All-creation and all-annihilation time-dependent 
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-symmetric bosonic Hamiltonians: An infinite squeezing degree at a finite time

Ponte, M. A. de; Luiz, F. S.; Duarte, O. S.; Moussa, M. H. Y.

doi:10.1103/physreva.100.012128

Cited by 13 publications

(27 citation statements)

References 53 publications

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“…As concluded in Ref. (27), when χ approaches the unit for a given instant t, |U | and consequently r diverge, thus resulting in an infinite squeezing degree in a finite time interval.…”

Section: Variances Of the Field Quadraturesmentioning

confidence: 75%

“…(20) for the time-independent case and in Ref. (27) for the time-dependent case. We propose a more generic approach than in the mentioned works by assuming a non-Hermitian Dyson map.…”

Section: Time-dependent Quadratic Non-hermitian Hamiltonian a Generic Approachmentioning

confidence: 98%

“…Moreover, we are going to generalize the analysis started in Ref. (27) for timedependent non-Hermitian Hamiltonians under the effect of parametric amplification, by proposing a more generic, non-Hermitian, Dyson map. At last, we aim to obtain extremely high (virtually infinite) squeezing degrees at finite and controllable times for a specific case, a harmonic oscillator with pure imaginary frequency.…”

Section: Squeezed Quadratures Of the Electromagnetic Fieldmentioning

confidence: 99%

“…In Ref. (27), the freedom on the choice of the Dyson map was constrained to the initial values for the parameters (t) and µ(t). In this sense, this work presents interesting generalizations, allowing for much more control over the behavior of the coefficients W and U of the Hermitian counterpart of H.…”

Section: The Td Parameters Of the Mapmentioning

confidence: 99%

“…The function of time |Υ(t)| indicates how far from the hermiticity is H. We can, for example, refer to Ref. (27) where the unbalance on the parametric pumping is taken to the extreme, for Υ = 0 one would find the all-annihilation Hamiltonian, while Υ → ±∞ would lead to the all-creation Hamiltonian. Evidently, the hermiticity of the starting Hamiltonian relates to |Υ(t)| = 1.…”

Section: The Td Parameters Of the Mapmentioning

confidence: 99%

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The superradiance-superabsorption interplay and a PT-symmetric harmonic oscillator with complex frequency

Dourado¹

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A superradiant pulse emitted by a sample of two-level atoms can be combined with superabsorption in order to increase the speed of the excitation interplay. We showcase this with two different experiments, first by subjecting the atomic sample to a competition between dissipation and amplification, the latter being a time-dependent multi-modal linear pumping; second, by coupling the atomic sample with a single mode of a high finesse cavity. The mean-field approximation was used in both cases. In the first, to solve the Schrödinger equation for the resulting time-dependent nonlinear Hamiltonian exactly we use the Lewis and Riesenfeld method. In the second case, we obtain a quantum master equation in the Lindblad form and solve it numerically. We observe that, in particular, the higher the number of atoms on the sample the higher will be the frequency of the interplay in comparison with that coming from the Jaynes-Cummings model. For a certain regime of parameters this system also leads to a superradiant laser, whose characteristics we discuss. These results show that many-particle effects can be further explored for the implementation of quantum information processes as well as for constructing of a superradiant laser. At last, we study non-Hermitian PT -symmetric bosonic nonautonomous Hamiltonians under linear and parametric amplifications. We present a generic approach to solve these Hamiltonians through the use of non-unitary similarity transformations. The choice for the metric associated with these transformations has a dramatic impact on the pseudo-Hermitian operators of the system.

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“…As concluded in Ref. (27), when χ approaches the unit for a given instant t, |U | and consequently r diverge, thus resulting in an infinite squeezing degree in a finite time interval.…”

Section: Variances Of the Field Quadraturesmentioning

confidence: 75%

“…(20) for the time-independent case and in Ref. (27) for the time-dependent case. We propose a more generic approach than in the mentioned works by assuming a non-Hermitian Dyson map.…”

Section: Time-dependent Quadratic Non-hermitian Hamiltonian a Generic Approachmentioning

confidence: 98%

Section: Squeezed Quadratures Of the Electromagnetic Fieldmentioning

confidence: 99%

Section: The Td Parameters Of the Mapmentioning

confidence: 99%

Section: The Td Parameters Of the Mapmentioning

confidence: 99%

See 3 more Smart Citations

The superradiance-superabsorption interplay and a PT-symmetric harmonic oscillator with complex frequency

Dourado¹

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Pseudo-Invariant Approach for a Particle in a Complex Time-Dependent Linear Potential

Koussa

Maamache

2020

Int J Theor Phys

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The Lewis and Riesenfeld method has been investigated, by Ramos et al in Ref.[1], for quantum systems governed by time-dependent PT symmetric Hamiltonians and particularly where the quantum system is a particle submitted to action of a complex time-dependent linear potential. We discuss the method they used and propose an alternative one which leads to physically acceptable uncertainty product and to complex x and p expectation values but describe the classical motion. We used, for this situation, a linear pseudo hermitian invariant operator which allow us to solve analytically the time-dependent Schrödinger equation for this problem and to construct a Gaussian wave packet solution. The normalization condition for the invariant eigenfunctions with the Dirac delta function is correctly obtained, contrary to what is stated in Ref. [1].

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Exact solution for the time-dependent non-Hermitian generalized Swanson oscillator

2023

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All-creation and all-annihilation time-dependent PT -symmetric bosonic Hamiltonians: An infinite squeezing degree at a finite time

Cited by 13 publications

References 53 publications

The superradiance-superabsorption interplay and a PT-symmetric harmonic oscillator with complex frequency

The superradiance-superabsorption interplay and a PT-symmetric harmonic oscillator with complex frequency

Pseudo-Invariant Approach for a Particle in a Complex Time-Dependent Linear Potential

Exact solution for the time-dependent non-Hermitian generalized Swanson oscillator

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