Transfer of quantum entangled states between superconducting qubits and microwave field qubits

Transferring entangled states between matter qubits and microwave-field (or optical-field) qubits is of fundamental interest in quantum mechanics and necessary in hybrid quantum information processing and quantum communication. We here propose a way for transferring entangled states between superconducting qubits (matter qubits) and microwave-field qubits. This proposal is realized by a system consisting of multiple superconducting qutrits and microwave cavities. Here, „qutrit” refers to a three-level quantum system with the two lowest levels encoding a qubit while the third level acting as an auxiliary state. In contrast, the microwave-field qubits are encoded with coherent states of microwave cavities. Because the third energy level of each qutrit is not populated during the operation, decoherence from the higher energy levels is greatly suppressed. The entangled states can be deterministically transferred because measurement on the states is not needed. The operation time is independent of the number of superconducting qubits or microwave-field qubits. In addition, the architecture of the circuit system is quite simple because only a coupler qutrit and an auxiliary cavity are required. As an example, our numerical simulations show that high-fidelity transfer of entangled states from two superconducting qubits to two microwave-field qubits is feasible with present circuit QED technology. This proposal is quite general and can be extended to transfer entangled states between other matter qubits (e.g., atoms, quantum dots, and NV centers) and microwave- or optical-field qubits encoded with coherent states.     

Transferring quantum entangled states between multiple single-photon-state qubits and coherent-state qubits in circuit QED

We present a way to transfer maximally- or partially-entangled states of n single-photon-state (SPS) qubits onto ncoherent-state (CS) qubits, by employing 2nmicrowave cavities coupled to a superconducting flux qutrit. The two logic states of a SPS qubit here are represented by the vacuum state and the single-photon state of a cavity, while the two logic states of a CS qubit are encoded with two coherent states of a cavity. Because of using only one superconducting qutrit as the coupler, the circuit architecture is significantly simplified. The operation time for the state transfer does not increase with the increasing of the number of qubits. When the dissipation of the system is negligible, the quantum state can be transferred in a deterministic way since no measurement is required. Furthermore, the higher-energy intermediate level of the coupler qutrit is not excited during the entire operation and thus decoherence from the qutrit is greatly suppressed. As a specific example, we numerically demonstrate that the high-fidelity transfer of a Bell state of two SPS qubits onto two CS qubits is achievable within the present-day circuit QED technology. Finally, it is worthy to note that when the dissipation is negligible, entangled states of n CS qubits can be transferred back onto n SPS qubits by performing reverse operations. This proposal is quite general and can be extended to accomplish the same task, by employing a natural or artificial atom to couple 2nmicrowave or optical cavities.     

One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED

We propose a single-step implementation of a muti-target-qubit controlled phase gate with one catstate qubit (cqubit) simultaneously controlling n–1 target cqubits. The two logic states of a cqubit are represented by two orthogonal cat states of a single cavity mode. In this proposal, the gate is implemented with n microwave cavities coupled to a superconducting transmon qutrit. Because the qutrit remains in the ground state during the gate operation, decoherence caused due to the qutrit’s energy relaxation and dephasing is greatly suppressed. The gate implementation is quite simple because only a single-step operation is needed and neither classical pulse nor measurement is required. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one cqubit simultaneously controlling two target cqubits is feasible with present circuit QED technology. This proposal can be extended to a wide range of physical systems to realize the proposed gate, such as multiple microwave or optical cavities coupled to a natural or artificial three-level atom.     

Dissipative generation for steady-state entanglement of two transmons in circuit QED

We present a dissipative scheme to generate an entangled steady-state between two superconducting transmon qutrits separately embedded in two coupled transmission line resonators in a circuit quantum electrodynamics(QED) setup. In our scheme, the resonant qutrit-resonator interaction and photon hopping between resonators jointly induce asymmetric energy gaps in the dressed state subspaces. The coherent driving fields induce the specific dressed state transition and the dissipative processes lead to the gradual accumulation in the population of target state, combination of both drives the system into a steady-state entanglement. Numerical simulation shows that the maximally entangled state can be produced with high fidelity and strong robustness against the cavity decay and qutrit decay, and no requirements for accurate time control. The scheme is achievable with the current experimental technologies.     

Speeding up the Generation of Entangled State between a Superconducting Qubit and Cavity Photons via Counterdiabatic Driving

Optimal generation of entangled states is of critical significance for robust quantum information processing. An effective scheme is presented for speeding up the generation of an entangled state between a superconducting qubit and microwave photons via counterdiabatic driving. At a magic bias point, the first three levels of a charge-phase quantum circuit constitute an effective qutrit. An entangled state based on adiabatic population transfer is first achieved. By the technique of shortcuts to adiabaticity, a counterdiabatic driving is applied to the qutrit, which then accelerates the entanglement generation significantly. Moreover, with the accessible decoherence rates, the rapid operations in a shortcut way are highly robust when compared with adiabatic manipulations. The scheme could offer a promising approach toward optimal preparation of entangled states with superconducting artificial atoms in circuit quantum electrodynamics, experimentally.     

Controllable preparation of entangled coherent states with superconducting system

Utilizing a current-biased Josephson junction (CBJJ) as a tunable coupler for superconducting transmission line resonators (TLRs), we propose a potentially practical scheme to create entangled coherent states of the two TLR modes. Then, the influence of TLRs decay on the prepared entangled states is analyzed. And an interesting phenomenon that even entangled coherent states are robustness against decay with small α is found. At last, the experimental feasibility and the challenge of our schemes have been discussed.     

Deterministic entanglement of photons in two superconducting microwave resonators

Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spinlike systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N-photon NOON states (entangled states |N0> + |0N>) as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two resonators, and we completely characterize the entangled states with bipartite Wigner tomography. These results demonstrate a significant advance in the quantum control of linear resonators in superconducting circuits.     

Efficient scheme for realizing a multiplex-controlled phase gate with photonic qubits in circuit quantum electrodynamics

We propose an efficient scheme to implement a multiplex-controlled phase gate with multiple photonic qubits simultaneously controlling one target photonic qubit based on circuit quantum electrodynamics (QED). For convenience, we denote this multiqubit gate as MCP gate. The gate is realized by using a two-level coupler to couple multiple cavities. The coupler here is a superconducting qubit. This scheme is simple because the gate implementation requires only one step of operation. In addition, this scheme is quite general because the two logic states of each photonic qubit can be encoded with a vacuum state and an arbitrary non-vacuum state |φ> (e.g., a Fock state, a superposition of Fock states, a cat state, or a coherent state, etc.) which is orthogonal or quasi-orthogonal to the vacuum state. The scheme has some additional advantages: because only two levels of the coupler are used, i.e., no auxiliary levels are utilized, decoherence from higher energy levels of the coupler is avoided; the gate operation time does not depend on the number of qubits; and the gate is implemented deterministically because no measurement is applied. As an example, we numerically analyze the circuit-QED based experimental feasibility of implementing a three-qubit MCP gate with photonic qubits each encoded via a vacuum state and a cat state. The scheme can be applied to accomplish the same task in a wide range of physical system, which consists of multiple microwave or optical cavities coupled to a two-level coupler such as a natural or artificial atom.     

Optical Non-Reciprocity in Coupled Resonators by Detailed Balance

Inspired by the photosynthetic energy transfer process, a method to realize non-reciprocal optical transmission in an array of coupled resonators is theoretically proposed. The optical non-reciprocity of the coupled resonators arises from the frequency gradient between adjacent cavities and the interaction with the environment, which is similar to photosynthetic energy transfer. An increase in the frequency gradient or the number of the cavities can lead to better non-reciprocity. However, although a higher environment temperature will increase the total photon number in the coupled cavities, non-reciprocity will be weakened. All these findings can be well described by the detailed balance. The similarity between the noise-induced optical non-reciprocity and exciton energy transfer in natural photosynthesis is revealed by the discovery.     

Transferring of a Two-Mode Entangled State Between Two Cavities via Cavity QED

We propose a scheme for transferring of a two-mode entanglement of zero- or one-photon entangled states between two cavities via atom-cavity field resonant interaction. In our proposal, in order to transfer the entangled state, we only need two identical two-level atoms and a two-mode cavity for receiving the teleported state. This scheme does not require Bell-state measurement and performing any transformations to reconstruct the initial state. And the transfer can occur with 100% success probability in a simple manner. And a network for transferring of a two-mode entangled state between cavities is suggested. This scheme can also be extended to transfer N-mode entangled state of cavity.     

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.     

Entanglement Generation Between Two Mechanical Resonators in Two Optomechanical Cavities

A standard model is suggested to explore correlation features of two spatially separated optomechanical cavities. The cavities are coupled through the photon-hopping process. In particular, we investigate the generation of entanglement between mechanical resonators in the strong coupling regime and the two cavities are assumed to be driven by a coherent laser field. In order to quantify entanglement we use the logarithmic negativity. The analytical solutions are presented for the system in a parameter regime very close to the current experimental results. We show that in the presence of the photon hopping process between the cavities, the two mechanical resonators and the field modes can be entangled. This shows clearly that the entanglement can be transfer via radiation pressure of a photon hopping coupling from the intracavity photon-phonon entanglements to an inter-cavity photon-photon or phonon-phonon entanglement.     

Putting mechanics into circuit quantum electrodynamics

We review the use of mechanical oscillators in circuit quantum electrodynamics. The capacitive coupling of nano-electromechanical systems with quantum bits and superconducting microwave resonators gives rise to a rich quantum physics involving electrons, photons and phonons. We focus in particular on the linear coupling between a mechanical oscillator and a microwave resonator and present the quantum dynamics that stems from the phonotonic Josephson junction. The microwave cavity turns out to be a powerful device to detect quantum phonon states and manipulate entangled states between phonons and photons.     

基于新型三环谐振器的诱导透明效应分析

针对谐振式微腔的应用需求, 提出了一种新型三环谐振式微腔结构, 类似于原子系统中的电磁诱导透明, 耦合诱导透明(CRIT)效应在一个新的光学微腔系统中已被实验证明. 该结构在硅基上由三个尺寸完全一样的微环腔组成, 通过理论分析、制备和实验测试, 能够观察到CRIT现象, 其频谱具有低群速的狭窄透明峰, 与光栅耦合器的耦合效率为34%, 并且谐振器的品质因数达到了0.65×10⁵, 同时, 失谐的谐振波长可以通过温度变化来控制, 这在旋转传感、光滤波器、光存储器等方面的应用有重要意义.     

超材料谐振子间的电耦合谐振理论与实验研究

通过将两个金属开口环谐振器口对口地放置, 实现了超材料谐振子间的电耦合谐振. 对电耦合谐振的微波等效电路进行了理论分析和数值计算, 结果表明耦合后的超材料谐振子能产生两个谐振频率, 其中一个随耦合强度的增加逐渐向低频方向移动, 而另一个固定在单谐振子的谐振频率处不变. 微波透射谱的实验测试和电磁仿真结果表明, 两个谐振峰随耦合强度的增加分别向低频和高频方向移动. 分析表明: 低频谐振峰的位置主要是由超材料谐振子间的电耦合强度决定的; 高频谐振偏离单谐振子的谐振频率主要是由不可避免的磁耦合引起的, 而且在耦合间距越小时磁耦合影响越大. 提出的基于超材料谐振子间的电磁耦合实现的双频谐振及其可调性极大地增加了超材料的设计与应用空间.     

Spin Ensembles Coupled to Superconducting Resonators: A Scalable Architecture for Solid-State Quantum Computing

A design is proposed for scalable solid-state quantum computing, which is based on collectively enhanced magnetic coupling between nitrogen-vacancy center ensembles and superconducting transmission line resonators interconnected by current-biased Josephson junction superconducting phase qubit. In this hybrid system, we realize distant multi-qubit controlled phase gate operations and generate distant multi-qubit entangled W-like states, being indispensable resource to quantum computation. Our proposed architecture consists of solid-state spin ensembles and circuit QED, and could achieve quantum computing in a solid-state environment with high-fidelity and scalable way. The experimental feasibility is discussed, and the implementation efficiency is demonstrated numerically.     

Spin Ensembles Coupled to Superconducting Resonators：A Scalable Architecture for Solid-State Quantum Computing

A design is proposed for scalable solid-state quantum computing, which is based on collectively enhanced magnetic coupling between nitrogen-vacancy center ensembles and superconducting transmission line resonators interconnected by current-biased Josephson junction superconducting phase qubit. In this hybrid system, we realize distant multi-qubit controlled phase gate operations and generate distant multi-qubit entangled W-like states, being indispensable resource to quantum computation. Our proposed architecture consists of solid-state spin ensembles and circuit QED, and could achieve quantum computing in a solid-state environment with high-fidelity and scalable way. The experimental feasibility is discussed, and the implementation efficiency is demonstrated numerically.     

Entangled photon states recovery and cloning via the micro ring resonators and an add/drop multiplexer

We propose a new system of the entangled photon generation and recovery using a Gaussian pulse traveling within the nonlinear micro ring resonators, whereas the cloning feasibility of the entangled photon states via an add/drop multiplexer is also proposed. Firstly, the optimum entangled photon visibility is generated by using the Gaussian pulse in the ring resonators, where the second harmonic pulses are generated by filtering the chaotic signals. Secondly, the small amount of the transmission power is coupled by the add/drop device, whereas the entangled photon states, i.e. cloning states, are regenerated by using the polarization control unit. Results obtained have shown that the recovery entangled photon states can be made and confirmed with the initial states, which means that the cloning of entangled photon states of the initial states is plausible. The amplified entangled photon for state recovery is also discussed.     

Protection of entanglement between two V-atoms in a multi-cavity coupling system

The protection of the entanglement between two V-atoms(EBTVA)in a multi-cavity coupling system is studied.The whole system consists of two V-atoms.The two V-atoms are initially in the maximum entangled state and interacts locally with its own dissipative cavity which is coupled to the external cavities with high quality factor(ECWHQF).The results show that,when there is no ECWHQF,the EBTVA can be protected effectively in the case where the V-atom and the dissipative cavity are weak coupled in large detuning,while when there are different numbers n of ECWHQF coupled to two dissipative cavities,by adjusting the parameters of the number n of ECWHQF and the coupling strength k between cavities,the EBTVA can be protected perfectly and continuously.Our result provides an effective method for protecting entanglement resources of three-level system.     

基于光子计数的纠缠微波压缩角锁定

针对基于超导180°混合环的纠缠微波制备方案探测效率低、信息处理难以及控制复杂等问题,设计了基于微波光子计数的压缩角锁定方案.对超导180°混合环的输出信号进行微波光子计数,通过贝叶斯准则估计输入压缩态微波场的相对压缩角,并将压缩角校正信息反馈于约瑟夫森参量放大器抽运源,调整两路单模压缩态微波场的相对压缩角为180°,达到控制输出纠缠性能最优的目的.该研究为路径纠缠微波的纠缠性能的提升以及高质量纠缠微波源的设计提供了理论参考.