Exact eigenstates of the two-photon Jaynes-Cummings model with the counter-rotating term

Ng, K.M.; Lo, Chi‐Fai; Liu, K.L.

doi:10.1007/pl00021611

Cited by 36 publications

(79 citation statements)

References 1 publication

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“…As discussed in Ref. [33,35,36], for single qubit case, this model is solvable only if M ≤ 2 and the coupling parameter is below a certain critical value. But in the following discussion, we will show that the case for more qubits is different: Dark-like eigenstates for H P Q (54) with N > 1 still exist, regardless of these constraints, although in usual cases this model is indeed not well-defined.…”

Section: Dark-like States For the Multi-qubit And Multi-photon Rabi Mmentioning

confidence: 92%

“…. , N) = 0, which does not affect the result [35]. In the basis formed by the eigenstates of σ jx (j = 1, 2, .…”

Section: Dark-like States For the Multi-qubit And Multi-photon Rabi Mmentioning

confidence: 96%

“…Thus the condition for the Hamiltonian (55) being diagonalizable is λ < 1 2 [35], and correspondingly we have…”

Section: Dark-like States For the Multi-qubit And Multi-photon Rabi Mmentioning

confidence: 99%

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Dark-like states for the multi-qubit and multi-photon Rabi models

Peng

zheng

Guo

et al. 2017

J. Phys. A: Math. Theor.

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Abstract. There are well-known dark states in the even-qubit Dicke models, which are the products of the two-qubit singlets and a Fock state, where the qubits are decoupled from the photon field. These spin singlets can be used to store quantum correlations since they preserve entanglement even under dissipation, driving and dipole-dipole interactions. One of the features for these dark states is that their eigenenergies are independent of the qubitphoton coupling strength. We have obtained a novel kind of dark-like states for the multi-qubit and multi-photon Rabi models, whose eigenenergies are also constant in the whole coupling regime. Unlike the dark states, the qubits and photon field are coupled in the dark-like states. Furthermore, the photon numbers are bounded from above commonly at 1, which is different from that for the one-qubit case. The existence conditions of the dark-like states are simpler than exact isolated solutions, and may be fine tuned in experiments. While the single-qubit and multi-photon Rabi model is well-defined only if the photon number M ≤ 2 and the coupling strength is below a certain critical value, the dark-like eigenstates for multi-qubit and multiphoton Rabi model still exist, regardless of these constraints. In view of these properties of the dark-like states, they may find similar applications like "dark states" in quantum information.

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Section: Dark-like States For the Multi-qubit And Multi-photon Rabi Mmentioning

confidence: 92%

“…. , N) = 0, which does not affect the result [35]. In the basis formed by the eigenstates of σ jx (j = 1, 2, .…”

Section: Dark-like States For the Multi-qubit And Multi-photon Rabi Mmentioning

confidence: 96%

See 1 more Smart Citation

Dark-like states for the multi-qubit and multi-photon Rabi models

Peng

zheng

Guo

et al. 2017

J. Phys. A: Math. Theor.

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“…In real space representation, the Hamiltonian is just a quantum harmonic oscillator. When → ω/2, the quadratic potential vanishes and becomes a free particle system, resulting in a continuum system with no bound state [22]. However, numerous studies pointed out that bound states exist at the collapse point when ω 0 = 0, which refers as the incomplete spectral collapse [25,26].…”

Section: Introductionmentioning

confidence: 99%

Bound states of two-photon Rabi model at the collapse point

Chan¹

2020

J. Phys. A: Math. Theor.

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This paper presents a proof of the existence of novel bound states of the two-photon quantum Rabi model at the collapse point. The two-photon Rabi model is interesting not only for its important role on non-linear light-matter interaction, but also for the exhibition of many-energy-levels degenerating process called the "spectral collapse". The squeezing property of the two-photon annihilation and creation operators is the origin for this phenomenon which is well studied without the energy-slitting term ω 0. However, many numerical studies have pointed out that with the presence of ω 0 , some low-level isolated states exist while other high energy states collapse to E = − ω 2 , which known as incomplete spectral collapse. From the eigenvalue equation in real space, pair of second order differential equations, which are similarly to the Schrodinger equation, are derived at the collapse point. These differential equations provide explanation to the existence of isolated bound states below E = − ω 2 with the presence of the spin slitting ω 0 and better numerical method to generate those bound states.

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“…Concurrently, researchers generated squeezed light using nondegenerate parametric down conversion to excite a twophoton transition in atomic cesium. [12][13][14] Theoretically, to obtain these types of processes, we have to introduce a Hamiltonian model consisting of a three-wave interaction. In the field of quantum optics, it is well known that the susceptibility χ (2) leads to cubic nonlinearity, which is responsible for three-wave mixing processes in parametric devices, as well as second harmonic and subharmonic generation.…”

mentioning

confidence: 99%

Time-dependent interaction between a two-level atom and a su(1,1) Lie algebra quantum system

Abdalla

Khalil

Obada

2017

Int. J. Mod. Phys. B

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The problem of the interaction between a two-level atom and a two-mode field in the parametric amplifier-type is considered. A similar problem appears in an ion trapped in a two-dimensional trap. The problem is transformed into an interaction governed by su(1, 1) Lie algebraic operators with phase and coupling parameter depending on time.Under an integrability condition, that relates phase and coupling, a solution to the wavefunction is obtained using the Schrödinger equation. The effects of the functional dependence of the coupling and the initial state of the two-level atom on atomic inversion, the degree of entanglement, the fidelity and the Glauber second-order correlation function are investigated. It is shown that the acceleration term plays an important role in controlling the function behavior of the considered quantities.

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Exact eigenstates of the two-photon Jaynes-Cummings model with the counter-rotating term

Cited by 36 publications

References 1 publication

Dark-like states for the multi-qubit and multi-photon Rabi models

Dark-like states for the multi-qubit and multi-photon Rabi models

Bound states of two-photon Rabi model at the collapse point

Time-dependent interaction between a two-level atom and a su(1,1) Lie algebra quantum system

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