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arXiv:1807.05717 · Physical Review A

Three-dimensional classical imaging of a pattern localized in a phase space

Mandip Singh, Samridhi Gambhir

Published Nov 19, 2018• 2 citations
arXivHTMLPDF

Abstract

In most imaging experiments, the structure of an object is defined in a position space. Such a structural pattern can be stationary, or for a dynamic object it can be nonstationary with time. An image of such an optically responsive object can be produced with a lens, therefore such an object can be seen with a camera or by the human eye. In this paper, we go beyond the conventional notion of imaging. A structural pattern of objects in our experiment is defined in a phase space, therefore such a pattern cannot be imaged with a lens or a camera, and the human eye cannot visualize it. A pattern in phase space is produced from object transparencies and imprinted onto the phase space of an atomic gaseous medium of a Doppler-broadened absorption profile at room temperature by utilizing velocity-selective hole burning in the absorption profile. The pattern is localized in a unique three-dimensional phase space, which is a subspace of the six-dimensional phase space. Tomographic images of the localized phase-space pattern are captured at different momentum locations by a laser light that has never interacted with actual objects. In addition, imaging of an imprinted phase-space pattern of an object of nonuniform transmittance is presented.

DOI
10.1103/physreva.98.053828

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In most imaging experiments, the structure of an object is defined in a position space. Such a structural pattern can be stationary, or for a dynamic object it can be nonstationary with time. An image of such an optically responsive object can be produced with a lens, therefore such an object can be seen with a camera or by the human eye. In this paper, we go beyond the conventional notion of imaging. A structural pattern of objects in our experiment is defined in a phase space, therefore such a pattern cannot be imaged with a lens or a camera, and the human eye cannot visualize it. A pattern in phase space is produced from object transparencies and imprinted onto the phase space of an atomic gaseous medium of a Doppler-broadened absorption profile at room temperature by utilizing velocity-selective hole burning in the absorption profile. The pattern is localized in a unique three-dimensional phase space, which is a subspace of the six-dimensional phase space. Tomographic images of the localized phase-space pattern are captured at different momentum locations by a laser light that has never interacted with actual objects. In addition, imaging of an imprinted phase-space pattern of an object of nonuniform transmittance is presented.
A transparent polarisation-sensitive phase pattern changes the phase of transmitted light without absorption, whereas this change of phase depends on the polarisation of incident light. A position-localised polarisation-dependent phase pattern is imprinted onto the phase-space of atoms by using atomic state dependent velocity-selective hole burning. A phase-space localised pattern is a higher dimensional generalisation of patterns localised in the position-space. Such a pattern cannot be imaged with a lens. The imprinted pattern is localised in a unique three-dimensional subspace of the six-dimensional phase-space of atoms. The phase-space localised pattern transforms the polarisation of light transmitting through it. This pattern is tomographically imaged at room temperature by measuring the intensity of the transmitted imaging laser beam of variable frequency with a camera after its polarisation analysis. Two sub-tomographs of the imprinted phase-space localised pattern are constructed. This paper presents a concept and experiment of imprinting and imaging of a polarisation-sensitive phase pattern localised in the phase-space.
Experimental results on phase-space imaging of a laser- cooled atomic cloud are presented. Both position and velocity information are encoded in the frequency of the signal coherently radiated from the cloud. This encoding is achieved by application of a position-dependent magnetic field. Fourier transformation of the signal yields a projection of the phase-space density of the atoms. Imprinting a structure on the cloud we observe its time `sheering' evolution in the phase-space. Since the projection direction is determined by the imposed field gradient, we can reconstruct the phase-space structure of the cloud.
We obtained the phase and intensity images of an object by detecting classical light which never interacted with it. With a double passage of a pump and a signal laser beams through a nonlinear crystal, we observe interference between the two idler beams produced by stimulated parametric down conversion. The object is placed in the amplified signal beam after its first passage through the crystal and the image is observed in the interference of the generated idler beams. High contrast images can be obtained even for objects with small transmittance coefficient due to the geometry of the interferometer and to the stimulated parametric emission. Like its quantum counterpart, this three-color imaging concept can be useful when the object must be probed with light at a wavelength for which detectors are not available.
A transparent polarisation sensitive phase pattern exhibits a position and polarisation dependent phase shift of transmitted light and it represents a unitary transformation. A quantum ghost image of this pattern is produced with hyper-entangled photons consisting of Einstein-Podolsky-Rosen (EPR) and polarisation entanglement. In quantum ghost imaging, a single photon interacts with the pattern and is detected by a stationary detector and a non-interacting photon is imaged on a coincidence camera. EPR entanglement manifests spatial correlations between an object plane and a ghost image plane, whereas a polarisation dependent phase shift exhibited by the pattern is detected with polarisation entanglement. In this quantum ghost imaging, the which-position-polarisation information of a photon interacting with the pattern is not present in the experiment. A quantum ghost image is constructed by measuring correlations of the polarisation-momentum of an interacting photon with polarisation-position of a non-interacting photon. The experiment is performed with a coincidence single photon detection camera, where a non-interacting photon travels a long optical path length of 17.83 m from source to camera and a pattern is positioned at an optical distance of 19.16 m from the camera.
“Ghost” imaging is a process utilizing entangled photon pairs, by which an image is produced indirectly, using photons that have never interacted with the object being imaged. We can do this by taking advantage of correlations inherent in Spontaneous Parametric Down Conversion (SPDC), which is used to produce these entangled photon pairs. SPDC is a classically forbidden process in which a photon of a high frequency is converted into a pair of photons. The change in frequency makes this a nonlinear process. Processes like absorption, reflection, refraction, and polarization are linear processes. These can affect the properties of a light field but cannot change the frequency. SPDC allows us to produce a pair of correlated photons. By utilizing a coincidence-counter, we will be able to measure photon pairs from the source beam arriving within a narrow time interval. With this restriction, we can limit our attention to these correlated photons. One of these photons, which does interact with the object to be imaged, is used to turn on a “camera” detecting the other photon. It is the correlations between these photons that allow for ghost imaging, the reconstruction of the image of an object, even though the object never interacts directly with those single photons that are going to our camera.