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/0602165 · Physical Review A

Bilinear and quadratic Hamiltonians in two-mode cavity quantum electrodynamics

F. O. Prado, N. G. de Almeida, M. H. Y. Moussa, Celso J. Villas-Bôas

Published Apr 11, 2006• 64 citations
arXivHTMLPDF

Abstract

In this work we show how to engineer bilinear and quadratic Hamiltonians in cavity quantum electrodynamics through the interaction of a single driven two-level atom with cavity modes. The validity of the engineered Hamiltonians is numerically analyzed even when considering the effects of both dissipative mechanisms, the cavity field and the atom. The present scheme can be used, in both optical and microwave regimes, for quantum state preparation, the implementation of quantum logical operations, and fundamental tests of quantum theory.

DOI
10.1103/physreva.73.043803

Related papers

Frequency Up- and Down-conversions in Two-mode Cavity

李斌 Li Bin, 冯勋立 FENG Xun-li, 张智明 Zhang Zhiming

A scheme was proposed to construct bilinear and quadratic Hamiltonians for frequency up-and down-conversions in cavity quantum electrodynamics(QED).Generally,in nonlinear optics,the interaction that the energe swaps between different optic modes without atomic transition is named frequency conversion.The proposed scheme was based on the interactions of a single four-level atom simultaneously with two classical driving fields and a two-mode cavity field,which is in the domain of four-wave mixing.By initially preparing the atom in a suitable state,each pump light was resonant with its transition,and two quantum modes were large tune to the other two transition,respectively,In the strong laser regime,the atomic degrees of freedom could be decoupled from the cavity degrees of freedom and the frequency conversion could be realized for the cavity modes.Due to the different initial states and interactions between optic fields and atom,frequency up-and down-conversions arose,respectively.After the preparation of squeezed operation respect to Frequency down-conversion,a discussion on the feasibility of experiment was given and the theoretical value was obtained.The advantage of this proposal is to realize the transition using two cascade photons,which is dipole-forbidden in a cascade structure atom,with high efficiency.The proposal will be useful for optical quantum control and fundamental tests of quantum theory.

ACTA PHOTONICA SINICA•Jan 1, 2011•1 citation

Frequency up- and down-conversions in two-mode cavity quantum electrodynamics

Roberto M. Serra, Celso J. Villas-Bôas, N. G. de Almeida +1 more

In this Brief Report we present a scheme for the implementation of frequency up- and down-conversion operations in two-mode cavity quantum electrodynamics (QED). This protocol for engineering bilinear two-mode interactions could enlarge perspectives for quantum-information manipulation and also be employed for fundamental tests of quantum theory in cavity QED. As an application we show how to generate a two-mode squeezed state in cavity QED (the original entangled state of Einstein, Podolsky, and Rosen).

arXiv:quant-ph/0306126•Physical Review A•Apr 29, 2005•65 citations

Atom-mediated effective interactions between modes of a bimodal cavity

F. O. Prado, F. S. Luiz, J. M. Villas-Bôas +3 more

We show a procedure for engineering effective interactions between two modes in a bimodal cavity. Our system consists of one or more two-level atoms, excited by a classical field, interacting with both modes. The two effective Hamiltonians have forms similar to beam-splitter and quadratic beam-splitter interactions. We also demonstrate that the nonlinear Hamiltonian can be used to prepare an entangled coherent state, also known as a multidimensional entangled coherent state, which has been pointed out as an important entanglement resource. We show that the nonlinear interaction parameter can be enhanced considering $N$ independent atoms trapped inside a high-finesse optical cavity.

arXiv:1111.2358•Physical Review A•Nov 21, 2011•14 citations

Quantum information in cavity quantum electrodynamics: logical gates, entanglement engineering and ‘Schrödinger–cat states’

S. Haroche

In cavity-quantum-electrodynamics experiments, two-level Rydberg atoms and single-photon microwave fields can be seen as qubits. Quantum gates based on resonant and dispersive atom-field effects have been realized, which implement various kinds of conditional dynamics between these qubits. We have also studied the interaction between a single atom and coherent fields stored in the cavity. By progressively increasing the number of photons in these fields, we have explored various aspects of the quantum-classical boundary. We have realized a complementarity experiment demonstrating the continuous evolution of an apparatus from a quantum to a classical behaviour. We have also prepared 'Schrödinger-cat'-like states of the field made of a few photons, and observed their decoherence. We present a brief review of these experiments along with a proposal to study larger systems, i.e. coherent fields with more photons. Fundamental limits to the size of mesoscopic superpositions of field states in a cavity will be briefly discussed.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Jul 15, 2003•37 citations

Efficient scheme for preparation of the multi-atom W state via cavity quantum electrodynamics

Jin Zhang, Liu Ye

We present an efficient scheme for preparation of the multi-atom W state via cavity quantum electrodynamics. Involved in this scheme are n identical two-level atoms and a single-mode cavity field. Discussion indicates that this scheme can be realized easily by current technologies.

Chinese Physics•Sep 1, 2004•12 citations

Efficient generation of Bell-cat states in remote cavities

Ying Zhang

In the context of cavity quantum electrodynamics (QED),a potential scheme is proposed to generate entangled coherent states. The scheme includes twice interactions of two-level atoms with cavities. In the first interaction,two atoms are sent into a microwave cavity with the large detuning respectively. And then the second interaction is that the two atoms enter another microwave cavity and are driven by a resonant classical field meantime. When we choose the proper interaction time and make measurement on the two atoms,the two microwave cavity mode fields are determinatively entangled. In addition,it is easy to generalize the scheme to multi-cavity and multi-atom.

•Jan 1, 2008•0 citations
In this work we show how to engineer bilinear and quadratic Hamiltonians in cavity quantum electrodynamics through the interaction of a single driven two-level atom with cavity modes. The validity of the engineered Hamiltonians is numerically analyzed even when considering the effects of both dissipative mechanisms, the cavity field and the atom. The present scheme can be used, in both optical and microwave regimes, for quantum state preparation, the implementation of quantum logical operations, and fundamental tests of quantum theory.
A scheme was proposed to construct bilinear and quadratic Hamiltonians for frequency up-and down-conversions in cavity quantum electrodynamics(QED).Generally,in nonlinear optics,the interaction that the energe swaps between different optic modes without atomic transition is named frequency conversion.The proposed scheme was based on the interactions of a single four-level atom simultaneously with two classical driving fields and a two-mode cavity field,which is in the domain of four-wave mixing.By initially preparing the atom in a suitable state,each pump light was resonant with its transition,and two quantum modes were large tune to the other two transition,respectively,In the strong laser regime,the atomic degrees of freedom could be decoupled from the cavity degrees of freedom and the frequency conversion could be realized for the cavity modes.Due to the different initial states and interactions between optic fields and atom,frequency up-and down-conversions arose,respectively.After the preparation of squeezed operation respect to Frequency down-conversion,a discussion on the feasibility of experiment was given and the theoretical value was obtained.The advantage of this proposal is to realize the transition using two cascade photons,which is dipole-forbidden in a cascade structure atom,with high efficiency.The proposal will be useful for optical quantum control and fundamental tests of quantum theory.
In this Brief Report we present a scheme for the implementation of frequency up- and down-conversion operations in two-mode cavity quantum electrodynamics (QED). This protocol for engineering bilinear two-mode interactions could enlarge perspectives for quantum-information manipulation and also be employed for fundamental tests of quantum theory in cavity QED. As an application we show how to generate a two-mode squeezed state in cavity QED (the original entangled state of Einstein, Podolsky, and Rosen).
We show a procedure for engineering effective interactions between two modes in a bimodal cavity. Our system consists of one or more two-level atoms, excited by a classical field, interacting with both modes. The two effective Hamiltonians have forms similar to beam-splitter and quadratic beam-splitter interactions. We also demonstrate that the nonlinear Hamiltonian can be used to prepare an entangled coherent state, also known as a multidimensional entangled coherent state, which has been pointed out as an important entanglement resource. We show that the nonlinear interaction parameter can be enhanced considering NNN independent atoms trapped inside a high-finesse optical cavity.
In cavity-quantum-electrodynamics experiments, two-level Rydberg atoms and single-photon microwave fields can be seen as qubits. Quantum gates based on resonant and dispersive atom-field effects have been realized, which implement various kinds of conditional dynamics between these qubits. We have also studied the interaction between a single atom and coherent fields stored in the cavity. By progressively increasing the number of photons in these fields, we have explored various aspects of the quantum-classical boundary. We have realized a complementarity experiment demonstrating the continuous evolution of an apparatus from a quantum to a classical behaviour. We have also prepared 'Schrödinger-cat'-like states of the field made of a few photons, and observed their decoherence. We present a brief review of these experiments along with a proposal to study larger systems, i.e. coherent fields with more photons. Fundamental limits to the size of mesoscopic superpositions of field states in a cavity will be briefly discussed.
In the context of cavity quantum electrodynamics (QED),a potential scheme is proposed to generate entangled coherent states. The scheme includes twice interactions of two-level atoms with cavities. In the first interaction,two atoms are sent into a microwave cavity with the large detuning respectively. And then the second interaction is that the two atoms enter another microwave cavity and are driven by a resonant classical field meantime. When we choose the proper interaction time and make measurement on the two atoms,the two microwave cavity mode fields are determinatively entangled. In addition,it is easy to generalize the scheme to multi-cavity and multi-atom.