Towards hybrid circuit quantum electrodynamics with quantum dots

Cavity quantum electrodynamics allows one to study the interaction between light and matter at the most elementary level. The methods developed in this field have taught us how to probe and manipulate individual quantum systems like atoms and superconducting quantum bits with an exquisite accuracy. There is now a strong effort to extend further these methods to other quantum systems, and in particular hybrid quantum dot circuits. This could turn out to be instrumental for a noninvasive study of quantum dot circuits and a realization of scalable spin quantum bit architectures. It could also provide an interesting platform for quantum simulation of simple fermion–boson condensed matter systems. In this short review, we discuss the experimental state of the art for hybrid circuit quantum electrodynamics with quantum dots, and we present a simple theoretical modeling of experiments.     

Photon-number squeezing in circuit quantum electrodynamics

A superconducting single-electron transistor (SSET) coupled to an anharmonic oscillator, e.g., a Josephson junction-L-C circuit, can drive the latter to a nonequilibrium photon-number distribution. By biasing the SSET at the Josephson quasiparticle cycle, cooling of the oscillator as well as a laserlike enhancement of the photon number can be achieved. Here, we show that the cutoff in the quasiparticle tunneling rate due to the superconducting gap, in combination with the anharmonicity of the oscillator, may create strongly squeezed photon-number distributions. For low dissipation in the oscillator, nearly pure Fock states can be produced.     

Implementing phase-covariant cloning in circuit quantum electrodynamics

An efficient scheme is proposed to implement phase-covariant quantum cloning by using a superconducting transmon qubit coupled to a microwave cavity resonator in the strong dispersive limit of circuit quantum electrodynamics (QED). By solving the master equation numerically, we plot the Wigner function and Poisson distribution of the cavity mode after each operation in the cloning transformation sequence according to two logic circuits proposed. The visualizations of the quasi-probability distribution in phase-space for the cavity mode and the occupation probability distribution in the Fock basis enable us to penetrate the evolution process of cavity mode during the phase-covariant cloning (PCC) transformation. With the help of numerical simulation method, we find out that the present cloning machine is not the isotropic model because its output fidelity depends on the polar angle and the azimuthal angle of the initial input state on the Bloch sphere. The fidelity for the actual output clone of the present scheme is slightly smaller than one in the theoretical case. The simulation results are consistent with the theoretical ones. This further corroborates our scheme based on circuit QED can implement efficiently PCC transformation.     

Lasing without inversion in circuit quantum electrodynamics

We study the photon generation in a transmission line oscillator coupled to a driven qubit in the presence of a dissipative electromagnetic environment. It has been demonstrated previously that a population inversion in the qubit can lead to a lasing state of the oscillator. Here we show that the circuit can also exhibit the effect of "lasing without inversion." It arises since the coupling to the dissipative environment enhances photon emission as compared to absorption, similar to the recoil effect predicted for atomic systems. While the recoil effect is very weak, and so far elusive, the effect described here should be observable with realistic circuits. We analyze the requirements for system parameters and environment.     

High-fidelity readout in circuit quantum electrodynamics using the Jaynes-Cummings nonlinearity

We demonstrate a qubit readout scheme that exploits the Jaynes-Cummings nonlinearity of a superconducting cavity coupled to transmon qubits. We find that, in the strongly driven dispersive regime of this system, there is the unexpected onset of a high-transmission "bright" state at a critical power which depends sensitively on the initial qubit state. A simple and robust measurement protocol exploiting this effect achieves a single-shot fidelity of 87% using a conventional sample design and experimental setup, and at least 61% fidelity to joint correlations of three qubits.     

Charge noise acting on graphene double quantum dots in circuit quantum electrodynamics architecture

We investigate the dephasing mechanisms induced by the charge noise and microwave heating effect acting on a graphene double quantum dot(DQD) capacitively coupled to a microwave resonator. The charge noise is obtained from DC transport current, and its contribution to dephasing is simultaneously determined by the amplitude response of the microwave resonator. A lowfrequency 1/f-type noise is demonstrated to be the dominant factor of the dephasing of graphene DQD. Furthermore, when the applied microwave power is larger than-90 d Bm, the dephasing rate of graphene DQD increases rapidly with the increase of microwave power, and fluctuates slightly with the applied microwave power smaller than-90 d Bm. Our results can be applied to suppress the impeditive influence on the dephasing of graphene-based devices associated with microwave input in the perspective investigations.     

Controllable cross-Kerr interaction between microwave photons in circuit quantum electrodynamics

We propose a scheme to enable a controllable cross-Kerr interaction between microwave photons in a circuit quantum electrodynamics(QED) system.In this scheme we use two transmission-line resonators(TLRs) and one superconducting quantum interference device(SQUID) type charge qubit,which acts as an artificial atom.It is shown that in the dispersive regime of the circuit-QED system,a controllable cross-Kerr interaction can be obtained by properly preparing the initial state of the qubit,and a large cross-phase shift between two microwave fields in the two TLRs can then be reached.Based on this cross-Kerr interaction,we show how to create a macroscopic entangled state between the two TLRs.     

Mesoscopic entangled coherent states implemented with a circuit quantum electrodynamics system

We show a scheme to generate entangled coherent states in a circuit quantum electrodynamics system, which consists of a nanomechanical resonator, a superconducting Cooper-pair box (CPB), and a superconducting transmission line resonator. In the system, the CPB plays the role of a nonlinear medium and can be conveniently controlled by a gate voltage including direct-current and alternating-current components. The scheme provides a powerful tool for preparing the multipartite mesoscopic entangled coherent states.     

Fast generation of W state via superadiabatic-based shortcut in circuit quantum electrodynamics

We propose a scheme to fast prepare the three-qubit W state via superadiabatic-based shortcuts in a circuit quantumelectrodynamics (circuit QED) system. We derive the effective Hamiltonian to suppress the unwanted transitions betweendifferent eigenstates by counterdiabatic driving, and obtain the W state with high-fidelity based on the superadiabaticpassage. The numerical simulation results demonstrate that the proposed scheme can accelerate the evolution, and is moreefficient than that with the adiabatic passage. In addition, the proposed scheme is robust to the decoherence caused by theresonator decay and qubit relaxation, and does not need additional parameters, which could be feasible in experiment.     

Predictions of quantum mechanics and stochastic electrodynamics in travelling wave second harmonic generation

We show that stochastic electrodynamics and quantum mechanics give quantitatively different predictions for the quantum nondemolition (QND) correlations in travelling wave second harmonic generation. Using phase space methods and stochastic integration, we calculate correlations in both the positive-P and truncated Wigner representations, the latter being equivalent to the semi-classical theory of stochastic electrodynamics. We show that the semi-classical results are different in the regions where the system performs best in relation to the QND criteria, and that they significantly overestimate the performance in these regions.     

Photonic phase transition in circuit quantum electrodynamics lattices coupled to superconducting phase qubits

A hybrid quantum architecture was proposed to engineer a localization-delocalization phase transition of light in a two-dimension square lattices of superconducting coplanar waveguide resonators, which are interconnected by current-biased Josephson junction phase qubits. We find that the competition between the on-site repulsion and the nonlocal photonic hopping leads to the Mott insulator-superfluid transition. By using the mean-field approach and the quantum master equation, the phase boundary between these two different phases could be obtained when the dissipative effects of superconducting resonators and phase qubit are considered. The good tunability of the effective on-site repulsion and photon-hopping strengths enable quantum simulation on condensed matter physics and many-body models using such a superconducting resonator lattice system. The experimental feasibility is discussed using the currently available technology in the circuit QED.     

Switching from positive to negative absorption with electromagnetically induced transparency in circuit quantum electrodynamics

We present a theoretical study of electromagnetically induced transparency(EIT) in a superconducting quantum circuit with a tunable V-shaped energy spectrum derived from two superconducting Josephson charge qubits coupled with each other through a superconducting quantum interference device. Using the density matrix formalism and the steady-state approximation, we obtain the analytical expressions of the first-order matrix element associated with the absorption and dispersion of the probe field for two different V-type schemes. Our results show that, for this superconducting quantum system, it is possible to realize a remarkable phenomenon that dynamic conversion between EIT and EIT with amplification without population inversion. Such a unique optical feature has potential applications in quantum optical devices and quantum information processing.     

Realization of superposition and entanglement of coherent and squeezed states in circuit quantum electrodynamics

We propose a new scheme for generating the superposition and entanglement of the coherent states and squeezed states by considering N superconducting charge qubits (or artificial two-level atoms) interacting with photons in a high finesse cavity on a chip, assisted by a strong driving field. By virtue of the parameters of this system, we can generate novel quantum states, for example, multiparty entangled states and Schro¨dinger cat states among the superconducting qubits, coherent states and squeezed state...     

A scheme for two-photon lasing with two coupled flux qubits in circuit quantum electrodynamics

We theoretically study the system of a superconducting transmission line resonator coupled to two interacting superconducting flux qubits.It is shown that under certain conditions the resonator mode can be tuned to two-photon resonance between the ground state and the highest excited state while the middle excited states are far-off resonance.Furthermore,we study the steady-state properties of the flux qubits and resonator,such as the photon statistics,the spectrum and squeezing of the resonator,and demonstrate that two-photon laser can be implemented with current experimental technology.     

Quantum mechanics derived from stochastic electrodynamics

The connection between stochastic electrodynamics (SED) and the quantum theory of matter is further explored. The main result is that the Fokker-Planck-like equation of SED can be recast into the form of a Schrödinger equation with radiative corrections, when the system is close to a state of equilibrium. The phase-space distribution can be written as Wigner's pseudo-distribution plus corrections due to the nonlinearity of the external force and to radiative effects. The radiative corrections predicted by the theory, namely the Lamb shift and the decay of excited atomic states, coincide with those predicted by QED. Moreover, the theory offers a clear physical interpretation of these phenomena as due to the coupling of the electric dipole of the system with the zero-point radiation field and to radiation reaction, respectively.     

Infrared problems in quantum electrodynamics

We present a self-contained treatment of the infrared problem in Quantum Electrodynamics. Our program includes a derivation and proof of finiteness of modified reduction formulae for scattering in Coulomb potentials and unitary extensions of the relativistic Coulomb amplitudes in the forward direction. The renormalization structure of the theory is discussed in connection with the infrared problem and the renormalization group is reconsidered and shown to be inadequate for the “improvement” of perturbation theoretic results. However, simple forms of the renormalization group equations are easily established, which allow for a simple discussion of the renormalization structure and the extraction of physical quantities out of Green functions normalized at an arbitrary mass μ < m (m is the fermion mass). As an example of such a quantity we consider the construction of a renormalized and infrared finite mass-operator in presence of external fields. Scattering theory in Quantum Electrodynamics is elaborated in the context of the coherent state formulation of the asymptotic condition. Dimensional regularization techniques are systematically used for the reduction of coherent states and the construction of S-matrix elements and the cross-section formulae. The latter are obtained in a relatively simple form, which allows for a direct comparison with the exact cross-section formulae derived in the traditional context. This establishes the equivalence of the two approaches at the cross-section level. Various applications illustrate the techniques presented here and relative topics are discussed.