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Physical Review A

Transverse correlations in triphoton entanglement: Geometrical and physical optics

Jianming Wen, Ping Xu, Morton H. Rubin, Yanhua H. Shih

Published Aug 30, 2007• 21 citations
Publisher

Abstract

The transverse correlation of triphoton entanglement generated within a single crystal is analyzed. Among many interesting features of the transverse correlation, they arise from the spectral function $F$ of the triphoton state produced in the parametric processes. One consequence of transverse effects of entangled states is quantum imaging, which is theoretically studied in photon counting measurements. Klyshko's two-photon advanced-wave picture is found to be applicable to the multiphoton entanglement with some modifications. We found that in the two-photon coincidence counting measurement by using triphoton entanglement, although the Gaussian thin lens equation (GTLE) holds, the imaging shown in coincidences is obscure and has a poor quality. This is because of tracing the remaining transverse modes in the untouched beam. In the triphoton imaging experiments, two kinds of cases have been examined. For the case that only one object with one thin lens is placed in the system, we found that the GTLE holds as expected in the triphoton coincidences and the effective distance between the lens and imaging plane is the parallel combination of two distances between the lens and two detectors weighted by wavelengths, which behaves as the parallel combination of resistors in the electromagnetism theory. Only in this case, a point-point correspondence for forming an image is well-accomplished. However, when two objects or two lenses are inserted in the system, though the GTLEs are well-satisfied, in general a point-point correspondence for imaging cannot be established. Under certain conditions, two blurred images may be observed in the coincidence counts. We have also studied the ghost interference-diffraction experiments by using double slits as apertures in triphoton entanglement. It was found that when two double slits are used in two optical beams, the interference-diffraction patterns show unusual features compared with the two-photon case. This unusual behavior is a destructive interference between two amplitudes for two photons crossing two double slits.

DOI
10.1103/physreva.76.023828

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We have analyzed the transverse correlation in multiphoton entanglement. The generalization of quantum ghost imaging is extended to the $N$-photon state. The Klyshko's two-photon advanced-wave picture is generalized to the $N$-photon case.

Physical Review A•Oct 23, 2007•9 citations
The transverse correlation of triphoton entanglement generated within a single crystal is analyzed. Among many interesting features of the transverse correlation, they arise from the spectral function FFF of the triphoton state produced in the parametric processes. One consequence of transverse effects of entangled states is quantum imaging, which is theoretically studied in photon counting measurements. Klyshko's two-photon advanced-wave picture is found to be applicable to the multiphoton entanglement with some modifications. We found that in the two-photon coincidence counting measurement by using triphoton entanglement, although the Gaussian thin lens equation (GTLE) holds, the imaging shown in coincidences is obscure and has a poor quality. This is because of tracing the remaining transverse modes in the untouched beam. In the triphoton imaging experiments, two kinds of cases have been examined. For the case that only one object with one thin lens is placed in the system, we found that the GTLE holds as expected in the triphoton coincidences and the effective distance between the lens and imaging plane is the parallel combination of two distances between the lens and two detectors weighted by wavelengths, which behaves as the parallel combination of resistors in the electromagnetism theory. Only in this case, a point-point correspondence for forming an image is well-accomplished. However, when two objects or two lenses are inserted in the system, though the GTLEs are well-satisfied, in general a point-point correspondence for imaging cannot be established. Under certain conditions, two blurred images may be observed in the coincidence counts. We have also studied the ghost interference-diffraction experiments by using double slits as apertures in triphoton entanglement. It was found that when two double slits are used in two optical beams, the interference-diffraction patterns show unusual features compared with the two-photon case. This unusual behavior is a destructive interference between two amplitudes for two photons crossing two double slits.
In recent years, quantum entanglement has attracted much; attention, because its unique properties provide potential; applications, which could not be achieved using conventional; techniques, such as quantum computing, quantum imaging and; lithography. To realize these advancements, one has to obtain an; entanglement-generation source, thoroughly master its physical; properties, and fully understand the light-matter interaction.; This dissertation is an attempt to address such issues as stated; above.; Conventionally, paired photons are created from; \textit{spontaneous parametric down-conversion} (SPDC). It is; known that the transverse correlation in biphotons may improve the; visibility and resolution in quantum imaging and lithography. In; this thesis, we described an alternative biphoton source --; Raman-EIT (\textit{electromagnetically induced transparency}); generator, and emphasize on its geometrical and optical; properties. We found that to utilize the transverse effects in; paired Stokes-anti-Stokes, it is necessary to make the product of; the EIT window times the group delay much greater than unity.; To gain further insight into quantum imaging and lithography, we; studied the transverse correlation in triphoton entanglement; theoretically. We found that in the two-image process, the quality; of images is determined by the optical path-lengths, even though; the Gaussian thin lens equations are satisfied. The ghost; interference-diffraction patterns of double slits show one more; fold interference, which is essentially different from the; biphoton case. Klyshko's advanced-wave model is still applicable,; with some modifications. We also generalized the transverse; correlation to the case of multi-photon entangled states.; To implement quantum computing, one key element is quantum memory.; In this thesis, we have theoretically explored the feasibility of; such a memory by using nonclassical SPDC light in an EIT system at; the single-photon level. We found that both the quantum coherence; of SPDC and atomic coherence of EIT can survive after interacting; within a vapor cell. Due to the inherent mismatch of magnitude; between the spectral bandwidth of SPDC and the very narrow; transmission width of EIT, the coincidence counts of the; two-photon interference is reduced to one pair per second, which; is barely doable in the current experimental situation.
One of the most surprising consequences of quantum mechanics is entanglement of two or more distance particles. The two-particle entangled state was mathematically formulated by Schrodinger. Based on this unusual quantum behavior, EPR defined their 'physical reality' and then asked the question: 'Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?' One may not appreciate EPR's criterion of physical reality and insist that 'no elementary quantum phenomenon is a phenomenon until it is a recorded phenomenon'. Optical spontaneous parametric down conversion (SPDC) is the most effective mechanism to generate an EPR type entangled two-photon state. In SPDC, an optical beam, called the pump, is incident on a birefringent crystal. The pump is intense enough so that nonlinear effects lead to the conversion of pump photons into pairs of photons, historically called signal and idler. Technically, the SPDC is said to be type-1 or type-2, depending on whether the signal and idler beams have parallel or orthogonal polarization. The SPDC conversion efficiency is typically on the order of 10(exp -9) to 10(exp -11), depending on the SPDC nonlinear material. The signal and idler intensities are extremely low, only single photon detection devices can register them. The quantum entanglement nature of SPDC has been demonstrated in EPR-Bohm experiments and Bell's inequality measurements. The following two experiments were recently performed in our laboratory, which are more closely related to the original 1935 EPR gedankenezperiment. The first experiment is a two-photon optical imaging type experiment, which has been named 'ghost image' by the physics community. The signal and idler beams of SPDC are sent in different directions, so that the detection of the signal and idler photons can be performed by two distant photon counting detectors. An aperture object (mask) is placed in front of the signal photon detector and illuminated by the signal beam through a convex lens. Surprisingly, an image of this aperture is observed in the idler beam, by scanning the idler photon detector in the transverse plane of the idler beam, if we are sure that the idler photon detector 'catches' the 'twin brother' of the signal, which can be easily performed by a coincidence measurement. This effect is even more striking when we found that the object-lens-image relationship satisfies the Gaussian thin lens equation. The second experiment demonstrates two-photon 'ghost' interference-diffraction. The experimental set up is similar to the image experiment, except that rather than a lens and an aperture it is a Young's double-slit (or a single-slit) inserted into the path of the signal beam. We could not find any interference (or diffraction) pattern behind the slit. Surprisingly, an interference (or diffraction) pattern is observed when scanning the detector in the idler beam, if we are sure that the idler photon detector 'catches' the 'twin brother' of the signal.
High-dimensional entanglement in the form of transverse spatial correlation between a pair of photons generated via spontaneous parametric downconversion is not only a valuable resource in many academic and real-life applications but also provides access to several intriguing quantum phenomena. One such non-intuitive phenomenon is phase entanglement, in which the biphoton state is correlated in the complex phase of its wavefunction. This state, which emerges during the propagation of the biphoton wavefunction, exhibits neither position nor momentum correlation, yet retains full entanglement. In this work, we experimentally explore this state in two distinct ways. The first is by tracking the vanishing spatial photon number correlation over propagation distances lying in [0,∞)\left[0,\infty\right)[0,∞), folded into a finite range using single-lens imaging. These observations show excellent agreement with our theoretical predictions based on the Double Gaussian (DG) approximation of the biphoton state. The second approach involves performing a two-photon interference experiment using a double slit and this state, which reveals the correlated phase front. We show, both theoretically and experimentally, that the observed two-photon interference structure is markedly different from that produced by position-correlated photons, as confirmed by computing the joint probability distribution of photons (JPD) and related metrics. Such interference using phase-entangled light has not been attempted before and opens avenues for advanced experiments and applications in the field of spatial entanglement.
We have analyzed the transverse correlation in multiphoton entanglement. The generalization of quantum ghost imaging is extended to the NNN-photon state. The Klyshko's two-photon advanced-wave picture is generalized to the NNN-photon case.