Imaging of spatial correlations of two-photon states

Bobrov, I. B.; Kalashnikov, Dmitry; Krivitsky, Leonid A.

doi:10.1103/physreva.89.043814

Cited by 7 publications

(12 citation statements)

References 34 publications

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“…The p soc (k 1 , k 2 ) map constitutes a distinct contribution to the total second-order momentum correlation maps, exhibiting a general form of a cosine-square quantum beat on the difference of the two momenta with fringes parallel to the main diagonal of the maps. Furthermore, we demonstrate that the NOON component of the two-atom wave function generates another distinct contribution to the total second-order momentum correlation maps exhibiting a general form of a sinusoidal quantum beat on the sum of the two particle momenta with fringes parallel to the antidiagonal of the maps; this behavior is in agreement with the findings from recent double-slit biphoton quantum-optics experiments [49][50][51][52].…”

Section: B Hong-ou-mandel and Other Interference Phenomenasupporting

confidence: 89%

“…Finally, we drew attention to analogies of the secondorder momentum correlations for two ultracold atoms trapped in a double well with the total coincidence measurements performed in most recent double-slit biphoton quantum-optics experiments [49][50][51][52] which, in addition to the EPR-Bell-Bohm component, include also a doubleoccupancy NOON component in the prepared biphoton state.…”

Section: Discussionmentioning

confidence: 99%

“…As a result, beyond the P 2 (x 1 , x 2 ) [p soc (k 1 , k 2 ) ∝ cos 2 (d(k 1 − k 2 ))] pattern with fringes parallel to the main diagonal, some of the interferograms considered in Refs. [49][50][51][52]79] correspond to additional terms in our Eq. (24); namely, they exhibit fringes along the antidiagonal or even plaid patterns.…”

Section: Similarities and Differences With The Biphoton Of Quantumentioning

confidence: 99%

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Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry

2019

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Aiming at elucidating similarities and differences between quantum-optics biphoton interference phenomena and the quantum physics of quasi-one-dimensional double-well optically-trapped ultracold neutral bosonic or fermionic atoms, we show that the analog of the optical biphoton jointcoincidence spectral correlations, studied with massless non-interacting biphotons emanating from EPR-Bell-Bohm single-occupancy sources, corresponds to a distinct contribution in the total secondorder momentum correlations of the massive, interacting, and time-evolving ultracold atoms. This single-occupancy contribution can be extracted from the total second-order momentum correlation function measured in time-of-flight experiments, which for the trapped atomic system contains, in general, a double-occupancy, NOON, component. The dynamics of the two-particle system are modeled by a Hubbard Hamiltonian. The general form of this partial coincidence spectrum is a cosine-square quantum beating dependent on the difference of the momenta of the two particles, while the corresponding coincidence probability proper, familiar from its role in describing the Hong-Ou-Mandel coincidence dip of overlapping photons, results from an integration over the particle momenta. Because the second-order momentum correlations are mirrored in the time-of-flight spectra in space, our theoretical findings provide impetus for time-of-flight experimental protocols for emulating with (massive) ultracold atoms venerable optical interferometries that use two space-time separated and entangled (massless) photons or double-slit optical sources. The implementation of such developments will facilitate testing of fundamental aspects and enable applications of quantum physics with trapped massive ultracold atoms, that is, investigations of nonlocality and violation of Bell inequalities, entanglement, and quantum information science. arXiv:1812.05977v2 [cond-mat.quant-gas]

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Section: B Hong-ou-mandel and Other Interference Phenomenasupporting

confidence: 89%

Section: Discussionmentioning

confidence: 99%

Section: Similarities and Differences With The Biphoton Of Quantumentioning

confidence: 99%

See 1 more Smart Citation

Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry

2019

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“…The standard deviations values are propagated according to Eqs. (3,6) for calculation of corresponding error bars for the crosstalk probability and . The curve is fitted by Eq.…”

Section: Assessing Photon Bunching With Mppcmentioning

confidence: 99%

Measurement of photon correlations with multipixel photon counters

Kalashnikov

Krivitsky

2014

J. Opt. Soc. Am. B

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Development of reliable photon number resolving detectors (PNRD), devices which are capable to distinguish 1,2,3.. photons, is of a great importance for quantum optics and its applications. A new class of affordable PNRD is based on multipixel photon counters (MPPC). Here we review results of experiments on using MPPCs for direct characterization of squeezed vacuum (SV) states, generated via parametric downconversion (PDC). We use MPPCs to measure the second order normalized intensity correlation function ( ) and directly detect the two-mode squeezing of SV states. We also present a method of calibration of crosstalk probability in MPPCs based on measurements of coherent states.

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“…To do so, we fabricated J x -arrays involving N ¼ 8 channels. The importance of exploring FTs of such states has been highlighted in several investigations, demonstrating interesting effects such as suppression of states and portraying biphoton spatial correlations [24][25][26] .…”

Section: à ámentioning

confidence: 99%

Implementation of Quantum and Classical Discrete Fractional Fourier Transforms

Pérez-Leija

Weimann

Lebugle

et al. 2015

Frontiers in Optics 2015

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Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

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Imaging of spatial correlations of two-photon states

Cited by 7 publications

References 34 publications

Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry

Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry

Measurement of photon correlations with multipixel photon counters

Implementation of Quantum and Classical Discrete Fractional Fourier Transforms

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