Construction of two-qubit logical gates by transmon qubits in a three-dimensional cavity

We report the implementation of qubit-qubit coupling in a three-dimensional(3 D) cavity, using the exchange of virtual photons, to realize logical operations. We measure single photon and multi-photon transitions in this qubit-qubit coupling system and obtain its energy avoided-crossing spectrum. With ac-Stark effect, fast control of the qubits is achieved to tune the effective coupling on and off and the state-swap gate (SWAP)~(1/2) is successfully constructed. Moreover, using two-photon transition between the ground state and doubly excited states, a kind of two-photon Rabi-like oscillation is observed. A quarter period of this oscillation corresponds to the logical gate (bSWAP)~(1/2), which is used for generating Bell states.(bSWAP)~(1/2) and (iSWAP)~(1/2) are the foundations of future preparation of two-qubit Bell states and realization of CNOT gate.     

三维传输子量子比特的退相干参数表征

超导量子比特的退相干时间是决定超导量子计算能否实现的重要指标之一. 文章以三维传输子量子比特(3D transmon)为研究对象, 在氧化硅衬底上制备了三维传输子量子比特, 并在超低温下(10 mK), 采用拉比振荡(Rabi oscillation)、能量弛豫(energy relaxation)、 拉姆齐条纹(Ramsey fringe)、自旋回波(spin echo)的方法, 对其进行了详细的退相干时间常数表征. 结果显示该量子比特的退相干时间在几百纳秒. 根据几种退相干时间的关系进行计算, 可以看出, 低频噪声目前不是影响量子比特退相干的最主要因素, 而氧化硅中的缺陷可能是样品退相干时间的主要瓶颈. 关键词： 三维传输子量子比特 拉比振荡 拉姆齐条纹 自旋回波     

Controlling the spontaneous emission of a superconducting transmon qubit

We present a detailed characterization of coherence in seven transmon qubits in a circuit QED architecture. We find that spontaneous emission rates are strongly influenced by far off-resonant modes of the cavity and can be understood within a semiclassical circuit model. A careful analysis of the spontaneous qubit decay into a microwave transmission-line cavity can accurately predict the qubit lifetimes over 2 orders of magnitude in time and more than an octave in frequency. Coherence times T1 and T_{2};{*} of more than a microsecond are reproducibly demonstrated.     

Engineering three-dimensional maximally entangled states for two modes in a bimodal cavity

An alternative scheme is proposed for engineering three-dimensional maximally entangled states for two modes of a superconducting microwave cavity. In this scheme, an appropriately prepared four-level atom is sent through a bimodal cavity. During its passing through the cavity, the atom is coupled resonantly with two cavity modes simultaneously and addressed by a classical microwave pulse tuned to the required transition. Then the atomic states are detected to collapse two modes onto a three-dimensional maximally entangled state. The scheme is different from the previous one in which two nonlocal cavities are used. A comparison between them is also made.     

Experimental test of a trace formula for a chaotic three-dimensional microwave cavity

We have measured resonance spectra in a superconducting microwave cavity with the shape of a three-dimensional generalized Bunimovich stadium billiard and analyzed their spectral fluctuation properties. The experimental length spectrum exhibits contributions from periodic orbits of nongeneric modes and from unstable periodic orbits of the underlying classical system. It is well reproduced by our theoretical calculations based on the trace formula derived by Balian and Duplantier for chaotic electromagnetic cavities.     

Observation of a collective mode of an array of transmon qubits

Arrays of transmon qubits coupled to a λ/2 superconducting coplanar waveguide resonator have been studied by microwave spectroscopy. The emergence of a collective mode has been discovered for a cluster of N > 5 qubits, whose coupling constant to the electromagnetic field in the resonator is √N times greater compared to a single qubit. In addition, the emergence of collective multiphoton transitions exciting higher levels of a qubit cluster has been demonstrated and the interaction of an individual qubit with such a cluster has been investigated.     

1.3 GHz 9单元Ichiro型模型铜腔的预调谐

 以常用的多单元超导腔预调谐方法为基础,搭建了一套完整的预调谐系统,并实现了超导腔预调谐测量的自动化。实验首先通过网络分析仪对超导腔进行测量,利用Labview进行数据采集,并协同控制步进电机。通过“拉小珠”的微扰法,测量沿小珠运动路径的场分布。编写了一套Java程序,通过矩阵运算,计算出9单元腔各个腔单元频率的校正量。根据计算结果对9单元腔的某个单元进行挤压或拉抻,经多次上述操作后,在较高精度范围内,可将9单元铜腔的每个腔单元调谐至预期的目标频率。     

1.3 GHz 9单元Ichiro型模型铜腔的预调谐

以常用的多单元超导腔预调谐方法为基础,搭建了一套完整的预调谐系统,并实现了超导腔预调谐测量的自动化。实验首先通过网络分析仪对超导腔进行测量,利用Labview进行数据采集,并协同控制步进电机。通过“拉小珠”的微扰法,测量沿小珠运动路径的场分布。编写了一套Java程序,通过矩阵运算,计算出9单元腔各个腔单元频率的校正量。根据计算结果对9单元腔的某个单元进行挤压或拉抻,经多次上述操作后,在较高精度范围内,可将9单元铜腔的每个腔单元调谐至预期的目标频率。     

Frequency-tunable 500-mW continuous-wave all-solid-state single-frequency source in the blue spectral region

A compact source of stable cw single-frequency radiation at 473 nm has been realized by second-harmonic generation of a diode-pumped miniature Nd:YAG ring laser operating on the (4)F(3/2) - (4)I(9/2) laser transition. By use of potassium niobate (KNbO(3)), single-longitudinal-mode output powers of 500 mW cw with high stability and maximum optical-to-optical conversion efficiencies >81% are achieved. An external semimonolithic cavity permits mode-hop-free frequency tuning of blue radiation over as much as 20 GHz.     

Frequency-tunable wireless access scheme based on the optoelectronic oscillating technique

A frequency-tunable wireless access scheme based on optoelectronic oscillating technology is proposed and experimentally demonstrated.By using this scheme,the frequency of the transmitted wireless signals can be tuned by adjusting the wavelength of the input light.The 1.25 Gb/s on-off keying signals with the carrier frequency of 8–14.5 GHz are generated and transmitted through a radio over fiber link.The envelope detecting technique is employed in the receiver to support the down-conversion and demodulation.Electrical local oscillators are not required in the transmitter and receiver end,which simplifies the system structure and lowers the cost.     

Visualisation and analysis of large-scale vortex structures in three-dimensional turbulent lid-driven cavity flow

In this paper, large eddy simulation (LES) of a three-dimensional turbulent lid-driven cavity (LDC) flow at Re = 10,000 has been performed using the multiple relaxation time lattice Boltzmann method. A Smagorinsky eddy viscosity model was used to represent the sub-grid scale stresses with appropriate wall damping. The prediction for the flow field was first validated by comparing the velocity profiles with previous experimental and LES studies, and then subsequently used to investigate the large-scale three-dimensional vortical structures in the LDC flow. The instantaneous three-dimensional coherent structures inside the cavity were visualised using the second invariant (Q), Δ criterion, λ₂ criterion, swirling strength (λ_ci) and streamwise vorticity. The vortex structures obtained using the different criteria in general agree well with each other. However, a cleaner visualisation of the large vortex structures was achieved with the λ_ci criterion and also when the visualisation is based on the vortex identification criteria expressed in terms of the swirling strength parameters. A major objective of the study was to perform a three-dimensional proper orthogonal decomposition (POD) on the fluctuating velocity fields. The higher energy POD modes efficiently extracted the large-scale vortical structures within the flow which were then visualised with the swirling strength criterion. Reconstruction of the instantaneous fluctuating velocity field using a finite number of POD modes indicated that the large-scale vortex structures did effectively approximate the large-scale motion. However, such a reduced order reconstruction of the flow based on the large-scale vortical structures was clearly not as effective in predicting the small-scale details of the fluctuating velocity field which relate to the turbulent transport.     

Measuring the performance of the coaxial HOM coupler on a 2-cell TESLA-shape copper cavity

Coaxial High Order Mode （HOM） couplers have been fabricated at Peking University and their RF performance has been measured on a test device consisting of a coaxial transmission line and a 2-cell TESLA-shape copper cavity. The test results on the 2-cell TESLA-shape copper cavity with HOM couplers indicate that the coupler can cut off the fundamental mode TM010 and absorb HOMs effectively after a careful adjustment. The optimal angle of the HOM coupler with the beam tube is found. The initial test results of HOM couplers are presented in this paper.     

Measuring the performance of the coaxial HOM coupler on a 2-cell TESLA-shape copper cavity

Coaxial High Order Mode (HOM) couplers have been fabricated at Peking University and their RF performance has been measured on a test device consisting of a coaxial transmission line and a 2-cellTESLA-shape copper cavity. The test results on the 2-cell TESLA-shape copper cavity with HOM couplers indicate that the coupler can cut off the fundamental mode TM010 and absorb HOMs effectively after a careful adjustment. The optimal angle of the HOM coupler with the beam tube is found. The initial test results of HOM couplers are presented in this paper.     

Bose-Einstein condensation in a cavity

The effect of the physically correct boundary conditions and the nonvanishing ground state energy on Bose-Einstein condensation of quantum particles confined to a cubic volumeV=L ³ is evaluated. The transition point is shifted towards higher temperatures by the confinement, the specific heat below the onset of condensation is no longer proportional toT ^3/2, and the pressure does depend on the volume. Precise expressions for the modification of the ground state population and for the shift of the condensation temperature are derived, together with an expansion of the internal energy and of the specific heat. Numerical computations confirm the accuracy of our analytical approximations.Dedicated to Herbert Wagner, whose work on quantum Fermi liquids proved to be also very stimulating for quantum Bose liquids.     

Performance studies of diode-side-pumped CW Nd:YAG laser in copper coated optical pump cavity

This paper reports the performance studies of Nd:YAG rods with different diameters and doping concentration in the CW diode-side-pumped geometry. We have used p-polarized diodes to pump the active medium and we studied the performance of different rods in terms of thermal lensing, its fluorescence profile, power output, and M² factor of the laser beam. We achieved a maximum of 378 W of output power for an input pump power of 757 W, which corresponds to optical conversion efficiency close to 50%. The slope efficiency of the system was 56.4%. These efficiencies are the highest reported to the best of our knowledge and we achieved with Nd:YAG rod at 1.1-at% doping.     

Exact results on cavity cooling in a system of a two-level atom and a cavity field

Using the algebraic dynamical method, this paper investigates the laser cooling of a moving two-level atom coupled to a cavity field. Analytical solutions of optical forces and the cooling temperatures are obtained. Considering Rb atoms as an example, it finds that the numerical results are relevant to the recent experimental laser cooling investigations.     

A unified incompressible lattice BGK model and its application to three-dimensional lid-driven cavity flow

A unified lattice Bhatnagar－Gross－Krook (ILBGK) model iDdQq for the incompressible Navier－Stokes equation is presented. To test its efficiency, the lid-driven cavity flow in three-dimensional space for Reynolds number Re=3200 and span aspect ratio SAR=1, 2 and 3 is simulated in detail on a 48×48×(48×SAR) uniform lattice using the model. The test results agree well with those in previous experiments and numerical works and show the efficiency and strong numerical stability of the proposed ILBGK model.     

Trapping atoms in a gravitational cavity

This paper is devoted to the study of a new atomic cavity consisting of a single horizontal concave mirror placed in the earth gravitational field. Gravity, by bending the atomic trajectories, plays the role of a second mirror closing the cavity. We first discuss the stability criterion for this cavity, assuming that the mirror has a parabolic shape. We then derive the quantum mechanical modes of such a configuration, with particular emphasis on the paraxial (i.e., close to vertical) motion. Finally, we discuss the possibility of populating those modes from an initial cold atomic cloud dropped above the mirror.Laboratoire associé au CNRS et à l'Université Pierre et Marie Curie