Quantum-state tomogram from s-parameterized quasidistributions

Quantum optomechanics uses optical means to generate and manipulate quantum states of motion of mechanical resonators. This provides an intriguing platform for the study of fundamental physics and the development of novel quantum devices.Yet, the challenge of reconstructing and verifying the quantum state of mechanical systems has remained a major roadblock in the field. Here, we present a novel approach that allows for tomographic reconstruction of the quantum state of a mechanical system without the need for extremely high quality optical cavities. We show that, without relying on the usual state transfer presumption between light an mechanics, the full optomechanical Hamiltonian can be exploited to imprint mechanical tomograms on a strong optical coherent pulse, which can then be read out using well-established techniques. Furthermore, with only a small number of measurements, our method can be used to witness nonclassical features of mechanical systems without requiring full tomography. By relaxing the experimental requirements, our technique thus opens a feasible route towards verifying the quantum state of mechanical resonators and their nonclassical behaviour in a wide range of optomechanical systems.

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“…The tomographic relation (33) can be generalized to arbitrary phase-space quasiprobability distributions with s 0 as [57] w…”

Section: Phase-space Tomographymentioning

confidence: 99%

Optomechanical state reconstruction and nonclassicality verification beyond the resolved-sideband regime

Shähandeh

Ringbauer

2019

Quantum

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“…As is well known, the density operator can be expanded in terms of a complete set of operators; one can clarify different aspects of the quantum state by using different representations to construct the corresponding density matrix. Analogously, the case can also be seen in the tomographic approach [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. For instance, in [9], a new tomographic representation (squeeze tomography), which is the photon number analogous to the case of photon-number tomographys, was introduced to study the relation of the squeeze tomograms to the symplectic tomograms.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, in [9], a new tomographic representation (squeeze tomography), which is the photon number analogous to the case of photon-number tomographys, was introduced to study the relation of the squeeze tomograms to the symplectic tomograms. In [14], the authors realized the map of the s-parameterized quasi-distribution function to the corresponding quantum-state tomogram. In this work, based on the fact that the Husimi operator h (q, p, κ) is just the squeezed coherent state projector [25,26], i.e.…”

Section: Introductionmentioning

confidence: 99%

Tomography of a quantum state related to the Husimi function

Xu¹,

Fang²,

Zang³

et al. 2012

Phys. Scr.

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“…We can calculate the above trace expression in terms of other quasiprobabilities [10]. For example, the normal form of the tomographic operator might be found as follows:…”

Section: Introductionmentioning

confidence: 99%

“…Also the relation between s-parameterized phase-space distributions and tomograms of a quantum state has been analyzed in [10]. Motivated by the above, in this paper we are going to study the relation between the Bargmann and tomographic representations and introduce a new map that relates the tomographic symbol of an operator directly to its Bargmann representation.…”

Section: Introductionmentioning

confidence: 99%

Relation of the tomographic representation of states to the bargmann representation of states

2012

Self Cite

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We introduce some equivalent forms of a map realizing the connection between the Bargmann and tomographic representations of states and observables. We perform the same task for a dual tomographic map. In spite of the fact that, due to the analyticity of the Bargmann representation, there exist many forms for such a map, we restrict ourselves to integral transforms. To perform our calculations, we also introduce a new technique for disentangling the SU (1, 1)-group operators.

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Quantum-state tomogram from s-parameterized quasidistributions

Cited by 3 publications

References 13 publications

Optomechanical state reconstruction and nonclassicality verification beyond the resolved-sideband regime

Optomechanical state reconstruction and nonclassicality verification beyond the resolved-sideband regime

Tomography of a quantum state related to the Husimi function

Relation of the tomographic representation of states to the bargmann representation of states

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