Preparation of a nonlinear coherent state of the mechanical resonator in an optomechanical microcavity

Yan, Yan; Zhu, Jia-pei; Li, Gao‐xiang

doi:10.1364/oe.24.013590

Cited by 17 publications

(14 citation statements)

References 93 publications

(134 reference statements)

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“…Multiplying both sides by e −2πijl/k , summing on l and using the orthogonality condition (27), we arrive to…”

Section: Exact Finite Circle Representation For Truncated K-hypercatsmentioning

confidence: 99%

“…On the physical side, the first proposal to generate f -CS was given in [26] as emergent stationary states of the motion of an appropriately laser-driven trapped ion. Later, many other generation schemes of f -CS have been explored, for example: single-atom lasers, micromaser under the intensity-dependent Jaynes-Cummings model, excitons in a wide quantum dot, or using a mechanical resonator in an optomechanical microcavity (see e.g [27] and references therein).…”

Section: Introductionmentioning

confidence: 99%

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Quantum statistical properties of multiphoton hypergeometric coherent states and the discrete circle representation

Calixto

Guerrero

2019

Journal of Mathematical Physics

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We review the definition of hypergeometric coherent states, discussing some representative examples. Then we study mathematical and statistical properties of hypergeometric Schrödinger cat states, defined as orthonormalized eigenstates of k-th powers of nonlinear f -oscillator annihilation operators, with f of hypergeometric type. These "k-hypercats" can be written as an equally weighted superposition of hypergeometric coherent states |z l , l = 0, 1, . . . , k − 1, with z l = ze 2πil/k a k-th root of z k , and they interpolate between number and coherent states. This fact motivates a continuous circle representation for high k. We also extend our study to truncated hypergeometric functions (finite dimensional Hilbert spaces) and a discrete exact circle representation is provided. We also show how to generate k-hypercats by amplitude dispersion in a Kerr medium and analyze their generalized Husimi Q-function in the super-and sub-Poissonian cases at different fractions of the revival time.

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“…Multiplying both sides by e −2πijl/k , summing on l and using the orthogonality condition (27), we arrive to…”

Section: Exact Finite Circle Representation For Truncated K-hypercatsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Quantum statistical properties of multiphoton hypergeometric coherent states and the discrete circle representation

Calixto

Guerrero

2019

Journal of Mathematical Physics

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“…So, if the nonlinear coherent states can be found to exist in real life experiment, the study of our system in the laboratory will not be far. Experimental attempts for nonlinear coherent states have been enormous [187][188][189], for more references; see, [19].…”

Section: Applicationsmentioning

confidence: 99%

Coherent States and Their Applications

2018

Springer Proceedings in Physics

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It was at the dawn of the historical developments of quantum mechanics when Schrödinger, Kennard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as "coherent states" today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowadays. Nonclassical states constitute one of the distinguished branches of coherent states having applications in various subjects including quantum information processing, quantum optics, quantum superselection principles and mathematical physics. On the other hand, the compelling advancements of non-Hermitian systems and related areas have been appealing, which became popular with the seminal paper by Bender and Boettcher in 1998. The subject of non-Hermitian Hamiltonian systems possessing real eigenvalues are exploding day by day and combining with almost all other subjects rapidly, in particular, in the areas of quantum optics, lasers and condensed matter systems, where one finds ample successful experiments for the proposed theory. For this reason, the study of coherent states for non-Hermitian systems have been very important. In this article, we review the recent developments of coherent and nonclassical states for such systems and discuss their applications and usefulness in different contexts of physics. In addition, since the systems considered here originate from the broader context of the study of minimal uncertainty relations, our review is also of interest to the mathematical physics community.

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“…More importantly, it has been shown that generalized nonclassical states provide higher degree of nonclassicality compared to the usual nonclassical states [16][17][18], which can be exploited to enhance the quantum entanglement of various nonclassical states within some protocols [19][20][21]. The usage of the generalized quantum optical states is not limited to the theoretical studies but there have been ample experimental investigations based on Kerr type nonlinear cavities [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Generalized photon-subtracted squeezed vacuum states

Dey,

Nair

2020

Preprint

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We construct a generalized version of the photon-subtracted squeezed vacuum states (PSSVS), which can be utilized to construct the same for nonlinear, deformed and any usual quantum mechanical models beyond the harmonic oscillator. We apply our general framework to trigonometric Pöschl-Teller potential and show that our method works accurately and produces a proper nonclassical state. We analyze the nonclassicality of the state using three different approaches, namely, quadrature squeezing, photon number squeezing and Wigner function and indicate how the standard definitions of those three techniques can be generalized and utilized to examine the nonclassicality of any generalized quantum optical states including the PSSVS. We observe that the generalized PSSVS are always more nonclassical than those arising from the harmonic oscillator. Moreover, within some quantification schemes, we find that the nonclassicality of the PSSVS increases almost proportionally with the number of photons subtracted from the generalized squeezed vacuum state. Thus, generalized PSSVS may provide an additional freedom with which one can regulate the nonclassicality and obtain an appropriate nonclassical state as per requirement.

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Preparation of a nonlinear coherent state of the mechanical resonator in an optomechanical microcavity

Cited by 17 publications

References 93 publications

Quantum statistical properties of multiphoton hypergeometric coherent states and the discrete circle representation

Quantum statistical properties of multiphoton hypergeometric coherent states and the discrete circle representation

Coherent States and Their Applications

Generalized photon-subtracted squeezed vacuum states

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