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:cond-mat/0411171 · Physical Review B

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

Marco Frasca

Published May 31, 2005• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.71.174513

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

Rabi Oscillations in a Josephson-Junction Charge Two-Level System

Yasunobu Nakamura, Yu. A. Pashkin, J. S. Tsai

We investigated temporal behavior of an artificial two-level system driven by a strong oscillating field; namely, quantum-state evolution between two charge states in a small Josephson-junction circuit irradiated with microwaves. Rabi oscillations corresponding to 0-, 1-, and 2-photon resonances were observed. As a function of microwave amplitude, the Rabi frequencies followed a first-kind Bessel function of the corresponding order to the number of photons.

Physical Review Letters•Nov 27, 2001•220 citations

Rabi flopping and Schr\"odinger cat 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 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.

•Nov 24, 2001•0 citations

Eigenstates of a small Josephson junction coupled to a resonant cavity

Wissam A. Al-Saidi, D. Stroud

We carry out a quantum-mechanical analysis of a small Josephson junction coupled to a single-mode resonant cavity. We find that the eigenstates of the combined junction-cavity system are strongly entangled only when the gate voltage applied at one of the superconducting islands is tuned to certain special values. One such value corresponds to the resonant absorption of a single photon by Cooper pairs in the junction. Another special value corresponds to a two-photon absorption process. Near the single-photon resonant absorption, the system is accurately described by a simplified model in which only the lowest two levels of the Josephson junction are retained in the Hamiltonian matrix. We noticed that this approximation does not work very well as the number of photons in the resonator increases. Our system shows also the phenomenon of ``collapse and revival'' under suitable initial conditions, and our full numerical solution agrees with the two level approximation result.

arXiv:cond-mat/0110117•Physical review. B, Condensed matter•Dec 4, 2001•55 citations

Several small Josephson junctions in a resonant cavity: Deviation from the Dicke model

Wissam A. Al-Saidi, D. Stroud

We have studied quantum mechanically a system of several small identical Josephson junctions in a lossless single-mode cavity for different initial states, under conditions such that the system is at resonance. This system is analogous to a collection of identical atoms in a cavity, which is described under appropriate conditions by the Dicke model. We find that our system can be well approximated by a reduced Hamiltonian consisting of two levels per junction. The reduced Hamiltonian is similar to the Dicke Hamiltonian, but contains an additional term resembling a dipole-dipole interaction between the junctions. This extra term can be understood as a natural consequence of degenerate second-order (L\"owdin) perturbation theory. For typical, physically reasonable values of the junction-cavity coupling, we find that this perturbation treatment is an adequate way to include the junction energy levels beyond the lowest two. As in the Dicke model, we find that, when N junctions are present in the cavity, the junction-cavity interaction is enhanced by $\sqrt{N},$ with a corresponding decrease in the Rabi oscillation period. We find that this enhancement survives even if the junctions differ slightly from one another, as expected in a realistic system. Since coherence effects thus reduce the Rabi period, it may become smaller than the decoherence time due to dissipation, making these oscillations observable.

arXiv:cond-mat/0203341•Physical review. B, Condensed matter•Jun 5, 2002•37 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
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.
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.
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.
We carry out a quantum-mechanical analysis of a small Josephson junction coupled to a single-mode resonant cavity. We find that the eigenstates of the combined junction-cavity system are strongly entangled only when the gate voltage applied at one of the superconducting islands is tuned to certain special values. One such value corresponds to the resonant absorption of a single photon by Cooper pairs in the junction. Another special value corresponds to a two-photon absorption process. Near the single-photon resonant absorption, the system is accurately described by a simplified model in which only the lowest two levels of the Josephson junction are retained in the Hamiltonian matrix. We noticed that this approximation does not work very well as the number of photons in the resonator increases. Our system shows also the phenomenon of ``collapse and revival'' under suitable initial conditions, and our full numerical solution agrees with the two level approximation result.
We have studied quantum mechanically a system of several small identical Josephson junctions in a lossless single-mode cavity for different initial states, under conditions such that the system is at resonance. This system is analogous to a collection of identical atoms in a cavity, which is described under appropriate conditions by the Dicke model. We find that our system can be well approximated by a reduced Hamiltonian consisting of two levels per junction. The reduced Hamiltonian is similar to the Dicke Hamiltonian, but contains an additional term resembling a dipole-dipole interaction between the junctions. This extra term can be understood as a natural consequence of degenerate second-order (L\"owdin) perturbation theory. For typical, physically reasonable values of the junction-cavity coupling, we find that this perturbation treatment is an adequate way to include the junction energy levels beyond the lowest two. As in the Dicke model, we find that, when N junctions are present in the cavity, the junction-cavity interaction is enhanced by N,\sqrt{N},N​, with a corresponding decrease in the Rabi oscillation period. We find that this enhancement survives even if the junctions differ slightly from one another, as expected in a realistic system. Since coherence effects thus reduce the Rabi period, it may become smaller than the decoherence time due to dissipation, making these oscillations observable.
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.