Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond

Zhu, Xiaobo; Saito, Shiro; Kemp, Alexander; Kakuyanagi, Kosuke; Karimoto, Shin–ichi; Nakano, Hideyuki; Munro, William J.; Tokura, Y.; Everitt, Mark S.; Nemoto, Kae; Kasu, Makoto; Mizuochi, Norikazu; Semba, Kouichi

doi:10.1364/qim.2012.qt1a.4

Cited by 69 publications

(104 citation statements)

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“…In recent years, special attention has been paid to studying the spectrum of self-adjoint operators with non-commutative coefficients, in other words, interacting quantum systems, like the quantum Rabi model, the Jaynes-Cumming (JC) model, etc., not only in mathematics [4,5] but also in theoretical physics [13,2,14,26] and experimental physics (see e.g. [3,29]). For instance, the quantum Rabi model [22] is known to be the simplest model used in quantum optics to describe interaction of light and matter and the JC model is the widely studied rotating-wave approximation of the Rabi model [13,5].…”

Section: Introductionmentioning

confidence: 99%

Equivalence Between the Eigenvalue Problem of Non-Commutative Harmonic Oscillators and Existence of Holomorphic Solutions of Heun Differential Equations, Eigenstates Degeneration, and the Rabi Model

Wakayama¹

2015

Int Math Res Notices

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The initial aim of the present paper is to provide a complete description for the eigenvalue problem of the non-commutative harmonic oscillator (NcHO), which is given by a two-by-two system of paritypreserving ordinary differential operator [19], in terms of Heun's ordinary differential equations, the second order Fuchsian differential equations with four regular singularities in a complex domain. This description has been achieved for odd eigenfunctions in Ochiai [16] nicely but missing for even eigenfunctions up to now. As a by-product of this study, using the monodromy representation of Heun's equation, we prove that the multiplicity of the eigenvalue of the NcHO is at most two. Moreover, we give a condition for the existence of a finite-type eigenfunction (essentially, given by a finite sum of Hermite functions) of the eigenvalue problem and an explicit example of such eigenvalues, from which one finds that doubly degenerate eigenstates of the NcHO actually exist even in the same parity. In the final section, as the second main purpose of this paper, we discuss a connection between the quantum Rabi model [2, 13, 28] and the operator naturally arising from the NcHO through the oscillator representation of the Lie algebra sl2, by the general confluence procedure for Heun's equation and Langlands' quotient realization of a different representation of sl2.

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Section: Introductionmentioning

confidence: 99%

Equivalence Between the Eigenvalue Problem of Non-Commutative Harmonic Oscillators and Existence of Holomorphic Solutions of Heun Differential Equations, Eigenstates Degeneration, and the Rabi Model

Wakayama¹

2015

Int Math Res Notices

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“…In this context, a superconducting flux qubit coherently coupled to a spin ensemble has been reported in Ref. [11], while interaction between ultracold atoms and mechanical systems has been studied in Ref. [12], and strong coupling between a Bose-Einstein condensate (BEC) and an optical cavity was experimentally reported in Refs.…”

Section: Introductionmentioning

confidence: 99%

Quantum correlations of quadratic optomechanical oscillator

Singh

Ooi

2014

J. Opt. Soc. Am. B

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The quantum optomechanical system serves as an interface for coupling between photons, excitons, and mechanical oscillations. We use the quantum Langevin approach to study a hybrid optomechanical system that contains a single undoped semiconductor quantum well in a cavity, where one of its mirrors is a thin dielectric membrane having quadratic response to the cavity fields. A decorrelation method is employed to solve for a large number of coupled equations. Transient mean numbers of cavity photons, moving membranes, and excitons that provide dynamical behavior are computed. We obtain the two-boson second-order correlation functions for the cavity field and the membrane oscillator, and their cross correlations that provide nonclassical quantum statistical properties and useful insights into the quadratic optomechanical system.

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“…Significant progress has been made recently in the field of quantum information processing (QIP) based on hybrid systems, especially for composite systems consisting of solid-state spin systems (e.g., nitrogen-vacancy center ensembles (NVEs), nitrogen substitution P 1 center ensembles or Y 2 SiO 5 spin ensembles) and superconducting resonators (SRs) 1 2 3 4 5 6 7 or superconducting qubits 8 9 10 11 , which provide a promising platform to study fundamental quantum information science 12 13 14 15 16 and intriguing quantum optical phenomenon 17 18 19 20 . The negative charged nitrogen-vacancy (NV − ) centers in diamond 21 22 23 24 25 26 27 28 29 30 31 feature excellent coherence properties (e.g., long coherence time in a wide temperature range even at room temperature), and have the ability to coherently couple to various external optical/microwave fields simultaneously 32 33 34 35 36 .…”

mentioning

confidence: 99%

“…More importantly, in contrast to the conventional methods relying on electric-dipole couplings, the collective magnetic coupling mechanism for manipulating spin ensembles owns the advantages of weak dissipation and strong coupling. These novel merits ensure the NVEs being one of the ideal candidates for integration into a hybrid quantum system which gathers the strength of each physical system and mitigates the individual weaknesses 8 12 37 38 .…”

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confidence: 99%

“…To date, successive experiments have demonstrated strong magnetic couplings between SR and NVE 1 2 3 4 (or P 1 center ensemble 5 ), and between superconducting gap-tunable flux qubit 39 40 and NVE 8 9 , for which, many researchers have paid much attention on the potential applications 41 42 43 and also been motivated to make theoretical efforts on intriguing quantum behaviors 19 20 , continuous variable entanglement 44 , and quantum simulation on the condensed matter physics 17 18 as well as many-body physics 45 46 in such systems.…”

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confidence: 99%

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Controllable quantum dynamics of inhomogeneous nitrogen-vacancy center ensembles coupled to superconducting resonators

Song

Yang

Yin

et al. 2016

Sci Rep

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We explore controllable quantum dynamics of a hybrid system, which consists of an array of mutually coupled superconducting resonators (SRs) with each containing a nitrogen-vacancy center spin ensemble (NVE) in the presence of inhomogeneous broadening. We focus on a three-site model, which compared with the two-site case, shows more complicated and richer dynamical behavior, and displays a series of damped oscillations under various experimental situations, reflecting the intricate balance and competition between the NVE-SR collective coupling and the adjacent-site photon hopping. Particularly, we find that the inhomogeneous broadening of the spin ensemble can suppress the population transfer between the SR and the local NVE. In this context, although the inhomogeneous broadening of the spin ensemble diminishes entanglement among the NVEs, optimal entanglement, characterized by averaging the lower bound of concurrence, could be achieved through accurately adjusting the tunable parameters.

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Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond

Cited by 69 publications

References 1 publication

Equivalence Between the Eigenvalue Problem of Non-Commutative Harmonic Oscillators and Existence of Holomorphic Solutions of Heun Differential Equations, Eigenstates Degeneration, and the Rabi Model

Equivalence Between the Eigenvalue Problem of Non-Commutative Harmonic Oscillators and Existence of Holomorphic Solutions of Heun Differential Equations, Eigenstates Degeneration, and the Rabi Model

Quantum correlations of quadratic optomechanical oscillator

Controllable quantum dynamics of inhomogeneous nitrogen-vacancy center ensembles coupled to superconducting resonators

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