A time-dependent pseudo-Hermitian Hamiltonian for a cavity mode with pure imaginary frequency

Dourado, R. A.; Ponte, M. A. de; Moussa, M. H. Y.

doi:10.1016/j.physa.2021.126195

Cited by 8 publications

(7 citation statements)

References 40 publications

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“…Moreover, we stress the introduction of the all-creation and all-annihilation TD pseudo-Hermitian bosonic Hamiltonians [25,26], able to generate an infinite squeezing degree at a finite time. A TD pseudo-Hermitian Hamiltonian for a cavity mode with complex frequency is also able to generate an infinite squeezing at a finite time [27]. Finally, we mention the enhancement of photon creation through the pseudo-Hermitian dynamical Casimir effect [28].…”

Section: Introductionmentioning

confidence: 92%

“…For example, our developments considerably broaden our understanding of those presented in Refs. [11,12,[25][26][27][28], where all the analysis on symmetry is reduced to the conditions for a TD Hamiltonian to be PT -symmetric. From our conclusions, we now know that there are close connections between the group algebra of the Hamiltonian, the symmetry and the metric operator.…”

Section: Introductionmentioning

confidence: 99%

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Beyond PT-symmetry: Towards a symmetry-metric relation for time-dependent non-Hermitian Hamiltonians

2022

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In this work we first propose a method for the derivation of a general continuous antilinear time-dependent (TD) symmetry operator I(t)I(t) for a TD non-Hermitian Hamiltonian H(t)H(t). Assuming H(t)H(t) to be simultaneously \rho(t)ρ(t)-pseudo-Hermitian and \Xi(t)Ξ(t)-anti-pseudo-Hermitian, we also derive the antilinear symmetry I(t)=\Xi^{-1}(t)\rho(t)I(t)=Ξ−1(t)ρ(t), which retrieves an important result obtained by Mostafazadeh [J. Math, Phys. 43, 3944 (2002)] for the time-independent (TI) scenario. We apply our method for the derivation of the symmetries associated with TD non-Hermitian linear and quadratic Hamiltonians. The computed TD symmetry operators for both cases are then particularized for their equivalent TI Hamiltonians and PT -symmetric restrictions. In the TI scenario we retrieve the well-known Bender-Berry-Mandilara result for the symmetry operator: I^{2k}=1I2k=1 with kk odd [J. Phys. A 35, L467 (2002)]. The results here derived allow us to propose a useful symmetry-metric relation for TD non-Hermitian Hamiltonians. From this relation the TD metric is automatically derived from the TD symmetry of the problem. Then, when placed in perspective with the antilinear symmetry I(t)=\Xi^{-1}(t)\rho(t)I(t)=Ξ−1(t)ρ(t), the symmetry-metric relation finally allow us to derive the \Xi(t)Ξ(t)-anti-pseudo-Hermitian operator. Our results reinforce the prospects of going beyond \mathcal{PT}𝒫𝒯-symmetric quantum mechanics making the field of pseudo-Hermiticity even more comprehensive and promising.

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Beyond PT-symmetry: Towards a symmetry-metric relation for time-dependent non-Hermitian Hamiltonians

2022

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“…In parallel, an intriguing result raises from the theoretical investigations on time-dependent non-Hermitian Hamiltonians [13], as in Refs. [14][15][16], where the authors shed light on the possibility of achieving an infinite degree of squeezing into a finite time interval by defining a suitable time-dependent metric.…”

Section: Introductionmentioning

confidence: 99%

“…(b) Disodium Phosphate (DSP) Na2HPO4 and the spectrum of 31 P nuclei are sketched. The green spheres represent 31 P nuclei, red spheres represent16 O nuclei, black spheres represent12 C nuclei, brown spheres represent blue ellipsoids represent23 clei. (c) The standard pre-saturation pulse sequence was modified in order to implement and to monitor the dynamics of the 31 P nuclei of the sample under a non-Hermitian Hamiltonian.…”

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confidence: 99%

Mixed states driven by Non-Hermitian Hamiltonians of a nuclear spin ensemble

Cius,

Consuelo-Leal,

Araujo-Ferreira

et al. 2021

Preprint

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We study the quantum dynamics of a non-interacting spin ensemble under the effect of a reservoir by applying the framework of the non-Hermitian Hamiltonian operators. Theoretically, the two-level model describes the quantum spin system and the Bloch vector to establish the dynamical evolution. Experimentally, phosphorous ( 31 P) nuclei with spin I = 1/2 are used to represent the two-level system and the magnetization evolution is measured and used to compare with the theoretical prediction. At room temperature, the composite dynamics of the radio-frequency pulse plus field inhomogeneities (or unknown longitudinal fluctuations) along the z-axis transform the initial quantum state and drives it into a mixed state at the end of the dynamics. The experimental setup shows a higher accuracy when compared with the theoretical prediction (>98%), ensuring the relevance and effectiveness of the non-Hermitian theory at a high-temperature regime.

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“…A TD pseudo-Hermitian Hamiltonian for a cavity mode with complex frequency is also able to generate an infinite squeezing at a finite time. (27) Finally, we mention the enhancement of photon creation through the pseudo-Hermitian dynamical Casimir effect. (28) Our subject, pseudo-Hermiticity beyond PT -symmetry, is in fact at the foundations of pseudo-Hermitian quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Beyond PT-symmetry: towards a symmetry-metric relation for time-dependent non-Hermitian Hamiltonians

Silva¹

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A new chapter in quantum mechanics has opened over the past 20 years with the fact that time-independent (TI) non-Hermitian Hamiltonians have a real spectrum and unitary time evolution when they exhibit an unbroken PT -symmetry and satisfy the pseudo-Hermiticity relation. In this Master's thesis, we first propose a method for the derivation of a general continuous antilinear time-dependent (TD) symmetry operator I(t) for non-Hermitian Hamiltonian H(t) and metric operator ρ(t) in a TD scenario. Assuming H(t) to be simultaneously ρ(t)-pseudo-Hermitian and Ξ(t)-anti-pseudo-Hermitian, we also derive the antilinear symmetry I(t) = Ξ −1 (t)ρ(t), which retrieves an important result obtained by Mostafazadeh [J. Math, Phys. 43, 3944 (2002)] for the time-independent (TI) scenario. We apply our method for the derivation of the symmetry associated with TD non-Hermitian linear and quadratic Hamiltonians. In the TI scenario, we retrieve the well-known Bender-Berry-Mandilara result for the symmetry operator:]. The results here derived allow us to propose a useful symmetry-metric relation for TD non-Hermitian Hamiltonians. From this relation, the TD metric is automatically derived from the TD symmetry of the problem. Our results reinforce the prospects of going beyond PT -symmetric quantum mechanics making the field of pseudo-Hermiticity even more comprehensive and promising.

show abstract

A time-dependent pseudo-Hermitian Hamiltonian for a cavity mode with pure imaginary frequency

Cited by 8 publications

References 40 publications

Beyond PT-symmetry: Towards a symmetry-metric relation for time-dependent non-Hermitian Hamiltonians

Beyond PT-symmetry: Towards a symmetry-metric relation for time-dependent non-Hermitian Hamiltonians

Mixed states driven by Non-Hermitian Hamiltonians of a nuclear spin ensemble

Beyond PT-symmetry: towards a symmetry-metric relation for time-dependent non-Hermitian Hamiltonians

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