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

Rabi flopping and Schr\"odinger cat states

Marco Frasca

Published Nov 24, 2001• 0 citations
OpenAlex

Abstract

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 flopping in a Josephson junction (Y. Nakamura, Yu. A. Pashkin and J. S. Tsai, to appear in Phys. Rev. Lett.), 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 Schr\\"odinger cat states. To approach this problem analytically use is made of the dual Dyson series and the rotating-wave approximation.

Related papers

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

N-Level System Interacting with Single Radiation Mode and Multi Cat States of Schrodinger in the Strong Coupling Regime

Kazuyuki Fujii

In this paper we consider some (generalized) models which deal with n--level atom interacting with a single radiation mode and study a general structure of Rabi floppings of these generalized ones in the strong coupling regime. To solve these models we introduce multi cat states of Schr{\" o}dinger in our terminology and extend the result in (quant--ph/0203135) which Rabi frequencies are given by matrix elements of generalized coherent operators (quant--ph/0202081) under the rotating--wave approximation. Our work is a full generalization of Frasca (quant--ph/0111134) and Fujii (quant--ph/0203135). In last we make a brief comment on an application to Quantum Computation on the space of qudits.

arXiv:quant-ph/0210166•Oct 24, 2002•7 citations

Cooperative effects in Josephson junctions in a cavity in the strong coupling regime

Marco Frasca

We analyze the behavior of systems of two and three qubits made by Josephson junctions, treated in the two level approximation, driven by a radiation mode in a cavity. The regime we consider is a strong coupling one recently experimentally reached for a single junction. Rabi oscillations are obtained with the frequency proportional to integer order Bessel functions in the limit of a large photon number, similarly to the case of the single qubit. A selection rule is derived for the appearance of Rabi oscillations. A quantum amplifier built with a large number of Josephson junctions in a cavity in the strong coupling regime is also described.

arXiv:cond-mat/0411171•Physical Review B•May 31, 2005•3 citations

Cavity QED and Quantum Computation in the Strong Coupling Regime

Kazuyuki Fujii

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.

arXiv:quant-ph/0305155•May 26, 2003•0 citations

Rabi flopping without resonance

Marco Frasca

A three-level atom interacting with laser fields of different frequencies out of resonance is studied. The corresponding theory of dressed states is applied and extended beyond the leading order to obtain the higher-order corrections. These higher-order corrections can be computed by a dual Dyson series. Rather than to apply perturbation theory, the equations for the probability amplitudes of the transformed Hamiltonian in the dual interaction picture are considered. This gives us the opportunity to study the resonance properties of the quantum dynamics of the three-level atom being driven out of resonance by the external laser fields. In this way, by different resonance conditions due both to the detunings and the couplings, one gets Rabi flopping without resonance of the external fields and the atom levels, with also the Rabi frequency originating both from the detunings and the couplings.

Physical Review A•Aug 14, 2001•2 citations

Schrödinger-cat-like states with dressed photons in renormalized adiabatic approximation for generalized quantum Rabi Hamiltonian with quadratic interaction

Masao Hirokawa

We give a mathematical procedure to obtain the renormalized adiabatic approximation for the generalized quantum Rabi Hamiltonian with a quadratic interaction. The Hamiltonian describes the energy of the interaction system of a two-level artificial atom and a one-mode microwave photon. Using the renormalized adiabatic approximation in the deep-strong coupling regime, we study the appearance of the Schrödinger-cat-like states with dressed photons in the eigenstates of the generalized quantum Rabi Hamiltonian with the quadratic interaction.

Physics Open•Sep 6, 2020•1 citation
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 flopping in a Josephson junction (Y. Nakamura, Yu. A. Pashkin and J. S. Tsai, to appear in Phys. Rev. Lett.), 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 Schr\"odinger cat states. To approach this problem analytically use is made of the dual Dyson series and the rotating-wave approximation.
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.
In this paper we consider some (generalized) models which deal with n--level atom interacting with a single radiation mode and study a general structure of Rabi floppings of these generalized ones in the strong coupling regime. To solve these models we introduce multi cat states of Schr{\" o}dinger in our terminology and extend the result in (quant--ph/0203135) which Rabi frequencies are given by matrix elements of generalized coherent operators (quant--ph/0202081) under the rotating--wave approximation. Our work is a full generalization of Frasca (quant--ph/0111134) and Fujii (quant--ph/0203135). In last we make a brief comment on an application to Quantum Computation on the space of qudits.
We analyze the behavior of systems of two and three qubits made by Josephson junctions, treated in the two level approximation, driven by a radiation mode in a cavity. The regime we consider is a strong coupling one recently experimentally reached for a single junction. Rabi oscillations are obtained with the frequency proportional to integer order Bessel functions in the limit of a large photon number, similarly to the case of the single qubit. A selection rule is derived for the appearance of Rabi oscillations. A quantum amplifier built with a large number of Josephson junctions in a cavity in the strong coupling regime is also described.
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.
A three-level atom interacting with laser fields of different frequencies out of resonance is studied. The corresponding theory of dressed states is applied and extended beyond the leading order to obtain the higher-order corrections. These higher-order corrections can be computed by a dual Dyson series. Rather than to apply perturbation theory, the equations for the probability amplitudes of the transformed Hamiltonian in the dual interaction picture are considered. This gives us the opportunity to study the resonance properties of the quantum dynamics of the three-level atom being driven out of resonance by the external laser fields. In this way, by different resonance conditions due both to the detunings and the couplings, one gets Rabi flopping without resonance of the external fields and the atom levels, with also the Rabi frequency originating both from the detunings and the couplings.
We give a mathematical procedure to obtain the renormalized adiabatic approximation for the generalized quantum Rabi Hamiltonian with a quadratic interaction. The Hamiltonian describes the energy of the interaction system of a two-level artificial atom and a one-mode microwave photon. Using the renormalized adiabatic approximation in the deep-strong coupling regime, we study the appearance of the Schrödinger-cat-like states with dressed photons in the eigenstates of the generalized quantum Rabi Hamiltonian with the quadratic interaction.