Quantum phase-sensitive diffraction and imaging using entangled photons

Abstract

We propose a novel quantum diffraction imaging technique whereby one photon of an entangled pair is diffracted off a sample and detected in coincidence with its twin. The image is obtained by scanning the photon that did not interact with matter. We show that when a dynamical quantum system interacts with an external field, the phase information is imprinted in the state of the field in a detectable way. The contribution to the signal from photons that interact with the sample scales as ∝ I 1/2 p , where Ip is the source intensity, compared to ∝ Ip of classical diffraction. This makes imaging with weak-field possible, avoiding damage to delicate samples. A Schmidt decomposition of the state of the field can be used for image enhancement by reweighting the Schmidt modes contributions.Rapid advances in short-wavelength ultrafast light sources, have revolutionized our ability to observe the microscopic world. With bright Free Electron Lasers and high harmonics tabletop sources, short time (femtosecond) and length (subnanometer) scales become accessible experimentally. These offer new exciting possibilities to study spatio-spectral properties of quantum systems driven out of equilibrium, and monitor dynamical relaxation processes and chemical reactions. The spatial features of small-scale charge distributions can be recorded in time. Far-field off-resonant X-ray diffraction measurements provide useful information on the charge density σ (Q) where Q is the diffraction wavector. The observed diffraction pattern S (Q) is given by the modulus square S (Q) ∝ |σ (Q)| 2 . Inverting these signals to real-space σ (r) requires a Fourier transform. Since the phase of σ (Q) is not available, the inversion requires phase retrieval which can be done using either algorithmic solutions [1,2] or more sophisticated and costly experimental setups such as heterodyne measurements [3]. Correlated beam techniques [4][5][6][7][8][9][10] in the visible regime, have been shown to circumvent this problem by producing the realspace image of mesoscopic objects. Such techniques have classical analogues using correlated light, and reveal the modulus square of the studied object |σ (r)| 2 [11,12]. In this paper we consider the setup shown in Fig.(1). We focus on off-resonant scattering of entangled photons in which only one photon, denoted as the "signal", interacts with a sample. Its entangled counterpart, the "idler", is spatially scanned and measured in coincidence with the arrival of the signal photon. The idler reveals the image and also uncovers phase information, as was recently shown in [13] for linear diffraction.Our first main result is that for small diffraction angles, using Schmidt decomposition of the two-photon amplitude Φ (q s , q i ) = ∞ n √ λ n u n (q s ) v n (q i ) where λ n is the respective mode weight -reads,Here β(1) nm = dr u n (r) σ (r) u * m (r), β(2) nm = dr u n (r) |σ (r)| 2 u * m (r) andρ i represents the transverse detection plane. σ (r) is the charge density of the target object prepared by an actinic pulse and p = (1...

Hong-Ou-Mandel interferometry and spectroscopy using entangled photons

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Measurement of Entropy and Quantum Coherence Properties of Two Type-I Entangled Photonic Qubits

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“…[3]). Among these one can remark, for example, EPR realization [4], the entanglement generation [5,6], quantum state teleportation [7], quantum ellipsometry [8,9], quantum illumination [10][11][12][13][14][15][16][17], quantum spectroscopy [18][19][20][21], squeezing generation [22], quantum imaging [23][24][25][26][27], quantum communication [28][29][30][31][32][33][34][35][36][37], nonlocal realism tests [4,[38][39][40][41][42].…”

Flux-Conserving Diagrammatic Formulation of Optical Spectroscopy of Open Quantum Systems

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