Polariton states in circuit QED for electromagnetically induced transparency

  1. Xiu Gu,
  2. Sai-nan Huai,
  3. Franco Nori,
  4. and Yu-xi Liu
Electromagnetically induced transparency (EIT) has been extensively studied in various systems. However, it is not easy to observe in superconducting quantum circuits (SQCs), because
the Rabi frequency of the strong controlling field corresponding to EIT is limited by the decay rates of the SQCs. Here, we show that EIT can be achieved by engineering decay rates in a superconducting circuit QED system through a classical driving field on the qubit. Without such a driving field, the superconducting qubit and the cavity field are approximately decoupled in the large detuning regime, and thus the eigenstates of the system are approximately product states of the cavity field and qubit states. However, the driving field can strongly mix these product states and so-called polariton states can be formed. The weights of the states for the qubit and cavity field in the polariton states can be tuned by the driving field, and thus the decay rates of the polariton states can be changed. We choose a three-level system with Λ-type transitions in such a driven circuit QED system, and demonstrate how EIT and ATS can be realized in this compound system. We believe that this study will be helpful for EIT experiments using SQCs.

Entangling superconducting qubits in a multi-cavity system

  1. Chui-Ping Yang,
  2. Qi-Ping Su,
  3. Shi-Biao Zheng,
  4. and Franco Nori
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 Greenberger-Horne-Zeilinger (GHZ) state, by using a single operation and without the need of measurements. The GHZ state is created without exciting the cavity modes; thus greatly suppressing the decoherence caused by the cavity-photon decay and the effect of unwanted inter-cavity crosstalk on the operation. We also introduce two simple methods for entangling the intra-cavity SC qubits in a GHZ state. As an example, our numerical simulations show that it is feasible, with current circuit-QED technology, to prepare high-fidelity GHZ states, for up to nine SC qubits by using SC qubits distributed in two cavities. This proposal can in principle be used to implement a GHZ state for {\it an arbitrary number} of SC qubits distributed in multiple cavities. The proposal is quite general and can be applied to a wide range of physical systems, with the intra-cavity qubits being either atoms, NV centers, quantum dots, or various SC qubits.

Generating nonclassical photon-states via longitudinal couplings between superconducting qubits and microwave fields

  1. Yan-Jun Zhao,
  2. Yu-Long Liu,
  3. Yu-xi Liu,
  4. and Franco Nori
Besides the conventional transverse couplings between superconducting qubits (SQs) and electromagnetic fields, there are additional longitudinal couplings when the inversion symmetry
of the potential energies of the SQs is broken. We study nonclassical-state generation in a SQ which is driven by a classical field and coupled to a single-mode microwave field. We find that the classical field can induce transitions between two energy levels of the SQs, which either generate or annihilate, in a controllable way, different photon numbers of the cavity field. The effective Hamiltonians of these classical-field-assisted multiphoton processes of the single-mode cavity field are very similar to those for cold ions, confined to a coaxial RF-ion trap and driven by a classical field. We show that arbitrary superpositions of Fock states can be more efficiently generated using these controllable multiphoton transitions, in contrast to the single-photon resonant transition when there is only a SQ-field transverse coupling. The experimental feasibility for different SQs is also discussed.

Robust manipulation of superconducting qubits in the presence of fluctuations

  1. Daoyi Dong,
  2. Chunlin Chen,
  3. Bo Qi,
  4. Ian R. Petersen,
  5. and Franco Nori
Superconducting quantum systems are promising candidates for quantum information processing due to their scalability and design flexibility. However, the existence of defects, fluctuations,
and inaccuracies is unavoidable for practical superconducting quantum circuits. In this paper, a sampling-based learning control (SLC) method is used to guide the design of control fields for manipulating superconducting quantum systems. Numerical results for one-qubit systems and coupled two-qubit systems show that the „smart“ fields learned using the SLC method can achieve robust manipulation of superconducting qubits even in the presence of large fluctuations and inaccuracies.

Toroidal qubits: naturally-decoupled quiet artificial atoms

  1. Alexandre M. Zagoskin,
  2. Arkadi Chipouline,
  3. Evgeni Il'ichev,
  4. J. Robert Johansson,
  5. and Franco Nori
The requirements of quantum computations impose high demands on the level of qubit protection from perturbations; in particular, from those produced by the environment. Here we propose
a superconducting flux qubit design that is naturally protected from ambient noise. This decoupling is due to the qubit interacting with the electromagnetic field only through its toroidal moment, which provides an unusual qubit-field interaction.

Quantum Bayesian rule for weak measurements of qubits in superconducting circuit QED

  1. Peiyue Wang,
  2. Lupei Qin,
  3. Xin-Qi Li,
  4. and Franco Nori
There exist two scenarios of quantum weak measurement theories. One is the well-known quantum trajectory theory which, in terms of continuous differential equation, has been broadly
applied in quantum optics and quantum control problems. Another is the relatively newer quantum Bayesian approach, which has the advantage of being more efficient to infer the state of the measured quantum system merely based on certain integrated output of measurements. In this work, we aim to develop a quantum Bayesian rule for weak measurements of qubits in circuit quantum electrodynamics (QED). Starting with the optical quantum trajectory equation, our analysis pays particular attention to the nature of the cavity field under continuous quadrature monitoring. This allows our treatment unrestricted to the „bad-cavity“ and weak-response limits, thus making the obtained rule applicable to general setup parameters. With accuracy well proven numerically in this work, we expect this proposed approach to be useful for future circuit-QED measurement and control experiments.

Optomechanical-like coupling between superconducting resonators

  1. J. R. Johansson,
  2. G. Johansson,
  3. and Franco Nori
We propose and analyze a circuit that implements a nonlinear coupling between two superconducting microwave resonators. The resonators are coupled through a superconducting quantum
interference device (SQUID) that terminates one of the resonators. This produces a nonlinear interaction on the standard optomechanical form, where the quadrature of one resonator couples to the photon number of the other resonator. The circuit therefore allows for all-electrical realizations of analogs to optomechanical systems, with coupling that can be both strong and tunable. We estimate the coupling strengths that should be attainable with the proposed device, and we find that the device is a promising candidate for realizing the single-photon strong-coupling regime. As a potential application, we discuss implementations of networks of nonlinearly-coupled microwave resonators, which could be used in microwave-photon based quantum simulation.

Spin-Orbit Qubit on a Multiferroic Insulator in a Superconducting Resonator

  1. P. Zhang,
  2. Ze-Liang Xiang,
  3. and Franco Nori
We propose a spin-orbit qubit in a nanowire quantum dot on the surface of a multiferroic insulator with a cycloidal spiral magnetic order. The spiral exchange field from the multiferroic
insulator causes inhomogeneous Zeeman-like interaction on the electron spin in the quantum dot, assisting the realization of a spin-orbit qubit. The absence of an external magnetic field benefits the integration of such spin-orbit qubit into high-quality superconducting resonators for manipulation. By exploiting the Rashba spin-orbit coupling in the quantum dot via a gate voltage, one can obtain an effective spin-photon coupling with an efficient on/off switching. This makes the proposed device promising for hybrid quantum communications.

Linear response of superconducting flux quantum circuits

  1. Hui-Chen Sun,
  2. Yu-xi Liu,
  3. J. Q. You,
  4. E. Il'ichev,
  5. and Franco Nori
We study the microwave absorption of a driven three-level quantum system, which is realized by a superconducting flux quantum circuit (SFQC), with a magnetic driving field applied to
the two upper levels. The interaction between the three-level system and its environment is studied within the Born-Markov approximations, and we take into account the effects of the driving field on the damping rates of the three-level system. We study the linear response of the driven three-level SFQC to a weak probe field. The susceptibility of the probe field can be changed by both the driving field and the bias magnetic flux. When the bias magnetic flux is at the optimal point,the transition from the ground state to the second excited state is forbidden and the three-level system has a ladder-type transition. Thus, the SFQC responds to the probe field like natural atomic systems with ladder-type transitions. However, when the bias magnetic flux is away from the optimal point, the three-level SFQC has Δ-type transition, thus it responds to the probe field like a combination of natural atoms with ladder-type transitions and natural atoms with Λ-type transitions. In particular, we give detailed discussions on the conditions for realizing electromagnetically induced transparency and Autler-Townes splitting in three-level SFQCs.

Feedback-induced nonlinearity and superconducting on-chip quantum optics

  1. Zhong-Peng Liu,
  2. Hui Wang,
  3. Jing Zhang,
  4. Yu-xi Liu,
  5. Re-Bing Wu,
  6. and Franco Nori
Quantum coherent feedback has been proven to be an efficient way to tune the dynamics of quantum optical systems and, recently, those of solid-state quantum circuits. Here, inspired
by the recent progress of quantum feedback experiments, especially those in mesoscopic circuits, we prove that superconducting circuit QED systems, shunted with a coherent feedback loop, can change the dynamics of a superconducting transmission line resonator, i.e., a linear quantum cavity, and lead to strong on-chip nonlinear optical phenomena. We find that bistability can occur under the semiclassical approximation, and photon anti-bunching can be shown in the quantum regime. Our study presents new perspectives for engineering nonlinear quantum dynamics on a chip.