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arXiv:1308.6435 · Physical Review A

Cavity polariton in a quasilattice of qubits and its selective radiation

Hou Ian, Yu-xi Liu

Published Apr 2, 2014• 7 citations
arXivHTMLPDF

Abstract

In a circuit quantum eletrodynamic system, a chain of $N$ qubits inhomogeneously coupled to a cavity field forms a mesoscopic quasilattice, which is characterized by its degree of deformation from a normal lattice. This deformation is a function of the relative spacing, that is the ratio of the qubit spacing to the cavity wavelength. A polariton mode arises in the quasilattice as the dressed mode of the lattice excitation by the cavity photon. We show that the transition probability of the polariton mode is either enhanced or decreased compared to that of a single qubit by the deformation, giving a selective spontaneous radiation spectrum. Further, unlike a microscopic lattice with large-$N$ limit and nearly zero relative spacing, the polariton in the quasilattice has uneven decay rate over the relative spacing. We show that this unevenness coincides with the cooperative emission effect expected from the superradiance model, where alternative excitations in the qubits of the lattice result in maximum decay.

DOI
10.1103/physreva.89.043804

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In a circuit quantum eletrodynamic system, a chain of NNN qubits inhomogeneously coupled to a cavity field forms a mesoscopic quasilattice, which is characterized by its degree of deformation from a normal lattice. This deformation is a function of the relative spacing, that is the ratio of the qubit spacing to the cavity wavelength. A polariton mode arises in the quasilattice as the dressed mode of the lattice excitation by the cavity photon. We show that the transition probability of the polariton mode is either enhanced or decreased compared to that of a single qubit by the deformation, giving a selective spontaneous radiation spectrum. Further, unlike a microscopic lattice with large-NNN limit and nearly zero relative spacing, the polariton in the quasilattice has uneven decay rate over the relative spacing. We show that this unevenness coincides with the cooperative emission effect expected from the superradiance model, where alternative excitations in the qubits of the lattice result in maximum decay.
Unlike atoms in a lattice, the spacings between neighboring qubits in a superconducting quantum circuit are mesoscopic and non-uniform. The strength of interaction between this quasi-lattice chain of qubits and a resonator mode in circuit transmission lines is inhomogeneous and geometrically dependent on the circuit layout. We propose a projection-deformation method to give analytically the eigenstates of the quasi-particle excitation that arise in the quasi-lattice. We further show that, during the quasi-particle excitation, the distribution of multi-photon resonances between the resonator photon and the quasi-lattice is determined by the degree the quasi-lattice is deformed from a normal lattice. The multi-photon resonances lead to simultaneous generation of GHZ-type and W-type of multipartite entanglement states of the qubits, which is enhanced by the inhomogeneous interaction. Comparing the concurrence and the 3-tangle generated, we find that the totally non-separable GHZ entanglement is specifically increased, up to two orders of magnitude.
Ultracold atoms uniformly filling an optical lattice can be treated like an artificial crystal. An implementation including the atomic occupation of a single excited atomic state can be represented by a two-component Bose-Hubbard model. Its phase diagram exhibits a quantum phase transition from a superfluid to a Mott insulator phase. The dynamics of electronic excitations governed by electrostatic dipole-dipole interactions in the ordered regime can be well described by wave-like collective excitations called excitons. Here we present an extensive study of such excitons for a wide range of geometries and dimensionality. Their lifetimes can vary over many orders of magnitude from metastable propagation to superradiant decay. Particularly strong effects occur in one dimensional atomic chains coupled to tapered optical fibers. For an optical lattice within a cavity the excitons are coupled to cavity photons and the resulting collective cavity QED model can be efficiently formulated in terms of polaritons. Their properties are explicitly calculated for different lattices and they constitute a non-destructive monitoring tool for important system properties. Even the formation of molecules in optical lattices manifests itself in modified polariton properties as e.g. an anisotropic optical spectrum. Partial dissipation of the exciton energy in the lattice leads to heating, which can be microscopically understood through a mechanism transferring atoms into higher Bloch bands via a resonant excitation transfer among neighboring lattice sites. The presence of lattice defects like vacancies in the Mott insulator induces a characteristic scattering of polaritons, which can be optically observed to monitor the lattice integrity. Our models can be applied to simulate and understand corresponding collective phenomena in solid crystals, where many effects are often masked by noise and disorder.
The mesoscopic scale of superconducting qubits makes their inter-spacings comparable to the scale of wavelength of a circuit cavity field to which they commonly couple. This comparability results in inhomogeneous coupling strengthes for each qubit and hence asynchronous Rabi excitation cycles among the qubits that form a quasi-lattice. We find that such inhomogeneous coupling benefits the formation of multi-photon resonances between the single-mode cavity field and the quasi-lattice. The multi-photon resonances lead, in turn, to the simultaneous generation of inequivalent GHZ and W types of multipartite entanglement states, which are not transformable to each other through local operations with classical communications. Applying the model on the 3-qubit quasi-lattice and using the entanglement measures of both concurrence and 3-tangle, we verify that the inhomogeneous coupling specifically promotes the generation of the totally inseparable GHZ state.
In this study, we present the superradiance effects of N identical molecular emitters inside Fabry–Pérot (FP) cavity systems in the framework of macroscopic quantum electrodynamics. The proposed theory can estimate the enhancement of spontaneous emission rates, including the effects of cavity geometry and material dielectric properties. Moreover, our study connects the multichromophoric excitation energy transfer theory and the Tavis–Cummings model via identical cooperative decay rates and dipole–dipole shifts. For molecules resonant with the cavity photon mode, we find that the enhancement is not exactly proportional to N even in a perfect FP cavity due to the effects of electrostatic dipole–dipole interactions. Moreover, in a silver FP cavity, our simulation shows that the enhancement saturates for a large N, indicating that the cavity photon mode can lead to only the collective emission of a limited number of molecules. For molecules in the proximity of the silver mirror, we demonstrate that under specific conditions, the subradiance of molecular emitters can occur through surface plasmon polaritons. Our study not only provides new insights into the mechanism of superradiance effects but also demonstrates that collective effects such as superradiance and subradiance can be controlled by manipulating the dielectric environments.
We present a general theory for calculating the damping rate of elementary density-wave excitations in a Bose-Einstein condensate strongly coupled to a single radiation field mode of an optical cavity. Thereby we give a detailed derivation of the huge resonant enhancement in the Beliaev damping of a density-wave mode, predicted recently by K\'onya et al. [Phys. Rev. A 89, 051601(R) (2014)]. The given density-wave mode constitutes the polaritonlike soft mode of the self-organization phase transition. The resonant enhancement takes place, in both the normal and the ordered phases, outside the critical region. We show that the large damping rate is accompanied by a significant frequency shift of this polariton mode. Going beyond the Born-Markov approximation and determining the poles of the retarded Green's function of the polariton, we reveal a strong coupling between the polariton and a collective mode in the phonon bath formed by the other density-wave modes.
Cavity-embedded quantum emitters show strong modifications of free space radiation properties such as an enhanced decay known as the Purcell effect. The central parameter is the cooperativity CCC, the ratio of the square of the coherent cavity coupling strength over the product of cavity and emitter decay rates. For a single emitter, CCC is independent of the transition dipole moment and dictated by geometric cavity properties such as finesse and mode waist. In a recent work [Phys. Rev. Lett. 119, 093601 (2017)], we have shown that collective excitations in ensembles of dipole-dipole coupled quantum emitters show a disentanglement between the coherent coupling to the cavity mode and spontaneous free space decay. This leads to a strong enhancement of the cavity cooperativity around certain collective subradiant antiresonances. Here, we present a quantum Langevin equations approach aimed at providing results beyond the classical coupled dipoles model. We show that the subradiantly enhanced cooperativity imprints its effects onto the cavity output field quantum correlations while also strongly increasing the cavity-emitter system's collective Kerr nonlinear effect.