An introduction to the quantum theory of nonlinear optics

Hillery, Mark

doi:10.2478/v10155-010-0094-8

Cited by 39 publications

(42 citation statements)

References 57 publications

(125 reference statements)

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“…Evidently, the average photon number for the TMSCS depends on the combination of the phases θ 1 ,θ 2 , and 2φ in . This result is not new [1], but as far as we are aware, the effect of the phases on the average photon number in coherently stimulated parametric down-conversion, as given in Eq. (15), has yet to be demonstrated experimentally.…”

Section: Coherently Stimulated Parametric Down-conversion and Thementioning

confidence: 80%

“…For many years now, parametric down-conversion has been a laboratory source of light with strong nonclassical properties [1]. The generated states of light have been used to study a variety of quantum effects and have had applications for fundamental tests of quantum mechanics as in twophoton interference at a beam splitter [2] and to Bell-type inequalities [3], as well as practical applications such as to quantum metrology [4], quantum information processing [5], and quantum imaging [6].…”

Section: Introductionmentioning

confidence: 99%

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Coherently stimulated parametric down-conversion, phase effects, and quantum-optical interferometry

2015

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We re-examine the properties of the states produced by nondegenerate coherently stimulated parametric down-conversion wherein the signal and idler modes are seeded with coherent states of light and where the nonlinear crystal is driven by a strong classical field as described by the parametric approximation. The states produced are the two-mode squeezed coherent states defined with a specific ordering of operators, namely, the displacement operators of the two modes acting on the double vacuum state followed by the action of the two-mode squeeze operator representing the down-conversion process. Though mathematically equivalent to the reverse ordering of operators, but with different displacement parameters, the ordering we consider is closely related to what could most easily be implemented in the laboratory. The statistical properties of the state are studied with an emphasis on how they, and its average photon number, are affected by the various controllable phases, namely, those of the classical pump field of the two input coherent states. We then consider the multiphoton interference effects that arise if the two beams are overlapped on a 50:50 beam splitter, investigating the role of the phases in controlling the statistical properties of the output states. Finally, we study the prospects for the application of the states to quantum-optical interferometry to obtain sensitivities in phase-shift measurements beyond the standard quantum limit.

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Section: Coherently Stimulated Parametric Down-conversion and Thementioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

Coherently stimulated parametric down-conversion, phase effects, and quantum-optical interferometry

2015

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“…Here VðzÞ ¼ C 6 =z 6 is the Rydberg-Rydberg interaction whose spatial nonlocality contrasts with typical nonlinear quantum optical systems [44][45][46].F P is a -correlated vacuum Langevin noise operator [47]. g is the collective atom-photon coupling constant, time and frequencies were rescaled by (the halfwidth of the jgi-jei transition), while z was rescaled by c=.…”

mentioning

confidence: 99%

Dissipative Many-Body Quantum Optics in Rydberg Media

2013

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We develop a theoretical framework for the dissipative propagation of quantized light under conditions of electromagnetically induced transparency in atomic media involving strongly interacting Rydberg states. The theory allows us to determine the peculiar spatiotemporal structure of the output of the recently demonstrated single-photon filter and the recently proposed single-photon subtractor, which, respectively, let through and absorb a single photon. In addition to being crucial for applications of these and other optical quantum devices, the theory opens the door to the study of exotic dissipative many-body dynamics of strongly interacting photons in nonlinear nonlocal media. DOI: 10.1103/PhysRevLett.110.153601 PACS numbers: 42.50.Nn, 32.80.Ee, 34.20.Cf, 42.50.Gy Dissipation has recently been recognized as a powerful tool for quantum information and many-body physics [1][2][3][4][5][6][7][8][9][10][11]. A particular example, realized in recent experiments [12][13][14], is the propagation of quantized light fields in Rydberg media [15][16][17][18] under the conditions of electromagnetically induced transparency (EIT) [19]. While Rydberg states provide strong long-range atom-atom interactions, EIT provides strong atom-light interactions with controlled dissipation. The resulting combination gives rise to strong and often dissipative photon-photon interactions [20][21][22][23], which can be used to generate a variety of nonclassical states of light [12][13][14][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] and to implement photon-photon and atom-photon quantum gates [21,23,39,40]. The first wave-function-based descriptions of two-photon propagation in Rydbeg EIT media have revealed the emergence of correlated two-photon losses that could enable the deterministic generation of single photons [13,21]. Yet, the fate of the remaining photon as well as the underlying dissipative many-body dynamics have remained unclear despite their essential role in the performance of future Rydberg-EIT-based nonlinear optical quantum devices.In this Letter, we address these outstanding questions and develop a theory for the dissipative many-body dynamics of quantized light fields in a strongly interacting medium. In contrast to earlier studies [13,21], our theory provides information about the many-body density matrix of the light field; i.e., it faithfully describes the process of populating the m-photon states from the (m þ 1)-photon manifold as a photon scatters. In addition to opening the door to the study of photonic dissipative many-body physics, the theory allows one to compute the complex spatiotemporal structure of the generated nonclassical light fields, whose understanding is crucial for applications. As two important examples that illustrate this point and evince the power of our method, we consider the recently demonstrated single-photon filter [13,21] and the recently proposed single-photon subtractor [26]. In the limit of strong interactions, our approach yields exact solutions to the dissipative ...

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“…In particular, the formalism of noncovariant quantum electrodynamics, commonly known as molecular QED [43][44][45], is adopted, as the system to be studied consists of matter possessing nonrelativistic energies. This contrasts with techniques commonly employed in studying down-conversion [46], where systems are studied using effective Hamiltonians which cast the material response in classical terms. A key advantage of QED methods is that it gives a microscopic description of the matter, including the explicit form of electrodynamic coupling between atoms or molecules.…”

Section: Theoretical Foundationmentioning

confidence: 99%

Quantum delocalization in photon-pair generation

et al. 2017

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The generation of correlated photon pairs is a key to the production of entangled quantum states, which have a variety of applications within the area of quantum information. In spontaneous parametric down-conversion-the primary method of generating correlated photon pairs-the associated photon annihilation and creation events are generally thought of as being colocated: The correlated pair of photons is localized with regards to the pump photon and its positional origin. A detailed quantum electrodynamical analysis highlights a mechanism exhibiting the possibility of a delocalized origin for paired output photons: The spatial extent of the region from which the pair is generated can be much larger than previously thought. The theory of both localized and nonlocalized degenerate down-conversion is presented, followed by a quantitative analysis using discrete-volume computational methods. The results may have significant implications for quantum information and imaging applications, and the design of nonlinear optical metamaterials.

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An introduction to the quantum theory of nonlinear optics

Cited by 39 publications

References 57 publications

Coherently stimulated parametric down-conversion, phase effects, and quantum-optical interferometry

Coherently stimulated parametric down-conversion, phase effects, and quantum-optical interferometry

Dissipative Many-Body Quantum Optics in Rydberg Media

Quantum delocalization in photon-pair generation

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