Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0305155

Cavity QED and Quantum Computation in the Strong Coupling Regime

Kazuyuki Fujii

Published May 26, 2003• 0 citations
arXivHTMLPDF

Abstract

In this paper we propose a Hamiltonian generalizing the interaction of the two--level atom and both the single radiation mode and external field $...$ a kind of cavity QED. We solve the Schrodinger equation in the strong coupling regime by making use of rotating wave approximation under new resonance conditions containing the Bessel functions and etc, and obtain unitary transformations of four types corresponding to Rabi oscillations which perform quantum logic gates in Quantum Computation.

DOI
10.48550/arxiv.quant-ph/0305155

Related papers

Cavity QED and Quantum Computation in the Strong Coupling Regime II : Two Atoms Case

Kazuyuki Fujii

In this paper we study the behavior of (laser--cooled) m--atoms trapped in a cavity interacting with a photon $...$ Cavity QED $...$ and attempt to solve the Schr{ö}dinger equation of this model in the strong coupling regime. In the case of m = 2 we construct Bell--Schr{\" o}dinger cat states (in our terminology) and obtain with such bases some unitary transformations by making use of the rotating wave approximation under new resonance conditionscontaining the Bessel functions, which will be applied to construct important quantum logic gates in Quantum Computation. Moreover we propose in the case of m = 3 a crucial problem to solve on Quantum Computation.

arXiv:quant-ph/0307168•Jul 24, 2003•0 citations

A Generalized Hamiltonian Characterizing the Interaction of the Two-Level Atom and both the Single Radiation Mode and External Field

Kazuyuki Fujii

In this paper we propose some Hamiltonian characterizing the interaction of the two-level atom and both the single radiation mode and external field, which might be a generalization of that of Sch{ö}n and Cirac (quant-ph/0212068). We solve them in the strong coupling regime under some conditions (the rotating wave approximation, resonance condition and etc), and obtain unitary transformations of four types to perform Quantum Computation.

arXiv:quant-ph/0303118•Mar 19, 2003•2 citations

Cavity QED and Quantum Computation in the Weak Coupling Regime II : Complete Construction of the Controlled-Controlled NOT Gate

Kazuyuki Fujii, Kyoko Higashida, Ryosuke Kato +1 more

In this paper we treat a cavity QED quantum computation. Namely, we consider a model of quantum computation based on n atoms of laser-cooled and trapped linearly in a cavity and realize it as the n atoms Tavis-Cummings Hamiltonian interacting with n external (laser) fields. We solve the Schr{\" o}dinger equation of the model in the weak coupling regime to construct the controlled NOT gate in the case of n=2, and to construct the controlled-controlled NOT gate in the case of n=3 by making use of several resonance conditions and rotating wave approximation associated to them. We also present an idea to construct general quantum circuits. The approach is more sophisticated than that of the paper [K. Fujii, Higashida, Kato and Wada, Cavity QED and Quantum Computation in the Weak Coupling Regime, J. Opt. B : Quantum Semiclass. Opt. {\bf 6} (2004), 502]. Our method is not heuristic but completely mathematical, and the significant feature is based on a consistent use of Rabi oscillations.

arXiv:quant-ph/0501046•Jan 11, 2005•15 citations

Cavity QED and quantum computation in the weak coupling regime

Kazuyuki Fujii, Kyoko Higashida, Ryosuke Kato +1 more

In this paper we consider a model of quantum computation based on n atoms, laser cooled and trapped linearly in a cavity, and realize it as the n -atom Tavis–Cummings Hamiltonian interacting with n external (laser) fields. We solve the Schrödinger equation of the model in the case of n = 2 and construct the controlled NOT gate by making use of a resonance condition and the rotating wave approximation associated with it. Our method is not heuristic but completely mathematical, and the significant feature is the consistent use of Rabi oscillations. We also present an idea for the construction of three controlled NOT gates in the case of n = 3 which gives a controlled–controlled NOT gate.

arXiv:quant-ph/0407014•Journal of Optics B Quantum and Semiclassical Optics•Oct 16, 2004•25 citations

Cavity QED and Quantum Computation in the Weak Coupling Regime (Dynamical Systems and Differential Geometry)

Kazuyuki Fujii, Kyoko Higashida, Ryosuke Kato +1 more

In this paper we consider a model of quantum computation based on $\mathrm{n}$ atoms of laser-pooled and trapped linearly in a cavity and realize it as the $\mathrm{n}$ atoms Tavis- Cummings Hamiltonian interacting with $\mathrm{n}$ external (laser) fields.We solve the Schrodinger equation of the model in the case of $\mathrm{n}=2$ and construct the controlled NOT gate by making use of a resonance condition and rotating wave approximation associated to it.We also present an idea of the construction of three controlled NOT gates in the case of $\mathrm{n}=3$ , which gives the controlled-controlled NOT gate.

数理解析研究所講究録•Dec 1, 2004•0 citations

Rabi oscillations and macroscopic quantum superposition states

Marco Frasca

A two-level atom interacting with a single radiation mode is considered, without the rotating-wave approximation, in the strong-coupling regime. It is shown that, in agreement with the recent results on Rabi oscillations in a Josephson junction [Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai, Phys. Rev. Lett. 87, 246601 (2001)], the Rabi frequency is indeed proportional to first kind integer order Bessel functions in the limit of a large number of photons and the dressed states are macroscopic quantum superposition states. To approach this problem, analytical use of the dual Dyson series and the rotating-wave approximation is made.

arXiv:quant-ph/0111134•Physical Review A•Aug 9, 2002•17 citations
In this paper we propose a Hamiltonian generalizing the interaction of the two--level atom and both the single radiation mode and external field ......... a kind of cavity QED. We solve the Schrodinger equation in the strong coupling regime by making use of rotating wave approximation under new resonance conditions containing the Bessel functions and etc, and obtain unitary transformations of four types corresponding to Rabi oscillations which perform quantum logic gates in Quantum Computation.
In this paper we study the behavior of (laser--cooled) m--atoms trapped in a cavity interacting with a photon ......... Cavity QED ......... and attempt to solve the Schr{ö}dinger equation of this model in the strong coupling regime. In the case of m = 2 we construct Bell--Schr{\" o}dinger cat states (in our terminology) and obtain with such bases some unitary transformations by making use of the rotating wave approximation under new resonance conditionscontaining the Bessel functions, which will be applied to construct important quantum logic gates in Quantum Computation. Moreover we propose in the case of m = 3 a crucial problem to solve on Quantum Computation.
In this paper we treat a cavity QED quantum computation. Namely, we consider a model of quantum computation based on n atoms of laser-cooled and trapped linearly in a cavity and realize it as the n atoms Tavis-Cummings Hamiltonian interacting with n external (laser) fields. We solve the Schr{\" o}dinger equation of the model in the weak coupling regime to construct the controlled NOT gate in the case of n=2, and to construct the controlled-controlled NOT gate in the case of n=3 by making use of several resonance conditions and rotating wave approximation associated to them. We also present an idea to construct general quantum circuits. The approach is more sophisticated than that of the paper [K. Fujii, Higashida, Kato and Wada, Cavity QED and Quantum Computation in the Weak Coupling Regime, J. Opt. B : Quantum Semiclass. Opt. {\bf 6} (2004), 502]. Our method is not heuristic but completely mathematical, and the significant feature is based on a consistent use of Rabi oscillations.
In this paper we consider a model of quantum computation based on n atoms, laser cooled and trapped linearly in a cavity, and realize it as the n -atom Tavis–Cummings Hamiltonian interacting with n external (laser) fields. We solve the Schrödinger equation of the model in the case of n = 2 and construct the controlled NOT gate by making use of a resonance condition and the rotating wave approximation associated with it. Our method is not heuristic but completely mathematical, and the significant feature is the consistent use of Rabi oscillations. We also present an idea for the construction of three controlled NOT gates in the case of n = 3 which gives a controlled–controlled NOT gate.
In this paper we consider a model of quantum computation based on n\mathrm{n}n atoms of laser-pooled and trapped linearly in a cavity and realize it as the n\mathrm{n}n atoms Tavis- Cummings Hamiltonian interacting with n\mathrm{n}n external (laser) fields.We solve the Schrodinger equation of the model in the case of n=2\mathrm{n}=2n=2 and construct the controlled NOT gate by making use of a resonance condition and rotating wave approximation associated to it.We also present an idea of the construction of three controlled NOT gates in the case of n=3\mathrm{n}=3n=3 , which gives the controlled-controlled NOT gate.
A two-level atom interacting with a single radiation mode is considered, without the rotating-wave approximation, in the strong-coupling regime. It is shown that, in agreement with the recent results on Rabi oscillations in a Josephson junction [Y. Nakamura, Yu. A. Pashkin, and J. S. Tsai, Phys. Rev. Lett. 87, 246601 (2001)], the Rabi frequency is indeed proportional to first kind integer order Bessel functions in the limit of a large number of photons and the dressed states are macroscopic quantum superposition states. To approach this problem, analytical use of the dual Dyson series and the rotating-wave approximation is made.