We propose a two-photon beating experiment based upon biphotons generated from a resonant pumping two-level system operating in a backward geometry. On the one hand, the linear optical-response leads biphotons produced from two sidebands in the Mollow triplet to propagate with tunable refractive indices, while the central-component propagates with unity refractive index. The relative phase difference due to different refractive indices is analogous to the pathway-length difference between long-long and short-short in the original Franson interferometer. By subtracting the linear Rayleigh scattering of the pump, the visibility in the center part of the two-photon beating interference can be ideally manipulated among [0, 100%] by varying the pump power, the material length, and the atomic density, which indicates a Bell-type inequality violation. On the other hand, the proposed experiment may be an interesting way of probing the quantum nature of the detection process. The interference will disappear when the separation of the Mollow peaks approaches the fundamental timescales for photon absorption in the detector.
We demonstrate the generation of narrowband biphotons with polarization-frequency coupled hy- perentanglement from spontaneous four-wave mixing in cold atoms. The coupling between polariza- tion and frequency is realized through a frequency shifter and linear optics. When the polarization- frequency degrees of freedom are decoupled, it is robust to create polarization and frequency Bell states, confirmed by the polarization quantum-state tomography and the two-photon temporal quan- tum beating. Making use of the polarization-frequency coupling to transfer polarization phase retard to the entan…
Inherent loss is always to be avoided in generating single photons or biphotons, but interestingly it provides opportunities for manipulating the photon wave packet. In this paper we show how inherent loss in parametric down-conversion can be employed to tailor the wave packets of single photons and biphotons. As an example, we propose a scheme to realize a single photon in a single cycle using inherent loss. Our work has potential applications in quantum communication, quantum computation, and quantum interface.
Using a basic Mach-Zehnder interferometer, we demonstrate experimentally the measurement of the photonic de Broglie wavelength of an entangled photon pair (a biphoton) generated by spontaneous parametric down-conversion. The observed interference manifests the concept of the photonic de Broglie wavelength. The result also provides a proof-of-principle of the quantum lithography that utilizes the reduced interferometric wavelength.
We study two-photon excitation using biphotons generated via the process of spontaneous parametric down-conversion in a nonlinear crystal. We show that the focusing of these biphotons yields an excitation distribution that is essentially the same as the distribution of one-photon excitation at the pump wavelength. We also demonstrate that biphoton excitation in the image region yields a distribution whose axial width is approximately that of the crystal thickness and whose transverse width is that of the pump at the input to the crystal.
We demonstrate a technique that allows to fully control the bandwidth of entangled photons independently of the frequency band of interest and of the nonlinear crystal. We show that this technique allows to generate nearly transform-limited biphotons with almost one octave of bandwidth (hundreds of THz) which corresponds to correlation times of just a few femtoseconds. The presented method becomes an enabling tool for attosecond entangled-photons quantum optics. The technique can also be used to generate paired photons with a very high degree of entanglement.
Correlations between photons are interesting for a number of applications and concepts in metrology in particular for resolution improvements in different methods of quantum imaging. Since Fock-states of N-photons of wavelength lambda in interference schemes acquire N-times the phase shift of single photons these states can appear as if they had a de Broglie wavelength of lambda/N. A biphoton beam diffracted at a blazed grating shows this reduced de Broglie wavelength. This experiment can be seen as a purification of biphotons of a certain correlation strength on the one hand. On the other han…
The goal of this research is to determine and study a physical system that will enable a fast and intrinsically two-photon detector, which would be of interest for quantum information and metrology applications. We consider two types of two-photon processes that can be observed using a very faint, but quantum-correlated biphoton field. These are optical up-conversion and an external photoelectric effect. We estimate the correlation enhancement factor for the biphoton light compared to coherent light, report and discuss the preliminary experimental results.
The cascade-emitted biphotons generated from the alkali metal atomic ensembles are an excellent entanglement resource which enables long-distance quantum communication. The communication of quantum information between distant locations can be realized by utilizing the low-loss telecom bandwidth in the upper transition of the cascaded photons in a fiber-based quantum network. Meanwhile, the infrared photon from the lower transition of this highly directional and frequency-correlated biphoton can be created under the four-wave mixing process and can be stored locally as a collective spin wave. H…
A double-slit experiment with entangled photons is theoretically analyzed. It is shown that, under suitable conditions, two entangled photons of wavelength $λ$ can behave like a \emph{biphoton} of wavelength $λ/2$. The interference of these biphotons, passing through a double-slit can be obtained by detecting both photons of the pair at the same position. This is in agreement with the results of an earlier experiment. More interestingly, we show that even if the two entangled photons are separated by a polarizing beam splitter, they can still behave like a biphoton of wavelength $λ/2$. In this…
We demonstrate optical interferometry beyond the limits imposed by the photon wavelength using 'triggered' entangled photon pairs from a semiconductor quantum dot. Interference fringes of the entangled biphoton state reveals a periodicity half of that obtained with the single photon, and much less than that of the pump laser. High fringe visibility indicates that biphoton interference is less sensitive to decoherence than interference of two sequential single photons. The results suggest that quantum interferometry may be possible using a semiconductor LED-like device.
Interference between an unknown two-photon state (a "biphoton") and the two-photon component of a reference state gives a phase-sensitive arrival-time distribution containing full information about the biphoton temporal wave function. Using a coherent state as a reference, we observe this interference and reconstruct the wave function of single-mode biphotons from a low-intensity narrowband squeezed vacuum state.
We analyze the quantum-state purity of heralded single photons produced from frequency-anti-correlated biphotons. We find that the quantum-state purity in time-frequency domain depends strongly on the response time uncertainty of the trigger-photon detector that heralds the generation of its paired photon. If the trigger response time is much shorter than the two-photon coherence time, the time-frequency quantum-state purity of heralded single photons approaches unity and the heralded single photon is in a nearly pure state. If the trigger response time is much longer than the two-photon coher…
In this work, 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. Unlike the previous independent manipulation schemes, here we perform joint manipulation on the biphoton spectrum. The technique in this work paves the way for arbitrary shaping of a multi-ph…
We present the first observation of two-photon polarization interference structure in the second-order Glauber's correlation function of two-photon light generated via type-II spontaneous parametric down-conversion. In order to obtain this result, two-photon light is transmitted through an optical fibre and the coincidence distribution is analyzed by means of the START-STOP method. Beyond the experimental demonstration of an interesting effect in quantum optics, these results also have considerable relevance for quantum communications.
In this chapter, we review recent advances in generating narrowband biphotons with long coherence time using spontaneous parametric interaction in monolithic cavity with cluster effect as well as in cold atoms with electromagnetically induced transparency. Engineering and manipulating the temporal waveforms of these long biphotons provide efficient means for controlling light-matter quantum interaction at the single-photon level. We also review recent experiments using temporally long biphotons and single photons.
Multiparticle interference is a fundamental phenomenon in the study of quantum mechanics.It was discovered in a recent experiment [Ra, Y.-S. et al, Proc. Natl Acad. Sci. USA \textbf{110}, 1227(2013)] that spectrally uncorrelated biphotons exhibited a nonmonotonic quantum-to-classical transition in a four-photon Hong-Ou-Mandel (HOM) interference. In this work, we consider the same scheme with spectrally correlated photons.By theoretical calculation and numerical simulation, we found the transition not only can be nonmonotonic with negative-correlated or uncorrelated biphotons, but also can be m…
We report on an experiment showing that the wavelength of a biphoton is clearly dependent on the measurement scheme and on the way it is defined. It is shown that it can take any value, depending on the control of the interferometer phase differences. It is possible to identify the interference of the single and two-photon wavepackets as particular cases of the most general interference process. The variable wavelength has no implication on the energy of the individual photons neither on the total energy of the biphoton.
In classical optics, Young's double-slit experiment with colored coherent light gives rise to individual interference fringes for each light frequency, referring to single-photon interference. However, two-photon double-slit interference has been widely studied only for wavelength-degenerate biphoton, known as subwavelength quantum lithography. In this work, we report double-slit interference experiments with two-color biphoton. Different from the degenerate case, the experimental results depend on the measurement methods. From a two-axis coincidence measurement pattern we can extract complete…
A conditioned unitary transformation ($90^o$ polarization rotation) is performed at single-photon level. The transformation is realized by rotating polarization for one of the photons of a polarization-entangled biphoton state (signal photon) by means of a Pockel's cell triggered by the detection of the other (idler) photon after polarization selection. As a result, polarization degree for the signal beam changes from zero to the value given by the idler detector quantum efficiency. This result is relevant to practical realization of various quantum information schemes and can be used for deve…
In spontaneous parametric down-conversion photons are known to be created coherently and with equal probability over the entire length of the crystal. Then, there is no particular position in the crystal where a photon pair is created. We make the seemingly contradictory observation that we can control the time delay with the crystal position along the propagation direction. We resolve this contradiction by showing that the spatio-temporal correlations critically affect the temporal properties of the pair of photons, when using a finite detector size. We expect this to have important implicati…
The well-known Hong-Ou-Mandel effect is revisited. Two physical reasons are discussed for the effect to be less pronounced or even to disappear: differing polarizations of photons coming to the beamsplitter and delay time of photons in one of two channels. For the latter we use the concepts of biphoton frequency and temporal wave functions depending, correspondingly, on two frequency continuous variables of photons and on two time variables $t_1$ and $t_2$ interpreted as the arrival times of photons to the beamsplitter. Explicit expressions are found for the probability densities and total pro…
Coherent and reversible storage of multi-photon entanglement with a multimode quantum memory is essential for scalable all-optical quantum information processing. Although single photon has been successfully stored in different quantum systems, storage of multi-photon entanglement remains challenging because of the critical requirement for coherent control of photonic entanglement source, multimode quantum memory, and quantum interface between them. Here we demonstrate a coherent and reversible storage of biphoton Bell-type entanglement with a holographic multimode atomic-ensemble-based quantu…
We report results of two-photon quantum holography where spatial information stored in phase holograms is retrieved by measuring quantum spatial correlations between two images formed by spatially entangled twin photons with a dimensionality of 1790 in the two-dimensional transverse space. In our experiments, the entire flux of spontaneous down converted photons illuminates the phase holograms and the photons of pairs signal-idler transmitted by the holograms are detected separately in far field on two electron-multiplying charge coupled device cameras.
Spectrally intrinsically uncorrelated biphoton states generated from nonlinear crystals are very important but rare resources for quantum photonics and quantum information applications. Previously, such biphoton states were generated from several kinds of crystals, however, their wavelength ranges and nonlinear efficiencies were still limited for various applications. In order to explore new crystal for wider wavelength range and higher nonlinear efficiency, here we theoretically study the generation of spectrally uncorrelated biphoton states from 14 crystals in the `BBO family', including BBO…
We describe and demonstrate a quantum state tomography for measuring the complex temporal waveform of narrowband biphotons. Through six sets of two-photon interference measurements projected in different polarization subspaces, we can construct the time-frequency entangled two-photon joint amplitude and phase functions in continuous-variable time domain. For the first time, we apply this technique to experimentally determine the temporal quantum states of narrowband biphotons generated from spontaneous four-wave mixing in cold atoms, and fully confirm the theoretical predictions.
We describe spontaneous parametric down-conversion experiments in which induced coherence across two coupled interferometers results in high-visibility single-photon interference. Opening additional photon channels allows "which-path" information and reduces the visibility of the singlephoton interference, but results in nearly perfect visibility when photons are counted in coincidence. A simplified theoretical model accounts for these complementary observations and attributes them directly to the relations among the vacuum fields at the different crystals.
A detailed theoretical analysis of the spatiotemporal mode of a single photon prepared via conditional measurements on a photon pair generated in the process of parametric down-conversion is presented. The maximum efficiency of coupling the photon into a transform-limited classical optical mode is calculated and ways for its optimization are determined. An experimentally feasible technique of generating the optimally matching classical mode is proposed. The theory is applied to a recent experiment on pulsed homodyne tomography of the single-photon Fock state (A. I. Lvovsky et al., Phys Rev. Le…
We experimentally study two-photon coherence in plasmon-assisted transmission with a two-photon Mach-Zehnder (MZ) interferometer. Two collinear photons of identical or orthogonal polarization are simultaneously incident on one optically thick metal film, perforated with a periodic array of subwavelength holes. The de Broglie wavelength of plasmon-assisted transmitted photons is measured, which shows that two photons are re-eradiated by the plasmons and the quantum coherence of biphoton is preserved in the conversion process of transforming biphoton to plasmons and then back to biphoton.
Orthogonality of two-photon polarization states belonging to a single frequency and spatial mode is demonstrated experimentally, in a generalization of the well-known anti-correlation 'dip' experiment.
In this letter, we report a polarization-entangled photon-pair source based on type-II spontaneous parametric down conversion at telecom O-band in periodically poled silica fiber (PPSF). The photon-pair source exhibits more than 130 nm (~24 THz) emission bandwidth centered at 1306.6 nm. The broad emission spectrum results in a short biphoton correlation time and we experimentally demonstrate a Hong-Ou-Mandel interference dip with a full width of 26.6 fs at half maximum. Owing to the low birefringence of the PPSF, the biphotons generated from type-II SPDC are polarization-entangled over the ent…
Bell states are a fundamental resource in photonic quantum information processing. These states have been generated successfully in many photonic degrees of freedom. Their manipulation, however, in the momentum space remains challenging. Here, we present a scheme for engineering the symmetry of two-photon states entangled in the transverse momentum degree of freedom through the use of a spatially variable phase object. We demonstrate how a Hong-Ou-Mandel interferometer must be constructed to verify the symmetry in momentum entanglement via photon "bunching"/"anti-bunching" observation. We also…
We investigate the set of qutrit states in terms of symmetric states of two qubits that violate the minimal contextual inequality, namely the Klyachko-Can-Binicoglu-Shumovsky (KCBS) inequality. The physical system that provides a natural framework for this problem is a biphoton which consists of two photons in the same spatio-temporal mode and whose effective polarization behaves as a three-level quantum system. The relationship between the KCBS contextual inequality and the Clauser-Horne-Shimony-Holt (CHSH) inequality is investigated. We find that every biphotonic state that is contextual wit…
For a general-form polarization biphoton qutrit, physically corresponding to a pair of arbitrarily polarized photons in a single frequency and wavevector mode, we explicitly find polarization Schmidt modes. A simple method is suggested for factorizing the state vector and the explicit expressions for the factorizing photon creation operators are found. The degrees of entanglement and polarization of a qutrit are shown to depend directly on the commutation features of the factorizing operators. Clear graphic representations for the Stokes vectors of the qutrit state as a whole, its Schmidt mode…
We theoretically investigate the spectral property of a biphoton state from multiplexed thermal atomic ensembles. This biphoton state originates from the cascade emissions, which can be generated by two weak pump fields under four-wave mixing condition. Under this condition, a signal photon from the upper transition, chosen in a telecommunication bandwidth, can be generated along with a correlated idler photon from the lower infrared transition. We can spectrally shape the biphoton state by multiplexing the atomic ensembles with frequency-shifted emissions, where the entropy of entanglement ca…
We systematically studied the temporal profile of biphotons, i.e., pairs of time-correlated single photons, generated from a hot atomic vapor via the spontaneous four-wave mixing process. The measured temporal width of biphoton wave packet or two-photon correlation function against the coupling power was varied from about 70 to 580 ns. We derived an analytical expression of the biphoton's spectral profile in the Doppler-broadened medium. The analytical expression reveals that the spectral profile is mainly determined by the effect of electromagnetically induced transparency (EIT), and behaves …
In this work, we present a theoretical and experimental study about the spatial correlations of paired photons generated by type-II spontaneous parametric down-conversion. In particular, we show how these correlations can be positive or negative depending on the direction in which the far field plane is scanned and the polarization post-selected. Our results provide a straightforward way to observe different kind of correlations, that complement other well known methods to tune the spatial correlations of paired photons.
As a tutorial to the spatial aspects of Spontaneous Parametric Downconversion (SPDC), we present a detailed first-principles derivation of the transverse correlation width of photon pairs in degenerate collinear SPDC. This width defines the size of a biphoton birth zone, the region where the signal and idler photons are likely to be found when conditioning on the position of the destroyed pump photon. Along the way, we discuss the quantum-optical calculation of the amplitude for the SPDC process, as well as its simplified form for nearly collinear degenerate phase matching. Following this, we …
Photonic time-frequency entanglement is a promising resource for quantum information processing technologies. We investigate swapping of continuous-variable entanglement in the time-frequency degree of freedom using three-wave mixing in the low-gain regime with the aim of producing heralded biphoton states with high purity and low multi-pair probability. Heralding is achieved by combining one photon from each of two biphoton sources via sum-frequency generation to create a herald photon. We present a realistic model with pulsed pumps, investigate the effects of resolving the frequency of the h…
The Hong-Ou-Mandel (HOM) experiment was a benchmark in quantum optics, evidencing the quantum nature of the photon. In order to go deeper, and obtain the complete information about the quantum state of a system, for instance, composed by photons, the direct measurement or reconstruction of the Wigner function or other quasi--probability distribution in phase space is necessary. In the present paper, we show that a simple modification in the well-known HOM experiment provides the direct measurement of the Wigner function. We apply our results to a widely used quantum optics system, consisting o…
Generation of two-photon wavepackets, produced by spontaneous parametric down conversion in crystals with linearly chirped quasi-phase matching grating, is analyzed. Although being spectrally broad, two-photon wavepackets produced this way are not Fourier transform limited. In the paper we discuss the temporal compression of the wavepackets, exploiting the insertion of a standard optical fiber in the path of one of the two photons. The effect is analyzed by means of full numerical calculation and the exact dispersion dependencies in both the crystal and the fiber are considered. The study open…
Frequency-Resolved Simulations of Highly Entangled Biphoton States: Beyond the Single-Pair Approximation. II. Application to Entanglement-based Quantum Key Distribution
Propagation of entangled photons in optical fiber is one of the fundamental issues for realizing quantum communication protocols. When entanglement in polarization is considered, arises the problem of compensating for the fiber effect on photons polarization. In this paper we demonstrate an effective solution where a Faraday mirror allows to cancel undesired effects of polarization drift in fiber. This technique is applied to a protocol for generating Bell states by a narrow temporal selection of the second-order intensity correlation function.
Generating nonclassical light offers a benchmark tool for the fundamental research and potential applications in quantum optics. Conventionally, it has become a standard technique to produce the nonclassical light through the nonlinear optical processes occurring in nonlinear crystals. In this review we describe using cold atomic-gas media to generate such nonclassical light, especially focusing on narrow-band biphoton generation. Compared with the standard procedure, the new biphoton source has such properties as long coherence time, long coherence length, high spectral brightness, and high c…
Photon pairs generated by spontaneous parametric down-conversion are essential for optical quantum information processing, in which the quality of biphoton states is crucial for the performance. To engineer the biphoton wavefunction (BWF) on-chip, the pump envelope function and the phase matching function are commonly adjusted, while the modal field overlap has been considered as a constant in the frequency range of interest. In this work, by utilizing modal coupling in a system of coupled waveguides, we explore the modal field overlap as a new degree of freedom for biphoton engineering. We pr…
We test two-dimensional TPSA of biphoton light emitted via ultrafast spontaneous parametric down-conversion (SPDC) using the effect of group-velocity dispersion in optical fibres. Further, we apply this technique to demonstrate the engineering of biphoton spectral properties by acting on the pump pulse shape.
In this paper we present a double slit experiment where two undistinguishable photons produced by type I PDC are sent each to a well defined slit. Data about the diffraction and interference patterns for coincidences are presented and discussed. An analysis of these data allows a first test of standard quantum mechanics against de Broglie-Bohm theory.
We demonstrate one- and two-photon diffraction and interference experiments utilizing parametric down-converted photon pairs (biphotons) and a transmission grating. With two-photon detection, the biphoton exhibits a diffraction-interference pattern equivalent to that of an effective single particle that is associated with half the wavelength of the constituent photons. With one-photon detection, however no diffraction-interference pattern is observed. We show that these phenomena originate from the spatial quantum correlation between the down-converted photons.
It is shown that parametric downconversion, with a short-duration pump pulse and a long nonlinear crystal that is appropriately phase matched, can produce a frequency-entangled biphoton state whose individual photons are coincident in frequency. Quantum interference experiments which distinguish this state from the familiar time-coincident biphoton state are described.
We demonstrate a silicon-chip biphoton source with an unprecedented quantum cross correlation up to ${\rm g_{si}^{(2)}(0) = (2.58 \pm 0.16) \times 10^4}$. The emitted biphotons are intrinsically single-mode, with self correlations of ${\rm g_{ss}^{(2)}(0) = 1.90 \pm 0.05}$ and ${\rm g_{ii}^{(2)}(0) = 1.87 \pm 0.06}$ for signal and idler photons, respectively. We observe the waveform asymmetry of cross correlation between signal and idler photons and reveal the identical and non-exponential nature of self correlations of individual signal and idler photon modes, which is a nature of cavity-enha…
