arXiv 2103.070822021-03-12quant-phmath-phmath.MP

Constructing Squeezed States of Light with Associated Hermite Polynomials

Kevin Zelaya, Véronique Hussin, Oscar Rosas-Ortiz

发表信息：: Eur. Phys. J. Plus 136 (2021) 534
DOI：: 10.1140/epjp/s13360-021-01536-3

英文摘要：

A new class of states of light is introduced that is complementary to the well-known squeezed states. The construction is based on the general solution of the three-term recurrence relation that arises from the saturation of the Schrödinger inequality for the quadratures of a single-mode quantized electromagnetic field. The new squeezed states are found to be linear superpositions of the photon-number states whose coefficients are determined by the associated Hermite polynomials. These results do not seem to have been noticed before in the literature. As an example, the new class of squeezed states includes superpositions characterized by odd-photon number states only, so they represent the counterpart of the prototypical squeezed-vacuum state which consists entirely of even-photon number states.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Squeezed States and Hermite polynomials in a Complex Variable

Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is …

2013-08-21math-phmath.MPquant-ph

ARBITRARY-ORDER HERMITE GENERATING FUNCTIONS FOR COHERENT AND SQUEEZED STATES

For use in calculating higher-order coherent- and squeezed- state quantities, we derive generalized generating functions for the Hermite polynomials. They are given by $\sum_{n=0}^{\infty}z^{jn+k}H_{jn+k}(x)/(jn+k)!$, for arbitrary integers $j\geq 1$ and $k\geq 0$. Along the way, the sums with the Hermite polynomials replaced by unity are also obtained. We also evaluate the action of the operators $\exp[a^j(d/dx)^j]$ on well-behaved functions and apply them to obtain other sums.

1995-06-07quant-ph

通过分束器条件测量产生厄米多项式激发压缩态

Generating Hermite polynomial excited squeezed states by means of conditional measurements on a beam splitter

本研究提出通过分束器条件测量产生厄米多项式激发压缩真空态的方案，探究其非经典效应与非高斯性，证实该方法可有效生成非高斯态。

2015-03-17quant-ph

与非旋转测度相关的Segal-Bargmann型空间及双组份压缩相干态的纠缠

Segal-Bargmann type spaces related to non-rotational measure, and entanglement of bipartite squeezed coherent states

本文利用基于Wigner分布的相空间方法，研究了双组份压缩态纠缠，揭示了压缩参数与非旋转测度参数的关系，并借助Peres-Horodecki判据和对数负性确定了纠缠的定量特征。

2025-08-14math-phmath.MPquant-ph

Nonclassical properties of Hermite polynomial's excitation on squeezed vacuum and its decoherence in phase-sensitive reservoirs

We introduce Hermite polynomial excitation squeezed vacuum (SV) H_{n}(O)S(r)|0> with O=u a+v a^{+}. We investigate analytically the nonclassical properties according to Mandel's Q parameter, second correlation function, squeezing effect and the negativity of Wigner function (WF). It is found that all these nonclassicalities can be enhanced by H_{n}(O)operation and adjustable parameters u and v. In particular, the optimal negative volume delta_{opt}of WF can be achieved by modulating u and v for n>=2,while delta is kept unchanged for n=1. Furthermore, the decoherence effect of phase-sensitive e…

2014-12-14quant-ph

Properties of Squeezed-State Excitations

The photon distribution function of a discrete series of excitations of squeezed coherent states is given explicitly in terms of Hermite polynomials of two variables. The Wigner and the coherent-state quasiprobabilities are also presented in closed form through the Hermite polynomials and their limiting cases. Expectation values of photon numbers and their dispersion are calculated. Some three-dimensional plots of photon distributions for different squeezing parameters demonstrating oscillatory behaviour are given.

1996-11-30quant-ph

更多相关论文收起更多论文

Photon Statistics for MUltimode Squeezed Schrödinger Cat States

Particle distributions in squeezed states, even and odd coherent states are given in terms of multivariable Hermite polynomials. The Q--function and Wigner function for nonclassical field states are discussed.

1995-02-27quant-ph

A new method for constructing squeezed states for the isotropic 2D harmonic oscillator

We introduce a new method for constructing squeezed states for the 2D isotropic harmonic oscillator. Based on the construction of coherent states in [1], we define a new set of ladder operators for the 2D system as a linear combination of the x and y ladder operators and construct the SU(2) coherent states. The new ladder operators are used for generalizing the squeezing operator to 2D and the SU(2) coherent states play the role of the Fock states in the expansion of the 2D squeezed states. We discuss some properties of the 2D squeezed states.

2020-01-21quant-ph

Non-critically squeezed light via spontaneous rotational symmetry breaking

We theoretically address squeezed light generation through the spontaneous breaking of the rotational invariance occuring in a type I degenerate optical parametric oscillator (DOPO) pumped above threshold. We show that a DOPO with spherical mirrors, in which the signal and idler fields correspond to first order Laguerre-Gauss modes, produces a perfectly squeezed vacuum with the shape of a Hermite-Gauss mode, within the linearized theory. This occurs at any pumping level above threshold, hence the phenomenon is non-critical. Imperfections of the rotational symmetry, due e.g. to cavity anisotrop…

2008-02-29quant-ph

Nonclassicality and decoherence of photon-added squeezed thermal state in thermal environment

Theoretical analysis is given of nonclassicality and decoherence of the field states generated by adding any number of photons to the squeezed thermal state (STS). Based on the fact that the squeezed number state can be considered as a single-variable Hermite polynomial excited state, the compact expression of the normalization factor is derived, a Legendre polynomial. The nonclassicality is investigated by exploring the sub-Poissonian and negative Wigner function (WF). The results show that the WF of single photon-added STS (PASTS) always has negative values at the phase space center. The dec…

2011-10-30quant-ph

Multi-spatial-mode effects in squeezed-light-enhanced interferometric gravitational wave detectors

Proposed near-future upgrades of the current advanced interferometric gravitational wave detectors include the usage of frequency dependent squeezed light to reduce the current sensitivity-limiting quantum noise. We quantify and describe the degradation effects that spatial mode-mismatches between optical resonators have on the squeezed field. These mode-mismatches can to first order be described by scattering of light into second-order Gaussian modes. As a demonstration of principle, we also show that squeezing the second-order Hermite-Gaussian modes $\mathrm{HG}_{02}$ and $\mathrm{HG}_{20}$,…

2017-07-06physics.opticsquant-ph

Statistical properties and decoherence of two-mode photon-subtracted squeezed vacuum

We investigate the statistical properties of the photon-subtractions from the two-mode squeezed vacuum state and its decoherence in a thermal environment. It is found that the state can be considered as a squeezed two-variable Hermite polynomial excitation vacuum and the normalization of this state is the Jacobi polynomial of the squeezing parameter. The compact expression for Wigner function (WF) is also derived analytically by using the Weyl ordered operators' invariance under similar transformations. Especially, the nonclassicality is discussed in terms of the negativity of WF. The effect o…

2009-05-16quant-ph

Nonclassicality of photon-added squeezed vacuum and its decoherence in thermal environment

We study the nonclassicality of photon-added squeezed vacuum (PASV) and its decoherence in thermal environment in terms of the sub-Poissonian statistics and the negativity of Wigner function (WF). By converting the PASV to a squeezed Hermite polynomial excitation state, we derive a compact expression for the normalization factor of m-PASV, which is an m-order Legendre polynomial of squeezing parameter r. We also derive the explicit expression of WF of m-PASV and find the negative region of WF in phase space. We show that there is an upper bound value of r for this state to exhibit sub-Poissoni…

2009-10-28quant-ph

Generalized Coherent States for q-oscillator connected with discrete q-Hermite polynomials

We are continuing here the study of generalized coherent states of Barut-Girardello type for the oscillator-like systems connected with the given set of orthogonal polynomials. In this work we construct the family of coherent states associated with discrete $q$-Hermite polynomials of the II-type and prove the over-completeness of this family of states by constructing the measure for unity decomposition for this family of coherent states.

2004-07-29quant-ph

Spatially single-mode source of bright squeezed vacuum

Bright squeezed vacuum, a macroscopic nonclassical state of light, can be obtained at the output of a strongly pumped non-seeded traveling-wave optical parametric amplifier (OPA). By constructing the OPA of two consecutive crystals separated by a large distance we make the squeezed vacuum spatially single-mode without a significant decrease in the brightness or squeezing.

2014-02-12quant-ph

Standard quantum limit of angular motion of a suspended mirror and homodyne detection of ponderomotively squeezed vacuum field

Compared to the quantum noise in the measurement of the translational motion of a suspended mirror using laser light, the quantum noise in the measurement of the angular motion of a suspended mirror has not been investigated intensively despite its potential importance. In this article, an expression for the quantum noise in the angular motion measurement is explicitly derived. The expression indicates that one quadrature of the vacuum field of the first-order Hermite-Gaussian mode of light causes quantum sensing noise and the other causes quantum backaction noise, or in other words the first-…

2016-07-06gr-qcquant-ph

Squeezed atom laser for Bose-Einstein condensate with minimal length

We study a protocol for constructing a squeezed atom laser for a model originating from the generalized uncertainty principle. We show that the squeezing effects arising from such systems do not require any squeezed light as an input, but the squeezing appears automatically because of the structure of the model it owns. The output atom laser beam becomes squeezed due to the nonlinear interaction between the Bose-Einstein condensate and the deformed radiation field created due to the noncommutative structure. We analyze several standard squeezing techniques based on the analytical expressions f…

2018-05-31hep-thquant-ph

Photon number and optical tomograms for Gaussian states

A review of probability representation of quantum states in given for optical and photon number tomography approaches. Explicit connection of photon number tomogram with measurable by homodyne detector optical tomogram is obtained. New integral relations connecting Hermite polynomials of two variables with Laguerre polynomials are found. Examples of generic Gaussian photon states (squeezed and correlated states) are studied in detail.

2019-03-06quant-ph

Photon distributions and information nonnegativity versus quadrature uncertainty relation

Using entropic inequalities for Shannon entropies new inequalities for some classical polynomials are obtained. To this end, photon distribution functions for one-, two- and multi-mode squeezed states in terms of Hermite, Laguerre, Legendre polynomials and Gauss' hypergeometric functions are used. The dependence between the violation of the quadrature uncertainty relation, the sign and the existence of the distribution function of such states is considered.

2016-03-04quant-ph

通过光学参量放大高效检测光谱多模压缩光

Efficient detection of spectrally multimode squeezed light through optical parametric amplification

本文首次实验演示了利用光学参量放大检测光谱多模压缩光，实现对宽带压缩真空态超过60个光谱模式的同时检测，压缩度均匀且达-6.5至-7 dB，为构建连续变量簇态及高维光子量子技术提供了新途径。

2025-08-06physics.opticsquant-ph