Interference in Phase Space of Squeezed States for the Time-Dependent Hamiltonian System

Choi, Jeong Ryeol

doi:10.1007/s10773-005-9016-9

Cited by 6 publications

(3 citation statements)

References 23 publications

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“…It can be used to represent this ensemble of waves with random initial phases, or of random classical fields. As a quasi-probability, it can acquire negative values indicating interference of waves in phase-space (Choi 2006) describing the undulatory behaviour that can be captured in this description.…”

Section: Bec In Wave Turbulence-kinetic Theorymentioning

confidence: 99%

Ultra-light dark matter

Ferreira

2021

Astron Astrophys Rev

259

126

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Ultra-light dark matter is a class of dark matter models (DM), where DM is composed by bosons with masses ranging from $$10^{-24}\, \mathrm {eV}< m < \mathrm {eV}$$ 10 - 24 eV < m < eV . These models have been receiving a lot of attention in the past few years given their interesting property of forming a Bose–Einstein condensate (BEC) or a superfluid on galactic scales. BEC and superfluidity are some of the most striking quantum mechanical phenomena that manifest on macroscopic scales, and upon condensation, the particles behave as a single coherent state, described by the wavefunction of the condensate. The idea is that condensation takes place inside galaxies while outside, on large scales, it recovers the successes of $$\varLambda $$ Λ CDM. This wave nature of DM on galactic scales that arise upon condensation can address some of the curiosities of the behaviour of DM on small-scales. There are many models in the literature that describe a DM component that condenses in galaxies. In this review, we are going to describe those models, and classify them into three classes, according to the different non-linear evolution and structures they form in galaxies: the fuzzy dark matter (FDM), the self-interacting fuzzy dark matter (SIFDM), and the DM superfluid. Each of these classes comprises many models, each presenting a similar phenomenology in galaxies. They also include some microscopic models like the axions and axion-like particles. To understand and describe this phenomenology in galaxies, we are going to review the phenomena of BEC and superfluidity that arise in condensed matter physics, and apply this knowledge to DM. We describe how ULDM can potentially reconcile the cold DM picture with the small-scale behaviour. These models present a rich phenomenology that is manifest in different astrophysical consequences. We review here the astrophysical and cosmological tests used to constrain those models, together with new and future observations that promise to test these models in different regimes. For the case of the FDM class, the mass where this model has an interesting phenomenology on small-scales $$ \sim 10^{-22}\, \mathrm {eV}$$ ∼ 10 - 22 eV , is strongly challenged by current observations. The parameter space for the other two classes remains weakly constrained. We finalize by showing some predictions that are a consequence of the wave nature of this component, like the creation of vortices and interference patterns, that could represent a smoking gun in the search of these rich and interesting alternative class of DM models.

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Section: Bec In Wave Turbulence-kinetic Theorymentioning

confidence: 99%

Ultra-light dark matter

Ferreira

2021

Astron Astrophys Rev

259

126

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“…The eigenfunctions and the corresponding coherent states of CK Hamiltonian were constructed in the literature [14,15], where it is shown that the general properties of coherent states are satisfied. Also, the squeezed states of the CK Hamiltonian are investigated [16] and it is proven that the eigenstates of this Hamiltonian satisfy the minimum uncertainty relation in a generalized form [17].…”

Section: Introductionmentioning

confidence: 99%

Damping effect in the interaction of a Ξ-type three-level atom with a single-mode field: Caldirola–Kanai approach

Daneshmand

Tavassoly

2016

Laser Phys.

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In this paper the damped interaction between a Ξ-type three-level atom and a quantized single-mode cavity field is studied, where the Hamiltonian of the field is performed based on the Caldirola-Kanai damping Hamiltonian. The amplitude probabilities of the atom-field entangled state associated with the system considered have been explicitly deduced and the time evolution of a few of its physical properties is discussed. In detail, the influence of the damping parameter on the temporal behavior of the linear entropy, sub-Poissonian statistics as well as quadrature and amplitude squared squeezing is numerically investigated. Besides these, as an additional purpose of the paper, the effects of the initial field type as well as the initial mean photon number of the field on the above-mentioned properties are evaluated numerically. It is shown that via adjusting the damping parameter, initial field and its intensity, one can tune the degree of entanglement and other nonclassicality features.

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“…Several researchers including us investigated the WDF for the time-dependent quadratic Hamiltonian system (TDQHS) in number, coherent and squeezed states [14,15]. For several decades, the study of quantum properties for the TDQHS has been attracting considerable interest in the literature [16][17][18][19][20][21][22][23][24][25][26][27][28][29]. For example, harmonic oscillators with time-variable mass and/or frequency are a typical kind of TDQHS.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent Wigner distribution function employed in coherent Schrödinger cat states: |Ψ(t)⟩=N^−1/2(|α⟩+e^iφ|-α⟩)

Choi¹,

Yeon²

2008

Phys. Scr.

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The Wigner distribution function for the time-dependent quadratic Hamiltonian system in the coherent Schrödinger cat state is investigated. The type of state we consider is a superposition of two coherent states, which are by an angle of π out of phase with each other. The exact Wigner distribution function of the system is evaluated under a particular choice of phase, δ c,q . Our development is employed for two special cases, namely, the Caldirola-Kanai oscillator and the frequency stable damped harmonic oscillator. On the basis of the diverse values of the Wigner distribution function that were plotted, we analyze the nonclassical behavior of the systems.

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Interference in Phase Space of Squeezed States for the Time-Dependent Hamiltonian System

Cited by 6 publications

References 23 publications

Ultra-light dark matter

Ultra-light dark matter

Damping effect in the interaction of a Ξ-type three-level atom with a single-mode field: Caldirola–Kanai approach

Time-dependent Wigner distribution function employed in coherent Schrödinger cat states: |Ψ(t)⟩=N^−1/2(|α⟩+e^iφ|-α⟩)

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Interference in Phase Space of Squeezed States for the Time-Dependent Hamiltonian System

Cited by 6 publications

References 23 publications

Ultra-light dark matter

Ultra-light dark matter

Damping effect in the interaction of a Ξ-type three-level atom with a single-mode field: Caldirola–Kanai approach

Time-dependent Wigner distribution function employed in coherent Schrödinger cat states: |Ψ(t)⟩=N−1/2(|α⟩+eiφ|-α⟩)

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Time-dependent Wigner distribution function employed in coherent Schrödinger cat states: |Ψ(t)⟩=N^−1/2(|α⟩+e^iφ|-α⟩)