The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investigated.The exact dynamic solutions in the general condition are obtained via Laplace transform.The simple analytical solutions are obtained in several particular cases,which demonstrate the clear and simple physical picture for the quantum state transition of the system.In the large detuning or hoppling case,the quantum states transferring between qubits follow a slow periodic oscillation induced by the very weak excitation of the cavity mode.In the large coupling case,the system can be interpreted as two Jaynes-Cummings model subsystems which interact through photon hop between the two cavities.In the case of λ≈△>> g,the quantum states transition of qubits is accompanied by the excitation of the cavity,and the cavity modes have the same dynamic behaviours and the amplitude of probability is equal to 0.25 which does not change with the variation of parameter.The dynamic behaviour of the two-site coupled cavities model which is doped with ta wo-level system is investigated.The exact dynamic solutions in the general condition are obtained via Laplace transform.The simple analytical solutions are obtained in several particular cases,which demonstrate the clear and simple physical picture for the quantum state transition of the system.In the large detuning or hoppling case,the quantum states transferring between qubits follow a slow periodic oscillation induced by the very weak excitation of the cavity mode.In the large coupling case,the system can be interpreted as two Jaynes-Cummings model subsystems which interact through photon hop between the two cavities.In the case of λ≈△>> g,the quantum states transition of qubits is accompanied by the excitation of the cavity,and the cavity modes have the same dynamic behaviours and the amplitude of probability is equal to 0.25 which does not change with the variation of parameter.

中国物理B：英文版Jan 1, 20120 citations

Dynamics in a system of four qubits in two cavities

Duong Hai Trieu

We study the dynamics of a closed system of four qubits in two coupled cavities. Each cavity contains two qubits which interact with it's quantum field and photons which may hop between the cavities. The state of the system is first expressed in delocalized modes and then is expressed in the system of local bases. Exact general solutions are obtained for one-excitation state with arbitrary initial condition. We consider in detail two cases of large and small hopping at resonance. In the case of resonance and large hopping the state of the first qubit may also be transferred to the second qubit in the same cavity without excitation of the field. Such transfer of states minimizes decoherence due to photon loss.We study the dynamics of a closed system of four qubits in two coupled cavities. Each cavity contains two qubits which interact with it's quantum field and photons which may hop between the cavities. The state of the system is first expressed in delocalized modes and then is expressed in the system of local bases. Exact general solutions are obtained for one-excitation state with arbitrary initial condition. We consider in detail two cases of large and small hopping at resonance. In the case of resonance and large hopping the state of the first qubit may also be transferred to the second qubit in the same cavity without excitation of the field. Such transfer of states minimizes decoherence due to photon loss.

Journal of Physics Conference SeriesSep 1, 20092 citations

Transfer behavior of quantum states between atoms in photonic crystal coupled cavities

Ke Zhang, Zhiyuan Li

In this article, we discuss the one-excitation dynamics of a quantum system consisting of two two-level atoms each interacting with one of two coupled single-mode cavities via spontaneous emission. When the atoms and cavities are tuned into resonance, a wide variety of time-evolution behaviors can be realized by modulating the atom-cavity coupling strength $g$ and the cavity-cavity hopping strength $\ensuremath{\lambda}$. The dynamics is solved rigorously via the eigenproblem of an ordinary coupled linear system and simple analytical solutions are derived at several extreme situations of $g$ and $\ensuremath{\lambda}$. In the large hopping limit where $g\ensuremath{\ll}\ensuremath{\lambda}$, the behavior of the system is the linear superposition of a fast and slow periodic oscillation. The quantum state transfers from one atom to the other atom accompanied with weak excitation of the cavity mode. In the large coupling limit where $g\ensuremath{\gg}\ensuremath{\lambda}$, the time-evolution behavior of the system is characterized by the usual slowly varying carrier envelope superimposed upon a fast and violent oscillation. At a certain instant, the energy is fully transferred from the one quantum subsystem to the other. When the two interaction strengths are comparable in magnitude, the dynamics acts as a continuous pulse having irregular frequency and line shape of peaks and valleys, and the complicated time-evolution behaviors are ascribed to the violent competition between all the one-excitation quantum states. The coupled quantum system of atoms and cavities makes a good model to study cavity quantum electrodynamics with great freedoms of many-body interaction.In this article, we discuss the one-excitation dynamics of a quantum system consisting of two two-level atoms each interacting with one of two coupled single-mode cavities via spontaneous emission. When the atoms and cavities are tuned into resonance, a wide variety of time-evolution behaviors can be realized by modulating the atom-cavity coupling strength $g$ and the cavity-cavity hopping strength $\ensuremath{\lambda}$. The dynamics is solved rigorously via the eigenproblem of an ordinary coupled linear system and simple analytical solutions are derived at several extreme situations of $g$ and $\ensuremath{\lambda}$. In the large hopping limit where $g\ensuremath{\ll}\ensuremath{\lambda}$, the behavior of the system is the linear superposition of a fast and slow periodic oscillation. The quantum state transfers from one atom to the other atom accompanied with weak excitation of the cavity mode. In the large coupling limit where $g\ensuremath{\gg}\ensuremath{\lambda}$, the time-evolution behavior of the system is characterized by the usual slowly varying carrier envelope superimposed upon a fast and violent oscillation. At a certain instant, the energy is fully transferred from the one quantum subsystem to the other. When the two interaction strengths are comparable in magnitude, the dynamics acts as a continuous pulse having irregular frequency and line shape of peaks and valleys, and the complicated time-evolution behaviors are ascribed to the violent competition between all the one-excitation quantum states. The coupled quantum system of atoms and cavities makes a good model to study cavity quantum electrodynamics with great freedoms of many-body interaction.

Physical Review AMar 26, 201056 citations

EVOLUTION OF ATOM-FIELD PROBABILITY IN A COUPLED CAVITY SYSTEM

K. V. PRIYESH, R. B. Thayyullathil

In this paper we have investigated the dynamics of two cavities each with a two-level atom, coupled together with photon hopping. The coupled cavity system is studied in single excitation subspace and the evolution of the atom (field) states probabilities are obtained analytically. The probability amplitude of states executes oscillations with different modes and amplitudes, determined by the coupling strengths. The evolution is examined in detail for different atom field coupling strength, g and field–field hopping strength, A. It is noticed that the exact atomic probability amplitude transfer occurs when g ≪ A with minimal field excitation probability and the period of probability transfer is calculated. In the limit g ≫ A there exists periodic exchange of probability between atom and field inside each cavity and also between cavity 1 and cavity 2. Periodicity of each exchange in this limit also obtained.In this paper we have investigated the dynamics of two cavities each with a two-level atom, coupled together with photon hopping. The coupled cavity system is studied in single excitation subspace and the evolution of the atom (field) states probabilities are obtained analytically. The probability amplitude of states executes oscillations with different modes and amplitudes, determined by the coupling strengths. The evolution is examined in detail for different atom field coupling strength, g and field–field hopping strength, A. It is noticed that the exact atomic probability amplitude transfer occurs when g ≪ A with minimal field excitation probability and the period of probability transfer is calculated. In the limit g ≫ A there exists periodic exchange of probability between atom and field inside each cavity and also between cavity 1 and cavity 2. Periodicity of each exchange in this limit also obtained.

Journal of Nonlinear Optical Physics & MaterialsSep 1, 20130 citations

Dynamics of interacting Dicke model in a coupled-cavity array

Fazal Badshah, Shahid Qamar, Mauro Paternostro

We consider the dynamics of an array of mutually interacting cavities, each containing an ensemble of $N$ two-level atoms. By exploring the possibilities offered by ensembles of various dimensions and a range of atom-light and photon-hopping values, we investigate the generation of multisite entanglement, as well as the performance of excitation transfer across the array, resulting from the competition between on-site nonlinearities of the matter-light interaction and intersite photon hopping. In particular, for a three-cavity interacting system it is observed that the initial excitation in the first cavity completely transfers to the ensemble in the third cavity through the hopping of photons between the adjacent cavities. Probabilities of the transfer of excitation of the cavity modes and ensembles exhibit characteristics of fast and slow oscillations governed by coupling and hopping parameters, respectively. In the large-hopping case, by seeding an initial excitation in the cavity at the center of the array, a tripartite W state, as well as a bipartite maximally entangled state, is obtained, depending on the interaction time. Population of the ensemble in a cavity has a positive impact on the rate of excitation transfer between the ensembles and their local cavity modes. In particular, for ensembles of five to seven atoms, tripartite W states can be produced even when the hopping rate is comparable to the cavity-atom coupling rate. A similar behavior of the transfer of excitation is observed for a four-coupled-cavity system with two initial excitations.We consider the dynamics of an array of mutually interacting cavities, each containing an ensemble of $N$ two-level atoms. By exploring the possibilities offered by ensembles of various dimensions and a range of atom-light and photon-hopping values, we investigate the generation of multisite entanglement, as well as the performance of excitation transfer across the array, resulting from the competition between on-site nonlinearities of the matter-light interaction and intersite photon hopping. In particular, for a three-cavity interacting system it is observed that the initial excitation in the first cavity completely transfers to the ensemble in the third cavity through the hopping of photons between the adjacent cavities. Probabilities of the transfer of excitation of the cavity modes and ensembles exhibit characteristics of fast and slow oscillations governed by coupling and hopping parameters, respectively. In the large-hopping case, by seeding an initial excitation in the cavity at the center of the array, a tripartite W state, as well as a bipartite maximally entangled state, is obtained, depending on the interaction time. Population of the ensemble in a cavity has a positive impact on the rate of excitation transfer between the ensembles and their local cavity modes. In particular, for ensembles of five to seven atoms, tripartite W states can be produced even when the hopping rate is comparable to the cavity-atom coupling rate. A similar behavior of the transfer of excitation is observed for a four-coupled-cavity system with two initial excitations.

Physical Review ASep 9, 201416 citations

Jaynes-Cummings dynamics in strong coupling for many-interacting-qubit quantum Rabi models

Roberto Grimaudo, Sagnik Chakraborty, Rosario Lo Franco +1 more

The present work focuses on the strong/weak interaction of many-body spin-systems with a cavity mode. It introduces the necessity of redefining the physical conditions determining the strong/weak coupling regime in those systems. In more complex systems, the effective coupling emerging from the collective dynamics may differ indeed from the actual coupling of each individual subsystem with the bosonic field. This is shown by highlighting some counter-intuitive dynamical effects properly related to the coupling regime: a Jaynes-Cummings dynamics emerging although a strong interaction is present. The universality of this result is demonstrated through the analysis of three distinct systems: a two-qubit, a two-qutrit, and an $N$ -qubit chain quantum Rabi models.The present work focuses on the strong/weak interaction of many-body spin-systems with a cavity mode. It introduces the necessity of redefining the physical conditions determining the strong/weak coupling regime in those systems. In more complex systems, the effective coupling emerging from the collective dynamics may differ indeed from the actual coupling of each individual subsystem with the bosonic field. This is shown by highlighting some counter-intuitive dynamical effects properly related to the coupling regime: a Jaynes-Cummings dynamics emerging although a strong interaction is present. The universality of this result is demonstrated through the analysis of three distinct systems: a two-qubit, a two-qutrit, and an $N$-qubit chain quantum Rabi models.

quant-pharXiv:2604.20363Apr 23, 20260 citations

g

and the cavity-cavity hopping strength $\ensuremath{\lambda}$. The dynamics is solved rigorously via the eigenproblem of an ordinary coupled linear system and simple analytical solutions are derived at several extreme situations of

g

and $\ensuremath{\lambda}$. In the large hopping limit where $g\ensuremath{\ll}\ensuremath{\lambda}$, the behavior of the system is the linear superposition of a fast and slow periodic oscillation. The quantum state transfers from one atom to the other atom accompanied with weak excitation of the cavity mode. In the large coupling limit where $g\ensuremath{\gg}\ensuremath{\lambda}$, the time-evolution behavior of the system is characterized by the usual slowly varying carrier envelope superimposed upon a fast and violent oscillation. At a certain instant, the energy is fully transferred from the one quantum subsystem to the other. When the two interaction strengths are comparable in magnitude, the dynamics acts as a continuous pulse having irregular frequency and line shape of peaks and valleys, and the complicated time-evolution behaviors are ascribed to the violent competition between all the one-excitation quantum states. The coupled quantum system of atoms and cavities makes a good model to study cavity quantum electrodynamics with great freedoms of many-body interaction.

We consider the dynamics of an array of mutually interacting cavities, each containing an ensemble of

N

two-level atoms. By exploring the possibilities offered by ensembles of various dimensions and a range of atom-light and photon-hopping values, we investigate the generation of multisite entanglement, as well as the performance of excitation transfer across the array, resulting from the competition between on-site nonlinearities of the matter-light interaction and intersite photon hopping. In particular, for a three-cavity interacting system it is observed that the initial excitation in the first cavity completely transfers to the ensemble in the third cavity through the hopping of photons between the adjacent cavities. Probabilities of the transfer of excitation of the cavity modes and ensembles exhibit characteristics of fast and slow oscillations governed by coupling and hopping parameters, respectively. In the large-hopping case, by seeding an initial excitation in the cavity at the center of the array, a tripartite W state, as well as a bipartite maximally entangled state, is obtained, depending on the interaction time. Population of the ensemble in a cavity has a positive impact on the rate of excitation transfer between the ensembles and their local cavity modes. In particular, for ensembles of five to seven atoms, tripartite W states can be produced even when the hopping rate is comparable to the cavity-atom coupling rate. A similar behavior of the transfer of excitation is observed for a four-coupled-cavity system with two initial excitations.

N

-qubit chain quantum Rabi models.