We give a unified approach to macroscopic QED in arbitrary linearly responding media, based on the quite general, nonlocal form of the conductivity tensor as it can be introduced within the framework of linear response theory, and appropriately chosen sets of bosonic variables. The formalism generalizes the quantization schemes that have been developed previously for diverse classes of linear media. In particular, it turns out that the scheme developed for locally responding linear magnetodielectric media can be recovered from the general scheme as a limiting case for weakly spatially dispersive media. With regard to practical applications, we furthermore address the dielectric approximation for the conductivity tensor and the surface impedance method for the calculation of the Green tensor of the macroscopic Maxwell equations, the two central quantities of the theory.
Recently, we have developed a unified approach to QED in arbitrary linearly responding media in equilibrium--media that give rise to absorption [Phys. Rev. A \textbf{75}, (2007) 053813]. In the present paper we show that, under appropriate conditions, the theory can be quite naturally generalized to amplifying media the effect of which is described within the framework of linear response theory. We discuss the limits of validity of the generalized theory and make contact with earlier quantization schemes suggested for the case of linearly and locally responding amplifying dielectric-type media…
The phenomenological Maxwell field is quantized for arbitrarily space- and frequency-dependent complex permittivity. The formalism takes account of the Kramers--Kronig relation and the dissipation-fluctuation theorem and yields the fundamental equal-time commutation relations of QED. Applications to the quantum-state transformation at absorbing and amplifying four-port devices and to the spontaneous decay of an excited atom in the presence of absorbing dielectric bodies are discussed.
We propose a scheme to generate arbitrary Fock states |N> in a cavity QED using N resonant Rydberg atoms. The atom-field interaction times are controlled via Stark-shifts adjusted in a way that each atom transfers a photon to the cavity, turning atomic detections useless. Fluctuations affecting the control of the atom-field interactions are also considered.
In this paper, we propose a scheme for the controlled teleportation of an arbitrary two-atom entangled state $|ϕ>_{12}=a|gg>_{12}+b|ge>_{12}+c|eg>_{12}+d|ee>_{12}$ in driven cavity QED. An arbitrary two-atom entangled state can be teleported perfectly with the help of the cooperation of the third side by constructing a three-atom GHZ entangled state as the controlled channel. This scheme does not involve apparent (or direct) Bell-state measurement and is insensitive to the cavity decay and the thermal field. The probability of the success in our scheme is 1.0.
I show a scheme which allows a perfect transfer of an unknown single-qubit atomic state from one atom to another by letting two atoms interact simultaneously with a cavity QED. During the interaction between atom and cavity, the cavity is only virtually excited and accordingly the scheme is insensitive to the cavity field states and cavity decay. Based on this scheme, a network for transfer of an arbitrary single-qubit atomic state between atoms is engineered. Then the scheme is generalized to perfectly transfer an arbitrary 2-qubit atomic state and accordingly a network for transfer of an arb…
After giving an outline of the quantization scheme based on the microscopic Hopfield model of a dielectric bulk material, we show how the classical phenomenological Maxwell equations of the electromagnetic field in the presence of dielectric matter of given space- and frequency-dependent complex permittivity can be transferred to quantum theory. Including in the theory the interaction of the medium-assisted field with atomic systems, we present both the minimal-coupling Hamiltonian and the multipolar-coupling Hamiltonian in the Coulomb gauge. To illustrate the concept, we discuss the input--ou…
Compared with a qubit, a qutrit (i.e., three-level quantum system) has a larger Hilbert space and thus can be used to encode more information in quantum information processing and communication. Here, we propose a scheme to transfer an arbitrary quantum state between two flux qutrits coupled to two resonators. This scheme is simple because it only requires two basic operations. The state-transfer operation can be performed fast because of using resonant interactions only. Numerical simulations show that high-fidelity transfer of quantum states between the two qutrits is feasible with current c…
We present results of numerical investigation of a microscopic dynamics of a two-level atom embedded into a ``linear crystal'' of other two-level atoms. These additional atoms play a role of a material media. All atoms interact with a multimode cavity field. We study how the decay of the initially excited atom is affected by the presence of material media and spectral properties of the cavity field.
A qudit ($d$-level quantum systems) has a large Hilbert space and thus can be used to achieve many quantum information and communication tasks. Here, we propose a method to transfer arbitrary $d$-dimensional quantum states (known or unknown) between two superconducting qudits coupled to a single cavity. The state transfer can be performed fast because of employing resonant interactions only. In addition, quantum states can be deterministically transferred without measurement. Numerical simulations show that high-fidelity transfer of quantum states between two superconducting transmon qudits ($…
Recently a quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive, and absorbing dielectric medium has been developed and applied to a system consisting of two infinite half-spaces with a common planar interface (H.T. Dung, L. Knoell, and D.-G. Welsch, Phys. Rev. A 57, in press). Here we show that the scheme, which is based on the classical Green-tensor integral representation of the electromagnetic field, applies to any inhomogeneous medium. For this purpose we prove that the fundamental equal-time commut…
We propose a cavity-QED-based scheme of generating entanglement between atoms. The scheme is scalable to an arbitrary number of atoms, and can be used to generate a variety of multipartite entangled states such as the Greenberger-Horne-Zeilinger, W, and cluster states. Furthermore, with a role switching of atoms with photons, the scheme can be used to generate entanglement between cavity fields. We also introduce a scheme that can generate an arbitrary multipartite field graph state.
The electromagnetic field inside an isotropic optically active medium is quantized on the base of Fedorov's model for optical activity. The modified photon propagator is derived. Using this result it is shown that the QED correction to the electron mass contains chiral terms which nevertheless are parity invariant. The spontaneous emission rate of a two-level atom is shown to increase in the medium. The spontaneously emitted radiation is partially polarized.
We propose a scheme to generate photonic tensor network states by sequential scattering of photons in waveguide QED systems. We show that sequential scatterings can convert a series of unentangled photons into any type of matrix product states. We also demonstrate the possibility of generating projected entangled pair states with arbitrary network representation by photon re-scattering.
We study the photon generation from arbitrary initial state in cavity QED due to the combined action of the anti-rotating term present in the Rabi Hamiltonian and Lindblad-type dephasing. We obtain a simple set of differential equations describing this process and deduce useful formulae for the moments of the photon number operator, demonstrating analytically that the average photon number increases linearly with time in the asymptotic limit.
An experimental scheme is proposed that allows direct measurement of the concurrence of a two-qubit cavity system. It is based on the cavity-QED technology using atoms as flying qubits and relies on the identity of the two-particle visibility of the atomic probability with the concurrence of the cavity system. The scheme works for any arbitrary pure initial state of the two-qubit cavity system.
We study the zero-temperature phase diagram of a one-dimensional array of QED cavities where, besides the single-photon hopping, an additional coupling between neighboring cavities is mediated by an N-type four-level system. By varying the relative strength of the various couplings, the array is shown to exhibit a variety of quantum phases including a polaritonic Mott insulator, a density-wave and a superfluid phase. Our results have been obtained by means of numerical density-matrix renormalization group calculations. The phase diagram was obtained by analyzing the energy gaps for the polarit…
In a recent remarkable experiment [R. B. Patel et al., Science advances 2, e1501531 (2016)], a 3-qubit quantum Fredkin (i.e., controlled-SWAP) gate was demonstrated by using linear optics. Here we propose a simple experimental scheme by utilizing the dispersive interaction in superconducting quantum circuit to implement a hybrid Fredkin gate with a superconducting flux qubit as the control qubit and two separated quantum memories as the target qudits. The quantum memories considered here are prepared by the superconducting coplanar waveguide resonators or nitrogen-vacancy center ensembles. In …
A new scheme of photon echo based quantum memory in the optimal optical QED cavity with off-resonant Raman atomic transition is proposed. The scheme employs the atomic ensembles characterized by an optically thin resonant transition and natural inhomogeneous broadening of the resonant line composed of the arbitrary narrow homogeneous spectral components. The scheme provides robust and quite simple coherent control of the light-atoms dynamics that can be implemented by using an existing optical technique and opens a practical way for realization of the efficient long-lived multi-mode optical qu…
We propose a scheme to generate Greenberger-Horne-Zeilinger (GHZ) state for N superconducting qubits in a circuit QED system. By sinusoidally modulating the qubit-qubit coupling, a synthetic magnetic field has been made which broken the time-reversal symmetry of the system. Directional rotation of qubit excitation can be realized in a three-qubit loop under the artificial magnetic field. Based on the special quality that the rotation of qubit excitation has different direction for single- and double-excitation loops, we can generate three-qubit GHZ state and extend this preparation method to a…
We propose a new scheme for quantum computation using flying qubits--propagating photons in a one-dimensional waveguide--interacting with matter qubits. Photon-photon interactions are mediated by the coupling to a three- or four-level system, based on which photon-photon π-phase gates (Controlled-NOT) can be implemented for universal quantum computation. We show that high gate fidelity is possible given recent dramatic experimental progress in superconducting circuits and photonic-crystal waveguides. The proposed system can be an important building block for future on-chip quantum networks.
We propose a scheme in which the Lipkin-Meshkov-Glick model is realized within a circuit QED system. An array of N superconducting qubits interacts with a driven cavity mode. In the dispersive regime, the cavity mode is adiabatically eliminated generating an effective model for the qubits alone. The characteristic long-range order of the Lipkin-Meshkov-Glick model is here mediated by the cavity field. For a closed qubit system, the inherent second order phase transition of the qubits is reflected in the intensity of the output cavity field. In the broken symmetry phase, the many-body ground st…
We analyze a coupling scheme for qubits in different cavities of circuit-QED architecture. In contrast to the usual scheme where the cavities are coupled by an interface capacitance we employ a bridge qubit connecting cavities to mediate two-qubit coupling. This active coupling scheme makes it possible to switch on/off and adjust the strength of qubit-qubit coupling, which is essential for scalability of quantum circuit. By transforming the Hamiltonian we obtain an exact expression of two-qubit coupling in the rotating-wave approximation. For the general case of $n$ qubits the Hamiltonian can …
