Direct Characterization of Ultrafast Energy-Time Entangled Photon Pairs

Effect of spectrum broadening on photon-counting fiber Bragg grating sensing

In a photon-counting fiber Bragg grating (FBG) sensing system, a shorter probe pulse width reaches a higher spatial resolution, which inevitably causes a spectrum broadening according to the Fourier transform theory, thus affecting the sensitivity of the sensing system. In this work, we investigate the effect of spectrum broadening on a photon-counting FBG sensing system with a dual-wavelength differential detection method. A theoretical model is developed, and a proof-of-principle experimental demonstration is realized. Our results give a numerical relationship between the sensitivity and spatial resolution at the different spectral widths of FBG. In our experiment, for a commercial FBG with a spectral width of 0.6 nm, an optimal spatial resolution of 3 mm and a corresponding sensitivity of 2.03 nm^-1 can be achieved.

Ultratunable Quantum Frequency Conversion in Photonic Crystal Fiber

Quantum frequency conversion of single photons between wavelength bands is a key enabler to realizing widespread quantum networks. We demonstrate the quantum frequency conversion of a heralded 1551 nm photon to any wavelength within an ultrabroad (1226-1408 nm) range in a group-velocity-symmetric photonic crystal fiber, covering over 150 independent frequency bins. The target wavelength is controlled by tuning only a single pump laser wavelength. We find internal, and total, conversion efficiencies of 12(1)% and 1.4(2)%, respectively. For the case of converting 1551 to 1300 nm we measure a heralded g^{(2)}(0)=0.25(6) for converted light from an input with g^{(2)}(0)=0.034(8). We expect that this photonic crystal fiber can be used for myriad quantum networking tasks.

Electro-Optic Fourier Transform Chronometry of Pulsed Quantum Light

The power spectrum of an optical field can be acquired without a spectrally resolving detector by means of Fourier-transform spectrometry, based on measuring the temporal autocorrelation of the optical field. Analogously, we here perform temporal envelope measurements of ultrashort optical pulses without time resolved detection. We introduce the technique of Fourier transform chronometry, where the temporal envelope is acquired by measuring the frequency autocorrelation of the optical field in a linear interferometer. We apply our technique, which is the time-frequency conjugate measurement to Fourier-transform spectrometry, to experimentally measure the pulse envelope of classical and single-photon light pulses.

Propagation-induced revival of entanglement in the angle-OAM bases

Although the continuous-variable position-momentum entanglement of photon pairs produced by parametric down-conversion has applicability in several quantum information applications, it is not suitable for applications involving long-distance propagation. This is because entanglement in the position-momentum bases, as seen through Einstein-Podolsky-Rosen (EPR)-correlation measurements, decays very rapidly with photons propagating away from the source. In contrast, in this article, we show that in the continuous-variable bases of angle-orbital angular momentum (OAM), the entanglement, as seen through EPR-correlation measurements, exhibits a remarkably different behavior. As with the position-momentum bases, initially, the entanglement in the angle-OAM bases also decays with propagation, and after a few centimeters of propagation, there is no angle-OAM entanglement left. However, as the photons continue to travel further away from the source, the entanglement in the angle-OAM bases revives. We theoretically and experimentally demonstrate this behavior and show that angle-OAM entanglement revives even in the presence of strong turbulence.

Ultrafast measurement of a single-photon wave packet using an optical Kerr gate

Ultrafast quantum optics with time-frequency entangled photons is at the forefront of progress towards future quantum technologies. However, to unravel the time domain structure of entangled photons and exploit fully their rich dimensionality, a single-photon detector with sub-picosecond temporal resolution is required. Here, we present ultrafast single-photon detection using an optical Kerr gate composed of a photonic crystal fiber (PCF) placed inside a Sagnac interferometer. A near-rectangle temporal waveform of a heralded single-photon generated via spontaneous parametric down-conversion is measured with temporal resolution as high as 224 ± 9 fs. The large nonlinearity and long effective interaction length of the PCF enables maximum detection efficiency to be achieved with only 30.5 mW gating pulse average power, demonstrating an order-of-magnitude improvement compared to optical gating with sum-frequency generation. Also, we discuss the trade-off relationship between detection efficiency and temporal resolution.

Measuring the Joint Spectral Mode of Photon Pairs Using Intensity Interferometry

The ability to manipulate and measure the time-frequency structure of quantum light is useful for information processing and metrology. Measuring this structure is also important when developing quantum light sources with high modal purity that can interfere with other independent sources. Here, we present and experimentally demonstrate a scheme based on intensity interferometry to measure the joint spectral mode of photon pairs produced by spontaneous parametric down-conversion. We observe correlations in the spectral phase of the photons due to chirp in the pump. We show that our scheme can be combined with stimulated emission tomography to quickly measure their mode using bright classical light. Our scheme does not require phase stability, nonlinearities, or spectral shaping and thus is an experimentally simple way of measuring the modal structure of quantum light.

Augmenting the Sensing Performance of Entangled Photon Pairs through Asymmetry

We analyze theoretically and experimentally cases of asymmetric detection, stimulation, and loss within a quantum nonlinear interferometer of entangled pairs. We show that the visibility of the SU(1,1) interference directly discerns between loss on the measured mode (signal) and the conjugated mode (idler). This asymmetry also affects the phase sensitivity of the interferometer, where coherent seeding is shown to mitigate losses that are suffered by the conjugated mode; therefore increasing the maximum threshold of loss that permits sub-shot-noise phase detection. Our findings can improve the performance of setups that rely on direct detection of entangled pairs, such as quantum interferometry and imaging with undetected photons.

Experimental Demonstration of Conjugate-Franson Interferometry

Franson interferometry is a well-known quantum measurement technique for probing photon-pair frequency correlations that is often used to certify time-energy entanglement. We demonstrate, for the first time, the complementary technique in the time basis called conjugate-Franson interferometry. It measures photon-pair arrival-time correlations, thus providing a valuable addition to the quantum toolbox. We obtain a conjugate-Franson interference visibility of 96±1% without background subtraction for entangled photon pairs generated by spontaneous parametric down-conversion. Our measured result surpasses the quantum-classical threshold by 25 standard deviations and validates the conjugate-Franson interferometer (CFI) as an alternative method for certifying time-energy entanglement. Moreover, the CFI visibility is a function of the biphoton's joint temporal intensity, and is therefore sensitive to that state's spectral phase variation: something that is not the case for Franson interferometry or Hong-Ou-Mandel interferometry. We highlight the CFI's utility by measuring its visibilities for two different biphoton states: one without and the other with spectral phase variation, observing a 21% reduction in the CFI visibility for the latter. The CFI is potentially useful for applications in areas of photonic entanglement, quantum communications, and quantum networking.

Interferometric spectroscopy with quantum light: Revealing out-of-time-ordering correlators

We survey the inclusion of interferometric elements in nonlinear spectroscopy performed with quantum light. Controlled interference of electromagnetic fields coupled to matter can induce constructive or destructive contributions of microscopic coupling sequences (histories) of matter. Since quantum fields do not commute, quantum light signals are sensitive to the order of light-matter coupling sequences. Matter correlation functions are thus imprinted by different field factors, which depend on that order. We identify the associated quantum information obtained by controlling the weights of different contributing pathways and offer several experimental schemes for recovering it. Nonlinear quantum response functions include out-of-time-ordering matter correlators (OTOCs), which reveal how perturbations spread throughout a quantum system (information scrambling). Their effect becomes most notable when using ultrafast pulse sequences with respect to the path difference induced by the interferometer. OTOCs appear in quantum-informatics studies in other fields, including black hole, high energy, and condensed matter physics.

Witnessing the survival of time-energy entanglement through biological tissue and scattering media

We demonstrate the preservation of the time-energy entanglement of near-IR photons through thick biological media (≤1.55 mm) and tissue (≤ 235 μm) at room temperature. Using a Franson-type interferometer, we demonstrate interferometric contrast of over 0.9 in skim milk, 2% milk, and chicken tissue. This work supports the many proposed opportunities for nonclassical light in biological imaging and analyses from sub-shot noise measurements to entanglement-enhanced fluorescence imaging, clearly indicating that the entanglement characteristics of photons can be maintained even after propagation through thick, turbid biological samples.

Entangled photons from subwavelength nonlinear films

Miniaturized entangled photon sources, in particular based on subwavelength metasurfaces, are highly demanded for the development of integrated quantum photonics. Here, as a first step towards the development of quantum optical metasurfaces (QOMs), we demonstrate generation of entangled photons via spontaneous parametric down-conversion (SPDC) from subwavelength films. We achieve photon pair generation with a high coincidence-to-accidental ratio in lithium niobate and gallium phosphide nanofilms. By implementing the fiber spectroscopy of SPDC in nanofilms, we measure a spectrum with a bandwidth of 500 nm, limited only by the overall detection efficiency. The spectrum reveals vacuum field enhancement due to a Fabry-Perot resonance inside the nonlinear films. It also suggests a strategy for observing SPDC from QOM. Our experiments lay the groundwork for future development of flat SPDC sources, including QOM.

Remotely projecting states of photonic temporal modes

Two-photon time-frequency entanglement is a valuable resource in quantum information. Resolving the wavepacket of ultrashort pulsed single-photons, however, is a challenge. Here, we demonstrate remote spectral shaping of single photon states and probe the coherence properties of two-photon quantum correlations in the time-frequency domain, using engineered parametric down-conversion (PDC) and a quantum pulse gate (QPG) in nonlinear waveguides. Through tailoring the joint spectral amplitude function of our PDC source we control the temporal mode structure between the generated photon pairs and show remote state-projections over a range of time-frequency mode superpositions.

Carving out configurable ultrafast pulses from a continuous wave source via the optical Kerr effect

Wavelength-tunable, time-locked pairs of ultrafast pulses are crucial in modern-day time-resolved measurements. We demonstrate a simple means of generating configurable optical pulse sequences: sub-picosecond pulses are carved out from a continuous wave laser via pump-induced optical Kerr switching in 10 cm of a commercial single-mode fiber. By introducing dispersion to the pump, the near transform-limited switched pulse duration is tuned between 305-570 fs. Two- and four-pulse signal trains are also generated by adding birefringent α-BBO plates in the pump beam. These results highlight an ultrafast light source with intrinsic timing stability and pulse-to-pulse phase coherence, where pulse generation could be adapted to wavelengths ranging from ultraviolet to infrared.

Direct measurement of the coupled spatiotemporal coherence of parametric down-conversion under negative group-velocity dispersion

We present a direct measurement of the spatiotemporal coherence of parametric down-conversion in the range of negative group-velocity dispersion. In this case, the frequency-angular spectra are ring-shaped, and temporal coherence is coupled to spatial coherence. Correspondingly, the lack of coherence due to spatial displacement can be compensated for with the introduction of time delay. We show a simple technique, based on a modified Mach-Zehnder interferometer, which allows us to measure time coherence and near-field space coherence simultaneously, with complete control over both variables. This technique is also suitable for the measurement of second-order coherence, where the main applications are related to two-photon spectroscopy.

Counter-propagating photon pair generation in a nonlinear waveguide

Counter-propagating parametric conversion processes in non-linear bulk crystals have been shown to feature unique properties for efficient narrowband frequency conversion. In quantum optics, the generation of photon pairs with a counter-propagating parametric down-conversion process (PDC) in a waveguide, where signal and idler photons propagate in opposite directions, offers unique material-independent engineering capabilities. However, realizing counter-propagating PDC necessitates quasi-phase-matching (QPM) with extremely short poling periods. Here, we report on the generation of counter-propagating single-photon pairs in a self-made periodically poled lithium niobate waveguide with a poling period on the same order of magnitude as the generated wavelength. The single photons of the biphoton state bridge GHz and THz bandwidths with a separable joint temporal-spectral behavior. Furthermore, they allow the direct observation of the temporal envelope of heralded single photons with state-of-the art photon counters.

Einstein-Podolsky-Rosen Energy-Time Entanglement of Narrow-Band Biphotons

We report the direct characterization of energy-time entanglement of narrow-band biphotons produced from spontaneous four-wave mixing in cold atoms. The Stokes and anti-Stokes two-photon temporal correlation is measured by single-photon counters with nanosecond temporal resolution, and their joint spectrum is determined by using a narrow linewidth optical cavity. The energy-time entanglement is verified by the joint frequency-time uncertainty product of 0.063±0.0044, which does not only violate the separability criterion but also satisfies the continuous variable Einstein-Podolsky-Rosen steering inequality.

Quantum Nonlocal Aberration Cancellation

Phase distortions, or aberrations, can negatively influence the performance of an optical imaging system. Through the use of position-momentum entangled photons, we nonlocally correct for aberrations in one photon's optical path by intentionally introducing the complementary aberrations in the optical path of the other photon. In particular, we demonstrate the simultaneous nonlocal cancellation of aberrations that are of both even and odd order in the photons' transverse degrees of freedom. We also demonstrate a potential application of this technique by nonlocally canceling the effect of defocus in a quantum imaging experiment and thereby recover the original spatial resolution.

Influence of pump coherence on the generation of position-momentum entanglement in optical parametric down-conversion

We examine experimentally how the degree of position-momentum entanglement of photon pairs depends on the transverse coherence of the pump beam that excites them in a process of spontaneous parametric down-conversion. Using spatially incoherent light from a light-emitting diode, we obtain strong position correlation of the photons, but we find that transverse momentum correlation, and thus entanglement, is entirely absent. When we continuously vary the degree of spatial coherence on the pump beam, we observe the emergence of stronger momentum correlations and entanglement. We present theoretical arguments that explain our experimental results. Our results shed light on entanglement generation and can be applied to control entanglement for quantum information applications.

Entangled Photon Resonance Energy Transfer in Arbitrary Media

Inspired by the unique nonclassical character of two-photon interactions induced by entangled photons, we develop a new comprehensive Förster-type formulation for entangled-two-photon resonance energy transfer (E2P-RET) mediated by inhomogeneous, dispersive, and absorptive media with any space-dependent and frequency-dependent dielectric function and with any size of donor/acceptor. In our theoretical framework, two uncoupled particles are jointly excited by the temporally entangled field associated with two virtual photons that are produced by three-level radiative cascade decay in a donor particle. The temporal entanglement leads to frequency anticorrelation in the virtual photon's field, and vanishing of one of the time-ordered excitation pathways. The underlying mechanism leads to more than 3 orders of magnitude enhancement in the E2P-RET rate compared with the uncorrelated photon case. With the power of our new formulation, we propose a way to characterize E2P-RET through an effective rate coefficient K_E2P, introduced here. This coefficient shows how energy transfer can be enhanced or suppressed depending on rate parameters in the radiative cascade, and by varying the donor-acceptor frequency differences.

Indistinguishable single-mode photons from spectrally engineered biphotons

We use pulsed spontaneous parametric down-conversion in KTiOPO ₄, with a Gaussian phase-matching function and a transform-limited Gaussian pump, to achieve near-unity spectral purity in heralded single photons at telecommunication wavelength. Theory shows that these phase-matching and pump conditions are sufficient to ensure that a biphoton state with a circularly symmetric joint spectral intensity profile is transform limited and factorable. We verify the heralded-state spectral purity in a four-fold coincidence measurement by performing Hong-Ou-Mandel interference between two independently generated heralded photons. With a mild spectral filter we obtain an interference visibility of 98.4±1.1% which corresponds to a heralded-state purity of 99.2%. Our heralded photon source is potentially an essential resource for measurement-based quantum information processing and quantum network applications.

Terahertz-bandwidth switching of heralded single photons

Optically induced ultrafast switching of single photons is demonstrated by rotating the photon polarization via the Kerr effect in a commercially available single-mode fiber. A switching efficiency of 97% is achieved with a ∼1.7  ps switching time and signal-to-noise ratio of ∼800. Preservation of the single-photon properties is confirmed by measuring no significant increase in the second-order autocorrelation function g⁽²⁾(0). These values are attained with only nanojoule-level pump energies that are produced by a laser oscillator with 80 MHz repetition rate. The results highlight a simple device capable of both high-bandwidth operations and preservation of single-photon properties for applications in photonic quantum processing and ultrafast time-gating or switching.

Compact generation of a two-photon multipath Dicke state from a single χ(2) nonlinear photonic crystal

Multipartite quantum entanglement is a powerful resource for enriching the functionality of quantum computation and quantum communication. In this Letter, we propose a new method to generate a two-photon multipath Dicke state with concurrent spontaneous parametric downconversion processes from a single periodically poled nonlinear photonic crystal. We design the poling structure to produce a three-path Dicke state where three quasi-phase-matching conditions are fulfilled simultaneously by a hybrid one- and two-dimensionally poled nonlinear photonic crystal. We use genuine multipartite entanglement concurrence to quantify the entanglement of the Dicke state. Using a more complicated poling configuration like multiple-periodically poled two-dimensional nonlinear photonic crystal, we can also produce four-path, five-path, or multipath Dicke states by a single crystal. The multiple-periodically poled two-dimensional nonlinear photonic crystal provides a new method, to the best of our knowledge, for the integrated generation of multipartite quantum light sources.

Polarization Toffoli gate assisted by multiple degrees of freedom

A Toffoli gate plays a critical role in many quantum algorithms due to its function as a building block, which is a fundamental element for feasible large-scale quantum computation. With the help of polarization, spatial, and temporal degrees of freedom (DOFs), a construction scheme of a nearly deterministic polarization Toffoli gate is proposed, where only two two-photon gates are required. The simple construction circuit together with available techniques and optical elements facilitate the realization of the scheme presented here. This construction scheme can be utilized as a reference for multiqubit quantum gates with multiple DOFs.

Assessing frequency correlation through a distinguishability measurement

The simplicity of a question, such as wondering whether or not correlations characterize a certain system, collides with the experimental difficulty of accessing such information. Here we present a low-demanding experimental approach that refers to the use of a metrology scheme to obtain a conservative estimate of the strength of frequency correlations. Our test bed is the widespread case of a photon pair produced per downconversion. The theoretical architecture used to put the correlation degree on a quantitative ground is also described.

Uncertainty Relations for Coarse-Grained Measurements: An Overview

Uncertainty relations involving incompatible observables are one of the cornerstones of quantum mechanics. Aside from their fundamental significance, they play an important role in practical applications, such as detection of quantum correlations and security requirements in quantum cryptography. In continuous variable systems, the spectra of the relevant observables form a continuum and this necessitates the coarse graining of measurements. However, these coarse-grained observables do not necessarily obey the same uncertainty relations as the original ones, a fact that can lead to false results when considering applications. That is, one cannot naively replace the original observables in the uncertainty relation for the coarse-grained observables and expect consistent results. As such, several uncertainty relations that are specifically designed for coarse-grained observables have been developed. In recognition of the 90th anniversary of the seminal Heisenberg uncertainty relation, celebrated last year, and all the subsequent work since then, here we give a review of the state of the art of coarse-grained uncertainty relations in continuous variable quantum systems, as well as their applications to fundamental quantum physics and quantum information tasks. Our review is meant to be balanced in its content, since both theoretical considerations and experimental perspectives are put on an equal footing.