Quantum Ghost Research Articles

Experimental Limits of Ghost Diffraction: Popper\u2019s Thought Experiment

Quantum ghost diffraction harnesses quantum correlations to record diffraction or interference features using photons that have never interacted with the diffractive element. By designing an optical system in which the diffraction pattern can be produced by double slits of variable width either through a conventional diffraction scheme or a ghost diffraction scheme, we can explore the transition between the case where ghost diffraction behaves as conventional diffraction and the case where it does not. For conventional diffraction the angular extent increases as the scale of the diffracting object is reduced. By contrast, we show that no matter how small the scale of the diffracting object, the angular extent of the ghost diffraction is limited (by the transverse extent of the spatial correlations between beams). Our study is an experimental realisation of Popper’s thought experiment on the validity of the Copenhagen interpretation of quantum mechanics. We discuss the implication of our results in this context and explain that it is compatible with, but not proof of, the Copenhagen interpretation.

The “Paradox” of Karl Popper and Its Connection with the Heisenberg Uncertainty Principle and Quantum Ghost Images

An experiment to verify the adequacy of the Heisenberg uncertainty principle, as proposed by Karl Popper and implemented in practice, is considered. As in the Einstein–Podolsky–Rosen paradox, the quantum properties of an entangled pair of elementary particles are used. In this case, a ghost image of a narrow slit is actually formed. The results of the experiment, at first glance, support a violation of the uncertainty principle. However, analysis of the spatial resolution of the slit ghost image shows that this is not correct. A more correct description of diffraction in the case of spatially limited light beams, gives no violation of the uncertainty principle. The results can be also used to estimate the extreme quality of diffraction limited ghost images.

Complementary Normalized Compressive Ghost Imaging With Entangled Photons

We demonstrate a compressive normalized ghost imaging system with entangled photons employing complementary compressive imaging (CCI) technique. The quantum ghost image reconstruction was achieved with 19.53% sampling ratio of raster scanning and average 0.78 photons/pixel of each measurement. Using the special +1/−1 type sensing matrix and appropriate optimal algorithm, the photon utilization efficiency, and robustness of the imaging system is enhanced significantly. Our results reveal the great potential of CCI technique applied in quantum imaging and other quantum optics field such as quantum characterizing and quantum state tomography to use the information loaded in each photon with high efficiency.

Resolution limits of quantum ghost imaging.

Quantum ghost imaging uses photon pairs produced from parametric downconversion to enable an alternative method of image acquisition. Information from either one of the photons does not yield an image, but an image can be obtained by harnessing the correlations between them. Here we present an examination of the resolution limits of such ghost imaging systems. In both conventional imaging and quantum ghost imaging the resolution of the image is limited by the point-spread function of the optics associated with the spatially resolving detector. However, whereas in conventional imaging systems the resolution is limited only by this point spread function, in ghost imaging we show that the resolution can be further degraded by reducing the strength of the spatial correlations inherent in the downconversion process.

Entangled-photons compressive ghost imaging based on spatial correlation of sensing matrix

Using the entangled photons generated by the spontaneous parametric down conversion as a light source, we demonstrate the first quantum ghost imaging system with a modified compressive sensing technique based on the spatial correlation of sensing matrix (SCCS). The ghost image is achieved at 16.27% sampling ratio of raster scanning and 0.65 photons/pixel at each measurement on average. Our results show that image quality and photon-utilization efficiency are remarkably enhanced in comparison with the traditional compressive imaging technique, due to the sensing matrix and noise-free measurement vector rebuilt by SCCS technique. It suggests the great potential of SCCS technique applied in quantum imaging and other quantum optics fields, such as quantum charactering and quantum state tomography to use the information loaded in each photon with high efficiency.

Ghost Imaging Using Optical Correlations

AbstractGhost imaging uses optical correlations to enable an alternative and intriguing image acquisition technique: even though information from either one of the detectors used for the acquisition does not yield an image, an image can be obtained by harnessing the optical correlations. This Review describes a variety of both quantum and classical ghost imaging techniques, and seeks to point out where these techniques may have practical applications.

Improvement of the optical image reconstruction based on multiplexed quantum ghost images

Ghost imaging allows one to obtain information on an object from the spatial correlation function between photons propagating through or reflected from the object and photons of the reference arm. In this case, detection in the object arm is performed over the entire aperture of the beam and, therefore, it does not give information on the object. The reference beam does not interact with the object, but is recorded with a scanning point detector or a CCD array permitting the measurement of the spatial correlation function of photons in two arms. The use of multimode entangled quantum light beams by illuminating the object by one beam and orienting other beams to reference arms makes it possible to obtain simultaneously several ghost images (GIs). Cross correlations of multiplexed GIs (MGIs) are determined by eighth-order field correlation functions. A special algorithm is developed for calculating higher-order correlations of Bose operators. The presence of GI cross correlations is used for improving the quality of the reconstructed object’s image by their processing using the measurement reduction method. An example of the computer simulation of the image reconstruction by MGIs formed in the field of four-frequency entangled quantum states is considered. It is found that in this case the reduced GI has a signal-to-noise ratio several times higher than that of GIs.

Digital spiral-slit for bi-photon imaging

Quantum ghost imaging using entangled photon pairs has become a popular field of investigation, highlighting the quantum correlation between the photon pairs. We introduce a technique using spatial light modulators encoded with digital holograms to recover both the amplitude and the phase of the digital object. Down-converted photon pairs are entangled in the orbital angular momentum basis, and are commonly measured using spiral phase holograms. Consequently, by encoding a spiral ring-slit hologram into the idler arm, and varying it radially we can simultaneously recover the phase and amplitude of the object in question. We demonstrate that a good correlation between the encoded field function and the reconstructed images exists.

Correlations of Multiplexed Quantum Ghost Images and Improvement of the Quality of Restored Image

The currently used ghost image schemes traditionally involve two-mode entangled light states or incoherent radiation. Here, application of four-mode entangled light states is considered. It is shown that multiplexed ghost images (MGI) formed by four-mode entangled quantum light states have mutual spatial correlations determined by the 8th order field correlation functions. A special algorithm to calculate high-order correlations of Bose operators was developed. We also demonstrate that the accounting of MGI correlations allows us to improve the quality of the restored image of an object when processing MGI by measurement reduction method. Computer modelling of recovery of the image from MGI was carried out. It is established that in the considered example the signal-to-noise ratio of the reduced ghost image is $4.6$ times higher than the best signal-to-noise ratio for the ghost images themselves.

Einstein-Podolsky-Rosen Entanglement of Narrow-Band Photons from Cold Atoms

Einstein-Podolsky-Rosen (EPR) entanglement introduced in 1935 deals with two particles that are entangled in their positions and momenta. Here we report the first experimental demonstration of EPR position-momentum entanglement of narrow-band photon pairs generated from cold atoms. By using two-photon quantum ghost imaging and ghost interference, we demonstrate explicitly that the narrow-band photon pairs violate the separability criterion, confirming EPR entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons. Our new source of EPR-entangled narrow-band photons is expected to play an essential role in spatially multiplexed quantum information processing, such as, storage of quantum correlated images, quantum interface involving hyperentangled photons, etc.

Security against jamming and noise exclusion in imaging

We describe a protocol by which an imaging system could be protected against jamming by a malevolent party. Our protocol not only allows recognition of the jamming, but also allows for the recovery of the true image from the jammed one. We apply the method to jamming of quantum ghost imaging, for which the jamming detection probability is increased when the imaging light is entangled. The method can also be used to provide image recovery in general noisy environments.

Resolution of ghost imaging with entangled photons for different types of momentum correlation

We present an analytical analysis of the spatial resolution of quantum ghost imaging implemented by entangled photons from a general, spontaneously parametric, down-conversion process. We find that the resolution is affected by both the pump beam waist and the nonlinear crystal length. Hence, we determined a method to improve the resolution for a certain imaging setup. It should be noted that the resolution is not uniquely related to the degree of entanglement of the photon pair since the resolution can be optimized for a certain degree of entanglement. For certain types of Einstein-Podolsky-Rosen (EPR) states——namely the momentum-correlated or momentum-positively correlated states——the resolution exhibits a simpler relationship with the pump beam waist and crystal length. Further, a vivid numerical simulation of ghost imaging is presented for different types of EPR states, which supports our analysis. This work discusses applicable references to the applications of quantum ghost imaging.

Long-distance temporal quantum ghost imaging over optical fibers.

Since the first quantum ghost imaging (QGI) experiment in 1995, many QGI schemes have been put forward. However, the position-position or momentum-momentum correlation required in these QGI schemes cannot be distributed over optical fibers, which limits their large-scale geographical applications. In this paper, we propose and demonstrate a scheme for long-distance QGI utilizing frequency correlated photon pairs. In this scheme, the frequency correlation is transformed to the correlation between the illuminating position of one photon and the arrival time of the other photon, by which QGI can be realized in the time domain. Since frequency correlation can be preserved when the photon pairs are distributed over optical fibers, this scheme provides a way to realize long-distance QGI over large geographical scale. In the experiment, long-distance QGI over 50 km optical fibers has been demonstrated.

Grayscale object authentication based on ghost imaging using binary signals

In recent years, either quantum or classical ghost imaging has attracted much attention in many fields. Here, we report grayscale object authentication based on ghost imaging using binary signals. It is found that binary signals can be applied at reference and object beam arms, which provides a promising alternative to explore the potential of ghost imaging for some applications. Reducing the data size with only two quantization levels is beneficial to the storage and transmission. One numerical example, i.e., grayscale object authentication, is given to illustrate the feasibility of the proposed method, and it is highly expected that more studies can further explore the ghost imaging system using binary signals for other applications.

Cloaking and illusion of quantum imaging with entangled photon pairs

Quantum ghost imaging is a nonlocal imaging technique in which the image or diffraction pattern of an object illuminated by photon pairs can be observed through the correlation measurement. This study theoretically demonstrates the cloaking effect of such a quantum imaging. Quantum ghost imaging completely offsets two objects that are placed at proper positions in the interferometer. Furthermore, illusion of quantum imaging, where an object transforms into another object, has also been observed. This phenomenon can be understood by quantum interferences in the correlation measurement.

Standoff two-color quantum ghost imaging through turbulence.

Recently, a two-color quantum ghost imaging configuration was proposed by Karmakar et al. [Phys. Rev. A81, 033845 (2010)]. By illuminating an object located far away from the source and detector, with a signal beam of long wavelength to avoid absorption of short wavelengths in the atmosphere while a reference beam of short wavelength is detected locally, this imaging configuration can be appropriate for standoff sensing. In practice, the signal beam must propagate through atmosphere in the presence of serious turbulence. We analyzed theoretically the performance of this ghost imaging configuration through turbulence. Based on the Gaussian state source model and extended Huygens-Fresnel integral, a formula is derived to depict the ghost image formed through turbulence of a standoff reflective object. Numerical calculations are also given according to the formula. The results show that the image quality will be degraded by the turbulence, but the resolution can be improved by means of optimizing the wavelengths of the reference and signal beams even when the turbulence is very serious.

Color of ghost imaging

In this paper, we investigate the color of ghost imaging with thermal and quantum sources. We find that the color of ghost imaging is a composite color that depends on the object and reference fields, which is different from the classical optical imaging. Furthermore, we find that the color of ghost image can be different from the color of the light interacted with the object, which is not achieved in the classic optical imaging. Generally, we can only obtain the monochromatic ghost image by the quantum ghost imaging, while the monochromatic and color ghost image can be obtained by the ghost imaging with thermal source.

Generation of positively-momentum-correlated biphotons from spontaneous parametric down-conversion

We propose to generate a counter-Einstein-Podolsky-Rosen (CEPR) state which possesses a positively-correlated momentum and anticorrelated position directly from spontaneous parametric down-conversion. The general CEPR state is given under a tightly focused Gaussian pump based on type II noncritical phase matching. We analytically and numerically study how a positively-correlated momentum and anticorrelated position of a biphoton can be achieved by choosing the proper focal parameter of the pump. To verify the degree of entanglement of the CEPR state, we calculate its entanglement entropy and it shows a unique dependence on the pump's focal parameter. Suggestions for practical engineering of the state are also given. Furthermore, based on an ideal CEPR state, we deduce a type of erect quantum ghost imaging which can be applied as the entanglement criterion. This work gives applicable references to the spatial control of an entangled photon source in experiments and may stimulate the development of new types of quantum technologies.

Lensless imaging by entangled photons from quadratic nonlinear photonic crystals

Lenses play a key role in quantum imaging but inevitably constrain the spatial resolution and working wavelength. In this work we develop and demonstrate a lensless quantum ghost imaging by engineering quadratic nonlinear photonic crystals. With a transverse parabolic domain modulation introduced into the lithium tantalate crystal, the entangled photon pairs generated from parametric down-conversion will self-focus. Therefore we can dispense with additional lenses to construct imaging in a nonlocal way. The lensless imaging is found to follow a specific imaging formula where the effective focal length is determined by the domain modulation and pump wavelength. Additionally, two nonlocal images can be retrieved when the entangled photon pair is generated under two concurrent noncollinear phase-matching geometries. Our work provides a principle and method to realize lensless ghost imaging, which may be extended to other wavelengths and stimulate new types of practical quantum technologies.

Entangled-photon compressive ghost imaging

We have experimentally demonstrated high-resolution compressive ghost imaging at the single-photon level using entangled photons produced by a spontaneous parametric down-conversion source and using single-pixel detectors. For a given mean-squared error, the number of photons needed to reconstruct a two-dimensional image is found to be much smaller than that in quantum ghost imaging experiments employing a raster scan. This procedure not only shortens the data acquisition time, but also suggests a more economical use of photons for low-light-level and quantum image formation.