Time-frequency duality plays a pivotal role in modern optical science and engineering. Conventional duality, which is connected by one-dimensional Fourier transformation, is insufficient for characterizing quantum mechanical correlations in the time-frequency behavior of multiple photons; a higher-dimensional treatment is required. The authors directly measure the two-photon distributions of generated biphotons in both frequency and time domains, and show that they satisfy the Fourier-limited condition in two-dimensional time and frequency space, but not in conventional one-dimensional space. This study helps to pave the way to tomorrow's quantum optical technologies.
Time-frequency duality plays a pivotal role in modern optical science and engineering. Conventional duality, which is connected by one-dimensional Fourier transformation, is insufficient for characterizing quantum mechanical correlations in the time-frequency behavior of multiple photons; a higher-dimensional treatment is required. The authors directly measure the two-photon distributions of generated biphotons in both frequency and time domains, and show that they satisfy the Fourier-limited condition in two-dimensional time and frequency space, but not in conventional one-dimensional space. This study helps to pave the way to tomorrow's quantum optical technologies.
Conventional optical synthesis, the manipulation of the phase and amplitude of spectral components to produce an optical pulse in different temporal modes, is revolutionizing ultrafast optical science and metrology. These technologies rely on the Fourier transform of light fields between time and frequency domains in one-dimensional space. However, within this treatment, it is impossible to incorporate the quantum correlation among photons. Here, we expand the Fourier synthesis into high-dimensional space to deal with the quantum correlation and carry out an experimental demonstration by manipulating the two-photon probability distribution of a biphoton in two-dimensional time and frequency space. As a potential application, we show the manipulation of a heralded single-photon wave packet, which is never explained by the conventional one-dimensional Fourier optics. Our approach opens up a new pathway to tailor the temporal characteristics of a photon wave packet with high-dimensional quantum-mechanical treatment. We anticipate that such high-dimensional treatment of light in time and frequency domains could bridge the research fields between quantum optics and ultrafast optical measurements.
The time-frequency duality of light is the fundamental concept for ultrafast laser science and technologies. Although the 1D Fourier transform connects electric field distributions between time and frequency domains, 1D treatment is insufficient for understanding the behavior of time-frequency entangled photons. Elucidation of the Fourier duality of entangled-photon wave packets is key for further development of quantum photonics in the ultrafast regime; unfortunately, it hasn’t yet been demonstrated. Here we present the duality as it appears in the frequency spectrum and the temporal shape of the entangled- photon wave packet with two-photon coincidence measurements in the time and frequency domains to extract two-photon time-frequency distributions. We also estimate the time-bandwidth product values in 2D time-frequency space to confirm the Fourier-limited conditions of the entangled-photon wave packets and discuss the prospects of ultrafast quantum optics with time-frequency entangled photons.
Precise manipulation of the time–frequency modes of entangled photons is crucial for future quantum science and technologies. Recently, the frequency-domain-quantum-optical-synthesis (FD-QOS) method was demonstrated by creating a superposition of different joint temporal amplitudes: those temporal distributions can be controlled by manipulating the joint spectral amplitude in 2D frequency space via a Fourier optical relation. This FD-QOS method provides an efficient, flexible, and easy-to-control way to precisely modulate the temporal distributions of the entangled photon in an ultrafast region. However, manipulation of only the temporal modes is not sufficient for various applications in quantum information, since spectral modulations are also needed on many occasions. Here, we present a proof-of-concept experiment of two-photon spectral modulation via temporal manipulation of a biphoton wave packet. This protocol, called time-domain-quantum-optical-synthesis (TD-QOS), is achieved by adjusting the relative phases between two joint temporal distributions. In addition, the two-photon joint spectral distributions are characterized by measuring the joint spectral intensities and Hong–Ou–Mandel interferences. The combination of FD-QOS and TD-QOS enables complete control over the biphoton states. Our work would further develop quantum technologies that rely on the time–frequency modes of entangled photons.
Quantum correlations of ultrafast quantum optical states in the time–frequency domain manifest prominently on femtosecond time scales, an elusive challenging regime. We develop a new method to probe the time–frequency mode structure of ultrafast two-photon states utilizing dual-comb-based asynchronously overlapping pulses with single-photon frequency upconversion through femtosecond optical sampling. This method enables quick, highly precise joint temporal intensity measurements over a broad temporal dynamic range with only a single linear scanning stage. We demonstrate full characterization of time–frequency entangled two-photon states in both time and frequency domains. We quantified the time–frequency mode structure in both time and frequency domains through Schmidt decomposition, resulting in temporal and spectral purities of 87.7% and 76.9%, respectively, for heralded single-photons without any spectral filtering. Furthermore, through the simple control of pump spectral bandwidth, we demonstrate the ability to tailor time–frequency entanglement, verifying the two-dimensional Fourier duality. This method paves the way for a substantial upgrade to ultrafast quantum optical techniques, enabling a rapid, detailed, and multi-dimensional characterization of entangled states with potential applications in quantum metrology and photon-deficient fluorescence imaging.
Time-frequency entangled photons ("biphotons") exhibit joint spectral and temporal correlations that are unattainable with classical light. Besides being deployed for tests of quantum nonlocality, these photonic states are desirable for a unique range of applications that can significantly impact communications and computation. In this dissertation, we describe novel schemes based on spectral and temporal domain processing for manipulating and characterizing broadband biphotons. Implementing frequency-dependent filters, first, we present and demonstrate a technique for controlling the relative delay between a pair of entangled photons, relying on pump frequency tuning and the quantum concept of nonlocal dispersion cancellation. Next, we demonstrate near-field frequency-to-time mapping, a technique adopted from classical photonics, for arbitrary control of biphoton temporal correlations. Subsequently, we generate temporal correlation trains by creating biphoton frequency combs through programmable spectral amplitude shaping and demonstrate the temporal Talbot effect with entangled photons for the first time. Moreover, in the absence of fast single-photon detectors, we show how electro-optic phase modulation (originally a time-dependent operation) can be used to examine the coherence of biphoton frequency combs. Lastly, we introduce a scheme based on electro-optic intensity modulation, another time-domain operation, for improving the resolution in biphoton temporal correlation measurements. Overall, our body of work could provide additional insight into the manipulation and characterization of biphoton states, as well as contribute towards the improvement of quantum technologies.
Arbitrary shaping of optical waveform is fundamental interest from basic science to advanced optical technologies. However, it is still challenging task for shaping a biphoton wave packet. Here we experimentally manipulate the spectrum and phase of a biphoton wave packet in a two-dimensional frequency space. The spectrum is shaped by adjusting the temperature of the crystal, and the phase is controlled by tilting the dispersive glass plate. The manipulating effects are confirmed by measuring the two-photon spectral intensity (TSI) and the Hong-Ou-Mandel (HOM) interference patterns. The technique in this work paves the way for arbitrary shaping of a multi-photon wave packet in a quantum manner.