Quantum Group Analogues of Squeezed States

1993 ◽  
pp. 705-713
Author(s):  
Allan I. Solomon
Keyword(s):  
Quantum Group ◽  
Squeezed States

QUANTUM OPTICS: GROUP AND NON-GROUP METHODS

1999 ◽  
Vol 13 (24n25) ◽  
pp. 3021-3038 ◽  
Author(s):  
ALLAN I. SOLOMON
Keyword(s):  
Quantum Optics ◽  
Coherent State ◽  
Quantum Group ◽  
Squeezed States ◽  
Theoretical Methods ◽  
Group Methods ◽  
Photon States

We give a brief review of some group and quantum group theoretical methods used for the construction of photon states, generalisations of coherent and squeezed states. We finally describe a more general approach, exemplified by a new generalized coherent state, a generalization of the Kerr state.

scholarly journals Overcoming detection loss and noise in squeezing-based optical sensing

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Gaetano Frascella ◽  
Sascha Agne ◽  
Farid Ya. Khalili ◽  
Maria V. Chekhova
Keyword(s):  
Shot Noise ◽  
Optical Sensing ◽  
Detection Efficiency ◽  
Signal To Noise Ratio ◽  
Real Life ◽  
Squeezed States ◽  
Squeezed Light ◽  
Noise Limit ◽  
Imaging And Spectroscopy ◽  
Shot Noise Limit

AbstractAmong the known resources of quantum metrology, one of the most practical and efficient is squeezing. Squeezed states of atoms and light improve the sensing of the phase, magnetic field, polarization, mechanical displacement. They promise to considerably increase signal-to-noise ratio in imaging and spectroscopy, and are already used in real-life gravitational-wave detectors. But despite being more robust than other states, they are still very fragile, which narrows the scope of their application. In particular, squeezed states are useless in measurements where the detection is inefficient or the noise is high. Here, we experimentally demonstrate a remedy against loss and noise: strong noiseless amplification before detection. This way, we achieve loss-tolerant operation of an interferometer fed with squeezed and coherent light. With only 50% detection efficiency and with noise exceeding the level of squeezed light more than 50 times, we overcome the shot-noise limit by 6 dB. Sub-shot-noise phase sensitivity survives up to 87% loss. Application of this technique to other types of optical sensing and imaging promises a full use of quantum resources in these fields.

scholarly journals RIESZ TRANSFORMS ON COMPACT QUANTUM GROUPS AND STRONG SOLIDITY

2021 ◽  
pp. 1-37
Author(s):  
Martijn Caspers
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Riesz Transform ◽  
Wreath Products ◽  
Compact Quantum Group ◽  
Riesz Transforms ◽  
Markov Semigroup ◽  
Markov Semigroups ◽  
Free Products ◽  
Compact Quantum Groups

Abstract One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semigroups and noncommutative Riesz transforms. We introduce a property for quantum Markov semigroups of central multipliers on a compact quantum group which we shall call ‘approximate linearity with almost commuting intertwiners’. We show that this property is stable under free products, monoidal equivalence, free wreath products and dual quantum subgroups. Examples include in particular all the (higher-dimensional) free orthogonal easy quantum groups. We then show that a compact quantum group with a quantum Markov semigroup that is approximately linear with almost commuting intertwiners satisfies the immediately gradient- ${\mathcal {S}}_2$ condition from [10] and derive strong solidity results (following [10]). Using the noncommutative Riesz transform we also show that these quantum groups have the Akemann–Ostrand property; in particular, the same strong solidity results follow again (now following [27]).

scholarly journals The Real Forms of the Fractional Supergroup SL(2,C)

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 933
Author(s):  
Yasemen Ucan ◽  
Resat Kosker
Keyword(s):  
Quantum Group ◽  
Lie Group ◽  
The Real ◽  
And Mathematics ◽  
Real Forms

The real forms of complex groups (or algebras) are important in physics and mathematics. The Lie group SL2,C is one of these important groups. There are real forms of the classical Lie group SL2,C and the quantum group SL2,C in the literature. Inspired by this, in our study, we obtain the real forms of the fractional supergroups shown with A3NSL2,C, for the non-trivial N = 1 and N = 2 cases, that is, the real forms of the fractional supergroups A31SL2,C and A32SL2,C.

Phase properties of superposed squeezed states

2001 ◽  
Vol 8 (6) ◽  
pp. 422-430
Author(s):  
Suc-Kyoung Hong ◽  
Chung-In Um ◽  
Kyu-Hwang Yeon
Keyword(s):  
Squeezed States ◽  
Phase Properties

Rotational spectra of deformed nuclei and the quantum group SUq (2)

1992 ◽  
Vol 42 (12) ◽  
pp. 1337-1344 ◽  
Author(s):  
M. Honusek ◽  
M. Vinduśka ◽  
V. Wagner
Keyword(s):  
Quantum Group ◽  
Deformed Nuclei ◽  
Rotational Spectra

scholarly journals Quantum frequency down-conversion of bright amplitude-squeezed states

2014 ◽  
Vol 22 (20) ◽  
pp. 24192 ◽  
Author(s):  
Dehuan Kong ◽  
Zongyang Li ◽  
Shaofeng Wang ◽  
Xuyang Wang ◽  
Yongmin Li
Keyword(s):  
Squeezed States ◽  
Quantum Frequency ◽  
Down Conversion
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