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Physical Review A

Robust holography of the temporal wave function via second-order interference

Yao-Kun Xu, Shi‐Hai Sun, Wei-Tao Liu, Jiying Liu, Ping‐Xing Chen

Published Oct 17, 2019• 4 citations
Publisher

Abstract

Containing the capacity to record both amplitude and phase information of the light field, holography is of great importance in science and technology. Here, we present robust holography via second-order interference, considering both single-photon states and coherent states. Temporal amplitude and phase distribution carried by a weak coherent state are reconstructed experimentally. By comparison between holography using first-order interference and second-order interference, the robustness against phase noise of our method is verified. Besides, information about the state can be directly retrieved, with no complex algorithm required.

DOI
10.1103/physreva.100.042317

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Containing the capacity to record both amplitude and phase information of the light field, holography is of great importance in science and technology. Here, we present robust holography via second-order interference, considering both single-photon states and coherent states. Temporal amplitude and phase distribution carried by a weak coherent state are reconstructed experimentally. By comparison between holography using first-order interference and second-order interference, the robustness against phase noise of our method is verified. Besides, information about the state can be directly retrieved, with no complex algorithm required.
As a kind of quantum phenomenon, Hong-Ou-Mandel (HOM) interference is more robust against phase noise. Due to this feature, robust quantum holography emerges, through which wave function of interested photon can be retrieved according to HOM interference pattern. For better understanding and developing this method, we derive a theoretical framework of robust HOM holography. In quantum holography scheme, test state and reference state interfere at beam splitter (BS). Then, degree of freedom (DOF) resolved detections (such as spatial resolved detection, temporal resolved detection or spectrum resolved detection) are applied at the BS output ports, respectively. Based on the single photon detection results, the DOF resolved coincidence counts are postselected, producing interference patterns. The information of the test states is retrieved from the patterns. According to different test states and reference states, four combinations are analysed, including measuring the wave function of single photon state using standard single photon state or coherent state and measuring the wave function of coherent state using standard single photon state or coherent state. In all cases, information of the test states is reflected in normalized second-order correlation function or interference patterns in similar forms. Specially, the wave function of test states can be directly retrieved from the interference patterns, with no complex algorithm required. Besides, phase noise from environment has no influence on this kind quantum holography. Comparison between traditional holography and quantum holography is analysed.
As a kind of quantum phenomenon, Hong-Ou-Mandel (HOM) interference is more robust against phase noise. Because of this feature, robust quantum holography emerges, through which wave function of interested photon can be retrieved according to HOM interference pattern. For better understanding and developing this method, we derive a theoretical framework of robust HOM holography. In the quantum holography scheme, test state and reference state interfere at beam splitter (BS). Then, degree of freedom (DOF) resolved detections (such as spatial resolved detection, temporal resolved detection or spectrum resolved detection) are used at the BS output ports, respectively. Based on the single photon detection results, the DOF resolved coincidence counts are postselected, producing interference patterns. The information of the test states is retrieved from the patterns. According to different test states and reference states, four combinations are analysed, including measuring the wave function of single photon state by using standard single photon state or coherent state and measuring the wave function of coherent state through using standard single photon state or coherent state. In all cases, information of the test states is reflected in normalized second-order correlation function or interference patterns in similar forms. Specially, the wave function of test states can be directly retrieved from the interference patterns, with no complex algorithm required. Besides, phase noise from environment has no influence on this kind quantum holography. Comparison between traditional holography and quantum holography is made and analysed.
The retrieval of the phase with single-photon states is a fundamentally and technically challenging endeavor. Here we report an experimental realization of hologram recordings with heralded single-photon illumination and continuous observation of photon statistics. Thereby, we demonstrate the basic principle of holography with single-photon states which cannot be described with the classical wave theory. Under conditions with illumination more than 200 times weaker than the noise of the detector, a hologram (interferogram) recorded with a heralded single-photon source revealed an object not visible with nonheralded illumination and slightly higher intensity. The dramatic improvement in retrieval of amplitude and phase information achieved with the heralded single-photon source can be explained by the strong suppression of noise due to the nonclassical temporal correlation between twin photons and the small coincidence time window. The method could be useful for recording and retrieving amplitude and phase information in the presence of strong noise, for covert imaging, and for imaging of photosensitive biological and material samples.
Holography exploits the interference of a light field reflected/transmitted from an object with a reference beam to obtain a reconstruction of the spatial shape of the object. Classical holography techniques have been very successful in diverse areas such as microscopy, manufacturing technology, and basic science. However, detection constraints for wavelengths outside the visible range restrict the applications for imaging and sensing in general. For overcoming these detection limitations, we implement phase-shifting holography with nonclassical states of light, where we exploit quantum interference between two-photon probability amplitudes in a nonlinear interferometer. We demonstrate that it allows retrieving the spatial shape (amplitude and phase) of the photons transmitted/reflected from the object and thus obtaining an image of the object despite those photons are never detected. Moreover, there is no need to use a well-characterized reference beam, since the two-photon scheme already makes use of one of the photons as reference for holography.
We analyze and further develop our method of quantum-state holography for reconstructing quantum superposition states in molecules or atoms [Phys. Rev. Lett. 80, 1418 (1998)]. The technique is based on mixing the unknown object state with a known reference state generated in the same system by two delayed laser pulses, and detecting the total time- and frequency-integrated fluorescence as a function of the delay. The feasibility of the method is demonstrated by reconstructing various vibrational wave packets in sodium dimers. Both the cases of completely controlled and noisy relative phase between the laser pulses are considered. In the latter case, we use the technique of coherence observation by interference noise to recover the interference component of the fluorescence signal. Our results clearly demonstrate the robustness of quantum-state holography and the high quality of reconstruction even in the presence of the external noise.
The time-energy entanglement of down-converted photon pairs is particularly difficult to characterize because direct measurements of photon arrival times are limited by the temporal resolution of photon detection. Here, we explore an alternative possibility of characterizing the temporal coherence of two-photon wave functions using single-photon interference with weak coherent light. Specifically, this method makes use of the fact that down conversion generates a coherent superposition of vacuum and two-photon states, so that the coincidence count rates for photon pairs after interference with weak coherent light are given by a superposition of the two-photon wave function from the down conversion with the product wave function defined by the weak coherent references. By observing the frequency-dependent interference pattern, it is possible to reconstruct the amplitudes and the phases of the two-photon wave function within the bandwidth of the reference pulses used in the single-photon interferences. The correlated single-photon interferences therefore provide a direct map of the entangled two-photon wave function generated in the down-conversion process.