strong temperature dependent resistance. In certain conditions of pump power and frequency, this nonlinearity leads to thermal self-oscillations appearing as sidebands in cavity transmission measurements with strong temperature dependence and gate tunability. The experimental observa…
We report on the magnetic levitation of a millimeter sized neodymium permanent magnet within the interior of a superconducting radio frequency (SRF) cavity. To the best of our knowledge, this is the first experimental work on levitating a magnet within an SRF cavity. The cavity is a coaxial quarter wave microwave resonator made from 6061 aluminum, having a resonance frequency of 10GHz and a loaded Q of 1400. The cylindrical magnet (N50) has a height of 1 mm, a diameter of 0.75 mm, a mass of 4 mg, and a remanence of 1.44 T. This produces a peak magnetic field 140 times greater than the critical…
A quantum-mechanical model for the interaction of Josephson vortices (fluxons) embedded in superconducting transmission line is presented. The vortices interact through emission and absorption of linear waves (electromagnetic cavity modes). We show that in a classical regime this peculiar type of interaction is determined by the product of instantaneous velocities of fluxons. In a quantum regime, this property provides tunable coupling between vortices which can be used for entanglement of vortex qubits. The physical mechanism of the vortex interaction is similar to that proposed for qubits ba…
We propose how to generate macroscopic quantum superposition states using a microwave cavity containing a superconducting charge qubit. Based on the measurement of charge states, we show that the superpositions of two macroscopically distinguishable coherent states of a single-mode cavity field can be generated by a controllable interaction between a cavity field and a charge qubit. After such superpositions of the cavity field are created, the interaction can be switched off by the classical magnetic field, and there is no information transfer between the cavity field and the charge qubit. We…
Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity
本研究针对非厄米量子系统中拓扑波包动力学的拓展难题，基于双正交形式推导含复贝里曲率的半经典运动方程，构建非厄米Haldane模型验证理论，并提出光学手性腔实验方案。
Superconducting parametric amplifiers are commonly fabricated using planar transmission lines with a non-linear inductance provided by either Josephson junctions or the intrinsic kinetic inductance of the thin film. However, Banys et al. [1] reported non-linear behaviour in a niobium pillbox cavity, hypothesising that below Tc, the pair iris-bulk resonator would act as a superconducting contact surface exploiting a Josephson-like non-linearity. This work investigates this effect further by applying Keysight Technologies' Advanced Design System (ADS) to simulate the cavity using an equivalent c…
We demonstrate coherent control and measurement of a superconducting qubit coupled to a superconducting coplanar waveguide resonator with a dynamically tunable qubit-cavity coupling strength. Rabi oscillations are measured for several coupling strengths showing that the qubit transition can be turned off by a factor of more than 1500. We show how the qubit can still be accessed in the off state via fast flux pulses. We perform pulse delay measurements with synchronized fast flux pulses on the device and observe $T_1$ and $T_2$ times of 1.6 and 1.9 $μ$s, respectively. This work demonstrates how…
Exploration of superconducting multi-mode cavity architectures for quantum computing
该研究针对超导射频腔量子计算平台的算力提升需求，基于粒子加速器现有设计开展多单元SRF腔的参数化电磁仿真优化，重点分析其与transmon电路的相互作用，为同类系统研究提供设计蓝本。
Hybrid quantum systems are essential for the realization of distributed quantum networks. In particular, piezo-mechanics operating at typical superconducting qubit frequencies features low thermal excitations, and offers an appealing platform to bridge superconducting quantum processors and optical telecommunication channels. However, integrating superconducting and optomechanical elements at cryogenic temperatures with sufficiently strong interactions remains a tremendous challenge. Here, we report an integrated superconducting cavity piezo-optomechanical platform where 10-GHz phonons are res…
We develop a theory for non-degenerate parametric resonance in a tunable superconducting cavity. We focus on nonlinear effects that are caused by nonlinear Josephson elements connected to the cavity. We analyze parametric amplification in a strong nonlinear regime at the parametric instability threshold, and calculate maximum gain values. Above the threshold, in the parametric oscillator regime the linear cavity response diverges at the oscillator frequency at all pump strengths. We show that this divergence is related to the continuous degeneracy of the free oscillator state with respect to t…
The superconducting circuits involving Josephson junction offer macroscopic quantum two-level system (qubit) which are coupled to cavity resonators and are operated via microwave signals. In this work, we study the dynamics of superconducting qubits coupled to a cavity with including dissipation in a subkelvin temperature domain. In the first step, a classical Finite Element Method is used to simulate the cavities and basic circuit elements to model Josephson junctions. Then the quantization of the circuit is done to obtain the full Hamiltonian of the system using energy partition ratios of th…
We demonstrate enhancement of the dispersive frequency shift in a coplanar waveguide resonator induced by a capacitively-coupled superconducting flux qubit in the straddling regime. The magnitude of the observed shift, 80 MHz for the qubit-resonator detuning of 5 GHz, is quantitatively explained by the generalized Jaynes-Cummings model which takes into account the contribution of the qubit higher energy levels. By applying the enhanced dispersive shift to the qubit readout, we achieved 90% contrast of the Rabi oscillations which is mainly limited by the energy relaxation of the qubit.
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