Bilinear and quadratic Hamiltonians in two-mode cavity quantum electrodynamics

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

doi:10.1103/physreva.73.043803

Cited by 62 publications

(46 citation statements)

References 25 publications

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“…This interaction occurs in beam splitters, however it may also be obtained by the interaction of two quantized fields with a two-level atom when the fields are far from resonance with the atom, in this case an effective Hamiltonian may be obtained, which has the form of the above Hamiltonian [17]. By transforming to the interaction picture, i.e.…”

Section: Two Fields Interacting: Beam Splittersmentioning

confidence: 98%

Many fields interaction: Beam splitters and waveguide arrays

2011

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Key words Master equations, nonclassical fields, evolution of coherent states.We study the interaction of many fields. We obtain an effective Hamiltonian for this system by using a method recently introduced that produces a small rotation to the Hamiltonian that allows to neglect some terms in the rotated Hamiltonian. We show that coherent states remain coherent under the action of a quadratic Hamiltonian and by solving the eigenvalue and eigenvector problem for tridiagonal matrices we also show that a system of n interacting harmonic oscillators, initially in coherent states, remain coherent during the interaction.

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Section: Two Fields Interacting: Beam Splittersmentioning

confidence: 98%

Many fields interaction: Beam splitters and waveguide arrays

2011

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“…We stress that the engeneering of PT -symmetric atom-field coupling can be pursued by applying a technique proposed in ref. [26], widely used for bulding effective interactions [27]. * * * We kindly acknowledge support from grant 2014/ 00485-7 São Paulo Research Foundation (FAPESP) and grant 150879/2017-2 National Council for Scientific and Technological Development (CNPq).…”

Section: Z Pure Imaginary (Extracting Energy)mentioning

confidence: 99%

Linear response theory for a pseudo-Hermitian system-reservoir interaction

Duarte

Luiz

Moussa

2018

EPL

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-We present here an extension of the Caldeira-Leggett linear response model considering a pseudo-Hermitian PT -symmetric system-reservoir interaction. Our generalized FeynmanVernon functional, derived from the PT -symmetric coupling, accounts for two influence channels: a velocity-dependent one, which can act in reverse, providing energy to the system instead of draining it as usual, and an acceleration-dependent drain, analogue to the radiation-emission process. Therefore, an adequate choice of the Hamiltonian's parameters may allow the system to extract energy from the reservoir even at absolute zero for a period that may be much longer than the characteristic relaxation time. After this energy supply, the system is driven to a steady state whose energy is necessarily higher than the thermodynamic equilibrium energy due to the velocity-dependent pump. This heating mechanism of the system is more pronounced the more distant from the hermiticity is its coupling with the reservoir. An analytical derivation of the high-temperature master equation is provided helping us to better understand the whole scenario and to compute the associated relaxation and decoherence rates. Introduction. -Quantum mechanics imposes the Hamiltonian to be self-adjoint for the spectrum to be real and the time evolution to be unitary. However, in the last two decades it has been demonstrated that self-adjointness can be replaced by the weaker requirement of symmetry under spatial reflection and time reversal (PT symmetry), which extends the set of available physical Hamiltonians and guarantee real spectrum and unitary evolution [1]. A great deal of research has been devoted to PTsymmetric systems, covering the most varied topics such as superconductivity [2], chaos in optomechanics [3], topological states [4], metrology [5], time-dependent pseudoHermitian Hamiltonians [6,7], etc. However, most of those initiatives deal with non-interacting and closed systems. Our purpose in the present article is to contribute filling this gap. In order to do so, we generalized, to the light of PT -symmetric quantum theory, the conventional systemreservoir model in which the open dynamics is modelled by considering the system of interest linearly coupled to a thermal bath responsible for its energy loss and decoherence process [8,9]. This model has been widely used to describe properties of open quantum systems in general situations [10][11][12]. Indeed, it has been extensively shown

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“…Under this large detuning condition, we choose that the detuning ∆ b between the laser field frequency and the resonant frequency of the cavity b satisfies this condition ∆ b = ω m and we can perform the standard adiabatic eliminate [36,37] of the single photon state |i and obtain an effective Hamiltonian H eff = −iV (t) V (t ′ )dt ′ , which describes the dynamics of the system containing the MR and the two states |g , |e . During this calculation, we apply the rotating wave approximation to discard the high oscillatory terms and obtain the second-order effective Hamiltonian…”

Section: Description Of the Systemmentioning

confidence: 99%

Nonclassical non-Gaussian state of a mechanical resonator via selectively incoherent damping in a three-mode optomechanical system

et al. 2016

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We theoretically propose a scheme for the generation of a non-classical single-mode motional state of a mechanical resonator (MR) in the three-mode optomechanical systems, in which two optical modes of the cavities are linearly coupled to each other and one mechanical mode of the MR is optomechanically coupled to the two optical modes with the same coupling strength simultaneously. One cavity is driven by a coherent laser light. By properly tuning the frequency of the weak driving field, we obtain engineered Liouvillian superoperator via engineering the selective interaction Hamiltonian confined to the Fock subspaces. In this case, the motional state of the MR can be prepared into a non-Gaussian state, which possesses the sub-Poisson statistics although its Wigner function is positive.

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Bilinear and quadratic Hamiltonians in two-mode cavity quantum electrodynamics

Cited by 62 publications

References 25 publications

Many fields interaction: Beam splitters and waveguide arrays

Many fields interaction: Beam splitters and waveguide arrays

Linear response theory for a pseudo-Hermitian system-reservoir interaction

Nonclassical non-Gaussian state of a mechanical resonator via selectively incoherent damping in a three-mode optomechanical system

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