Can Two-Photon Interference be Considered the Interference of Two Photons?

Photon Phase Delay Sensing with Sub-Attosecond Uncertainty

The application of statistical estimation theory to Hong-Ou-Mandel interferometry led to enticing results in terms of the detection limit for photon reciprocal delay and polarisation measurement. In the following paper, a fully fibre-coupled setup operating in the telecom wavelength region proves to achieve, for the first time, in common-path Hong-Ou-Mandel-based interferometry, a detection limit for photon phase delay at the zeptosecond scale. The experimental results are then framed in a theoretical model by calculating the Cramer-Rao bound (CRB) and, after comparison with the obtained experimental results, it is shown that our setup attains the optimal measurement, nearly saturating CRB.

Full Spatial Characterization of Entangled Structured Photons

Vector modes are fully polarized modes of light with spatially varying polarization distributions, and they have found widespread use in numerous applications such as microscopy, metrology, optical trapping, nanophotonics, and communications. The entanglement of such modes has attracted significant interest, and it has been shown to have tremendous potential in expanding existing applications and enabling new ones. However, due to the complex spatially varying polarization structure of entangled vector modes (EVMs), a complete entanglement characterization of these modes remains challenging and time consuming. Here, we have used a time-tagging event camera to demonstrate the ability to completely characterize the entanglement of EVMs. Leveraging the camera's capacity to provide independent measurements for each pixel, we simultaneously characterize the entanglement of approximately 2.6×10^{6} modes between a bipartite EVM through measuring only 16 observables in polarization. We reveal that EVMs can naturally generate various polarization-entangled Bell states. This achievement is an important milestone in high-dimensional entanglement characterization of structured light, and it could significantly impact the implementation of related quantum technologies. The potential applications of this technique are extensive, and it could pave the way for advancements in quantum communication, quantum imaging, and other areas where structured entangled photons play a crucial role.

Attosecond-Level Delay Sensing via Temporal Quantum Erasing

Traditional Hong-Ou-Mandel (HOM) interferometry, insensitive to photons phase mismatch, proved to be a rugged single-photon interferometric technique. By introducing a post-beam splitter polarization-dependent delay, it is possible to recover phase-sensitive fringes, obtaining a temporal quantum eraser that maintains the ruggedness of the original HOM with enhanced sensitivity. This setup shows promising applications in biological sensing and optical metrology, where high sensitivity requirements are coupled with the necessity to keep light intensity as low as possible to avoid power-induced degradation. In this paper, we developed a highly sensitive single photon birefringence-induced delay sensor operating in the telecom range (1550 nm). By using a temporal quantum eraser based on common path Hongr-Ou-Mandel Interferometry, we were able to achieve a sensitivity of 4 as for an integration time of 2·104 s.

Spectral Considerations of Entangled Two-Photon Absorption Effects in Hong-Ou-Mandel Interference Experiments

Recently, different experimental methods intended to detect the entangled two-photon absorption (ETPA) phenomenon in a variety of materials have been reported. The present work explores a different approach in which the ETPA process is studied based on the changes induced in the visibility of a Hong-Ou-Mandel (HOM) interferogram. By using an organic solution of Rhodamine B as a model of nonlinear material interacting with entangled photons at ∼800 nm region produced by spontaneous parametric down-conversion (SPDC) Type-II, the conditions that make possible to detect changes in the visibility of a HOM interferogram upon ETPA are investigated. We support the discussion of our results by presenting a model in which the sample is considered as a spectral filtering function which fulfills the energy conservation conditions required by ETPA, allowing us to explain the experimental observations with good agreement. We believe that this work represents a new perspective to studying the ETPA interaction, by using an ultrasensitive quantum interference technique and a detailed mathematical model of the process.

Multiphoton non-local quantum interference controlled by an undetected photon

The interference of quanta lies at the heart of quantum physics. The multipartite generalization of single-quanta interference creates entanglement, the coherent superposition of states shared by several quanta. Entanglement allows non-local correlations between many quanta and hence is a key resource for quantum information technology. Entanglement is typically considered to be essential for creating non-local quantum interference. Here, we show that this is not the case and demonstrate multiphoton non-local quantum interference that does not require entanglement of any intrinsic properties of the photons. We harness the superposition of the physical origin of a four-photon product state, which leads to constructive and destructive interference with the photons' mere existence. With the intrinsic indistinguishability in the generation process of photons, we realize four-photon frustrated quantum interference. This allows us to observe the following noteworthy difference to quantum entanglement: We control the non-local multipartite quantum interference with a photon that we never detect, which does not require quantum entanglement. These non-local properties pave the way for the studies of foundations of quantum physics and potential applications in quantum technologies.

The deep space quantum link: prospective fundamental physics experiments using long-baseline quantum optics

The National Aeronautics and Space Administration's Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. This publication summarizes the principal experimental goals of the Deep Space Quantum Link. These goals, identified through a multi-year design study conducted by the authors, include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality.

Manipulating the symmetry of transverse momentum entangled biphoton states

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 show how this approach allows generating states that acquire an arbitrary phase under the exchange operation.

High-speed imaging of spatiotemporal correlations in Hong-Ou-Mandel interference

The Hong-Ou-Mandel interference effect lies at the heart of many emerging quantum technologies whose performance can be significantly enhanced with increasing numbers of entangled modes one could measure and thus utilize. Photon pairs generated through the process of spontaneous parametric down conversion are known to be entangled in a vast number of modes in the various degrees of freedom (DOF) the photons possess such as time, energy, and momentum, etc. Due to limitations in detection technology and techniques, often only one such DOFs can be effectively measured at a time, resulting in much lost potential. Here, we experimentally demonstrate, with the aid of a time tagging camera, high speed measurement and characterization of two-photon interference. With a data acquisition time of only a few seconds, we observe a bi-photon interference and coalescence visibility of ∼64% with potentially up to ∼2 × 10³ spatial modes. These results open up a route for practical applications of using the high dimensionality of spatiotemporal DOF in two-photon interference, and in particular, for quantum sensing and communication.

Two-photon interferences of weak coherent lights

Multiphoton interference is an important phenomenon in modern quantum mechanics and experimental quantum optics, and it is fundamental for the development of quantum information science and technologies. Over the last three decades, several theoretical and experimental studies have been performed to understand the essential principles underlying such interference and to explore potential applications. Recently, the two-photon interference (TPI) of phase-randomized weak coherent states has played a key role in the realization of long-distance quantum communication based on the use of classical light sources. In this context, we investigated TPI experiments with weak coherent pulses at the single-photon level and quantitatively analyzed the results in terms of the single- and coincidence-counting rates and one- and two-photon interference-fringe shapes. We experimentally examined the Hong–Ou–Mandel-type TPI of phase-randomized weak coherent pulses to compare the TPI effect with that of correlated photons. Further experiments were also performed with two temporally- and spatially separated weak coherent pulses. Although the observed interference results, including the results of visibility and fringe shape, can be suitably explained by classical intensity correlation, the physics underlying the TPI effect needs to be interpreted as the interference between the two-photon states at the single-photon level within the utilized interferometer. The results of this study can provide a more comprehensive understanding of the TPI of coherent light at the single-photon level.

Two-photon interference: the Hong-Ou-Mandel effect

Nearly 30 years ago, two-photon interference was observed, marking the beginning of a new quantum era. Indeed, two-photon interference has no classical analogue, giving it a distinct advantage for a range of applications. The peculiarities of quantum physics may now be used to our advantage to outperform classical computations, securely communicate information, simulate highly complex physical systems and increase the sensitivity of precise measurements. This separation from classical to quantum physics has motivated physicists to study two-particle interference for both fermionic and bosonic quantum objects. So far, two-particle interference has been observed with massive particles, among others, such as electrons and atoms, in addition to plasmons, demonstrating the extent of this effect to larger and more complex quantum systems. A wide array of novel applications to this quantum effect is to be expected in the future. This review will thus cover the progress and applications of two-photon (two-particle) interference over the last three decades.

Two-boson quantum interference in time

The celebrated Hong-Ou-Mandel effect is the paradigm of two-particle quantum interference. It has its roots in the symmetry of identical quantum particles, as dictated by the Pauli principle. Two identical bosons impinging on a beam splitter (of transmittance 1/2) cannot be detected in coincidence at both output ports, as confirmed in numerous experiments with light or even matter. Here, we establish that partial time reversal transforms the beam splitter linear coupling into amplification. We infer from this duality the existence of an unsuspected two-boson interferometric effect in a quantum amplifier (of gain 2) and identify the underlying mechanism as time-like indistinguishability. This fundamental mechanism is generic to any bosonic Bogoliubov transformation, so we anticipate wide implications in quantum physics.

Multiparticle Interference of Pairwise Distinguishable Photons

One of the central principles of quantum mechanics is that if there are multiple paths that lead to the same event and there is no way to distinguish between them, interference occurs. It is often assumed that distinguishing information in the preparation, evolution, or measurement of a system is sufficient to destroy interference. However, it is still possible for photons in distinguishable, separable states to interfere due to the indistinguishability of paths corresponding to possible exchange processes. Here we experimentally measure an interference signal that depends only on the multiparticle interference of four photons in a four-port interferometer despite pairs of them occupying distinguishable states.

Frequency-Domain Quantum Interference with Correlated Photons from an Integrated Microresonator

Frequency encoding of quantum information together with fiber and integrated photonic technologies can significantly reduce the complexity and resource requirements for realizing all-photonic quantum networks. The key challenge for such frequency domain processing of single photons is to realize coherent and selective interactions between quantum optical fields of different frequencies over a range of bandwidths. Here, we report frequency-domain Hong-Ou-Mandel interference with spectrally distinct photons generated from a chip-based microresonator. We use four-wave mixing to implement an active "frequency beam splitter" and achieve interference visibilities of 0.95±0.02. Our work establishes four-wave mixing as a tool for selective high-fidelity two-photon operations in the frequency domain which, combined with integrated single-photon sources, provides a building block for frequency-multiplexed photonic quantum networks.

Experimental interference of uncorrelated photons

The distinguishing of the multiphoton quantum interference effect from the classical one forms one of the most important issues in modern quantum mechanics and experimental quantum optics. For a long time, the two-photon interference (TPI) of correlated photons has been recognized as a pure quantum effect that cannot be simulated with classical lights. In the meantime, experiments have been carried out to investigate the classical analogues of the TPI. In this study, we conduct TPI experiments with uncorrelated photons with different center frequencies from a luminescent light source, and we compare our results with the previous ones of correlated photons. The observed TPI fringe can be expressed in the form of three phase terms related to the individual single-photon and two-photon states, and the fringe pattern is strongly affected by the two single-photon-interference fringes and also by their visibilities. With the exception of essential differences such as valid and accidental coincidence events within a given resolving time and the two-photon spectral bandwidth, the interference phenomenon itself exhibits the same features for both correlated and uncorrelated photons in the single-photon counting regime.

Quantum Interference between Light Sources Separated by 150 Million Kilometers

We report an experiment to test quantum interference, entanglement, and nonlocality using two dissimilar photon sources, the Sun and a semiconductor quantum dot on the Earth, which are separated by ∼150  million kilometers. By making the otherwise vastly distinct photons indistinguishable in all degrees of freedom, we observe time-resolved two-photon quantum interference with a raw visibility of 0.796(17), well above the 0.5 classical limit, providing unambiguous evidence of the quantum nature of thermal light. Further, using the photons with no common history, we demonstrate postselected two-photon entanglement with a state fidelity of 0.826(24) and a violation of Bell inequality by 2.20(6). The experiment can be further extended to a larger scale using photons from distant stars and open a new route to quantum optics experiments at an astronomical scale.

Tunable Two-Photon Quantum Interference of Structured Light

Structured photons are nowadays an important resource in classical and quantum optics due to the richness of properties they show under propagation, focusing, and in their interaction with matter. Vectorial modes of light in particular, a class of modes where the polarization varies across the beam profile, have already been used in several areas ranging from microscopy to quantum information. One of the key ingredients needed to exploit the full potential of complex light in the quantum domain is the control of quantum interference, a crucial resource in fields like quantum communication, sensing, and metrology. Here we report a tunable Hong-Ou-Mandel interference between vectorial modes of light. We demonstrate how a properly designed spin-orbit device can be used to control quantum interference between vectorial modes of light by simply adjusting the device parameters and no need of interferometric setups. We believe our result can find applications in fundamental research and quantum technologies based on structured light by providing a new tool to control quantum interference in a compact, efficient, and robust way.

Informationally symmetrical Bell state preparation and measurement

Bell state measurement (BSM) plays crucial roles in photonic quantum information processing. The standard linear optical BSM is based on Hong-Ou-Mandel interference where two photons meet and interfere at a beamsplitter (BS). However, a generalized two-photon interference is not based on photon-photon interaction, but interference between two-photon probability amplitudes. Therefore, it might be possible to implement BSM without interfering photons at a BS. Here, we investigate a linear optical BSM scheme which does not require two photon overlapping at a BS. By unleashing the two photon coexistence condition, it can be symmetrically divided into two parties. The symmetrically dividable property suggests an informationally symmetrical BSM between remote parties without a third party. We also present that our BSM scheme can be used for Bell state preparation between remote parties without a third party. Since our BSM scheme can be easily extended to multiple photons, it can be useful for various quantum communication applications.

Revealing the Behavior of Photons in a Birefringent Interferometer

The interferometer is one of the most important devices for revealing the nature of light and for precision optical metrology. Although many experiments were performed for probing photon behavior in various configurations, a complete study of photon behavior in a birefringent interferometer has not been performed, to our knowledge. By using an environmental turbulence immune Mach-Zehnder interferometer, we observe tunable photonic beatings by rotating a birefringent crystal versus the temperature of the crystal for both the single photon and two photons. Furthermore, the two-photon interference fringes beat 2 times faster than the single-photon interference fringes. This beating effect is used to determine the thermal dispersion coefficients of the two principal refractive axes with a single measurement: the two-photon interference shows superresolution and high sensitivity. Obvious differences between two-photon and single-photon interference are also revealed in unbalanced situations. In addition, the influence of the photon bandwidth on the beating behaviors that come from polarization-dependent decoherence is also investigated. Our findings will be important for better understanding the behavior of two-photon interference in a birefringent interferometer and for precision optical metrology with quantum enhancement.

Photon statistics as an interference phenomenon

Interference of light fields, first postulated by Young, is one of the fundamental pillars of physics. Dirac extended this observation to the quantum world by stating that each photon interferes only with itself. A precondition for interference to occur is that no welcher-weg information labels the paths the photon takes; otherwise, the interference vanishes. This remains true, even if two-photon interference is considered, e.g., in the Hong-Ou-Mandel-experiment. Here, the two photons interfere only if they are indistinguishable, e.g., in frequency, momentum, polarization, and time. Less known is the fact that two-photon interference and photon indistinguishability also determine the photon statistics in the overlapping light fields of two independent sources. As a consequence, measuring the photon statistics in the far field of two independent sources reveals the degree of indistinguishability of the emitted photons. In this Letter, we prove this statement in theory using a quantum mechanical treatment. We also demonstrate the outcome experimentally with a simple setup consisting of two statistically independent thermal light sources with adjustable polarizations. We find that the photon statistics vary indeed as a function of the polarization settings, the latter determining the degree of welcher-weg information of the photons emanating from the two sources.

Two-photon interference of polarization-entangled photons in a Franson interferometer

We present two-photon interference experiments with polarization-entangled photon pairs in a polarization-based Franson-type interferometer. Although the two photons do not meet at a common beamsplitter, a phase-insensitive Hong-Ou-Mandel type two-photon interference peak and dip fringes are observed, resulting from the two-photon interference effect between two indistinguishable two-photon probability amplitudes leading to a coincidence detection. A spatial quantum beating fringe is also measured for nondegenerate photon pairs in the same interferometer, although the two-photon states have no frequency entanglement. When unentangled polarization-correlated photons are used as an input state, the polarization entanglement is successfully recovered through the interferometer via delayed compensation.

Observation of two-photon interference effect with a single non-photon-number resolving detector

Multiphoton interference effects can be measured with a single detector when two input photons are temporally well separated when compared with the dead time of the single-photon avalanche detector. Here we experimentally demonstrate that the Hong-Ou-Mandel interference effect can be observed with a single non-photon-number resolving detector via a time-delayed coincidence measurement of successive electrical signals from the detector. The two-photon interference experiment is performed by utilizing temporally well-separated pairwise weak coherent pulses, and the interference fringes are successfully measured with high visibility in the range of the limited upper bound for the weak coherent photon source.

Point-spread function in ghost imaging system with thermal light

The point-spread function (PSF) is fundamental importance in estimating the imaging resolution in optical imaging systems. By using the Collins formula, a analytical imaging formula for ghost imaging system is obtained. The intensity fluctuation correlation function can be viewed as the convolution of the original object and a PSF. The imaging resolution is determined by the width of PSF. Based on the optical transfer matrix theory, we present the analytical formula describing the width of the PSF, by which one can estimate imaging resolution of a new-designed imaging scheme when compared with that of the existing imaging system. Several typical ghost imaging systems are chosen to verify experimentally our theoretical results.

Two-photon interference of temporally separated photons

We present experimental demonstrations of two-photon interference involving temporally separated photons within two types of interferometers: a Mach-Zehnder interferometer and a polarization-based Michelson interferometer. The two-photon states are probabilistically prepared in a symmetrically superposed state within the two interferometer arms by introducing a large time delay between two input photons; this state is composed of two temporally separated photons, which are in two different or the same spatial modes. We then observe two-photon interference fringes involving both the Hong-Ou-Mandel interference effect and the interference of path-entangled two-photon states simultaneously in a single interferometric setup. The observed two-photon interference fringes provide simultaneous observation of the interferometric properties of the single-photon and two-photon wavepackets. The observations can also facilitate a more comprehensive understanding of the origins of the interference phenomena arising from spatially bunched/anti-bunched two-photon states comprised of two temporally separated photons within the interferometer arms.

Few-photon heterodyne spectroscopy

We perform a high-resolution Fourier transform spectroscopy of optical sources in the few-photon regime based on the phenomenon of two-photon interference in a beam splitter. From the heterodyne interferogram, between test and reference sources, it is possible to obtain the spectrum of the test source relative to that of the reference. The method proves to be a useful asset for spectral characterization of faint optical sources below the range covered by classical heterodyne beating techniques.

Engineering two-photon high-dimensional states through quantum interference

Many protocols in quantum science, for example, linear optical quantum computing, require access to large-scale entangled quantum states. Such systems can be realized through many-particle qubits, but this approach often suffers from scalability problems. An alternative strategy is to consider a lesser number of particles that exist in high-dimensional states. The spatial modes of light are one such candidate that provides access to high-dimensional quantum states, and thus they increase the storage and processing potential of quantum information systems. We demonstrate the controlled engineering of two-photon high-dimensional states entangled in their orbital angular momentum through Hong-Ou-Mandel interference. We prepare a large range of high-dimensional entangled states and implement precise quantum state filtering. We characterize the full quantum state before and after the filter, and are thus able to determine that only the antisymmetric component of the initial state remains. This work paves the way for high-dimensional processing and communication of multiphoton quantum states, for example, in teleportation beyond qubits.

Generalized quantum interference of correlated photon pairs

Superposition and indistinguishablility between probability amplitudes have played an essential role in observing quantum interference effects of correlated photons. The Hong-Ou-Mandel interference and interferences of the path-entangled photon number state are of special interest in the field of quantum information technologies. However, a fully generalized two-photon quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and path-entangled photon number states has not yet been proposed. Here we report the experimental demonstrations of the generalized two-photon interferometry with both the interferometric properties of the Hong-Ou-Mandel effect and the fully unfolded version of the path-entangled photon number state using photon-pair sources, which are independently generated by spontaneous parametric down-conversion. Our experimental scheme explains two-photon interference fringes revealing single- and two-photon coherence properties in a single interferometer setup. Using the proposed interferometric measurement, it is possible to directly estimate the joint spectral intensity of a photon pair source.

Nonmonotonic quantum-to-classical transition in multiparticle interference

Quantum-mechanical wave-particle duality implies that probability distributions for granular detection events exhibit wave-like interference. On the single-particle level, this leads to self-interference--e.g., on transit across a double slit--for photons as well as for large, massive particles, provided that no which-way information is available to any observer, even in principle. When more than one particle enters the game, their specific many-particle quantum features are manifested in correlation functions, provided the particles cannot be distinguished. We are used to believe that interference fades away monotonically with increasing distinguishability--in accord with available experimental evidence on the single- and on the many-particle level. Here, we demonstrate experimentally and theoretically that such monotonicity of the quantum-to-classical transition is the exception rather than the rule whenever more than two particles interfere. As the distinguishability of the particles is continuously increased, different numbers of particles effectively interfere, which leads to interference signals that are, in general, nonmonotonic functions of the distinguishability of the particles. This observation opens perspectives for the experimental characterization of many-particle coherence and sheds light on decoherence processes in many-particle systems.

Experimental observation of a skewed X-type spatiotemporal correlation of ultrabroadband twin beams

This work presents the experimental observation of the nonfactorable near-field spatiotemporal correlation of ultrabroadband twin beams generated by parametric down-conversion, in an interferometric-type experiment using sum frequency generation, where both the temporal and the spatial degrees of freedom of parametric down-conversion light are controlled with high resolution. The revealed correlation is skewed in space-time in accordance with the X structure predicted by the theory.

Broadband source of polarization entangled photons

A broadband source of polarization entangled photons based on type-II spontaneous parametric down conversion from a chirped PPKTP crystal is presented. With numerical simulation and experimental evaluation, we report a source of broadband polarization entangled states with a bandwidth of approximately 125 nm for use in quantum interferometry. The technique has the potential to become a basis for the development of flexible broadband sources with designed spectral properties.

Experimental implementation of the multifunctional compact two-photon state analyzer

We report on experimental implementation of a multifunctional two-photon state analyzer. The device aims to be compact and able to provide several important characteristics about any two-photon quantum state. It operates in two modes: first mode is the two-photon interference analysis giving the information about spectral properties of the photons and the degree of mutual indistinguishability. The second mode provides polarization analysis and complete two-photon state tomography. Density matrix estimated from the tomography data reveals namely the quantum state purity or negativity. This device was tested on the photon pairs generated by the Kwiat source.

Quantum interference and entanglement of photons that do not overlap in time

We discuss the possibility of quantum interferences and entanglement of photons that exist at different intervals of time, i.e., one photon being recorded before the other has been created. The corresponding two-photon correlation function is shown to violate Bell's inequalities.

Quantum random number generator using photon-number path entanglement

We report a quantum random number generator based on the photon-number-path entangled state that is prepared by means of two-photon quantum interference at a beam splitter. The randomness in our scheme is truly quantum mechanical in origin since it results from the projection measurement of the entangled two-photon state. The generated bit sequences satisfy the standard randomness test.

The Hong-Ou-Mandel interferometer: a new procedure for alignment

Two major requirements in the construction of the Hong-Ou-Mandel interferometer are the alignment and length balancing of two optical paths. A new method is presented for meeting these requirements that requires no custom optics or expensive equipment. Using this method, a two photon interferometer sourced by degenerate noncollinear parametric photon pairs was aligned and the optical paths were balanced to within an average of 11.6 microm, yielding two-photon interference features with visibilities of approximately 0.9. The method is applicable to arbitrary noncollinear emission angles, including nondegenerate downconversion situations where the signal and idler emission angles differ.

Complete deterministic linear optics Bell state analysis

We show how hyperentanglement allows us to deterministically distinguish between all four polarization Bell states of two photons. In this proof-of-principle experiment, we employ the intrinsic time-energy correlation of photon pairs generated with high temporal definition in addition to the polarization entanglement obtained from parametric down-conversion. For the identification, no nonlinear optical elements or auxiliary photons are needed. The new possibilities this complete Bell measurement offers are demonstrated by realizing an optimal dense coding protocol.

Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?

Two-photon correlation phenomena, including the historical experiment of Hanbury Brown and Twiss, may have to be described quantum mechanically, regardless of whether the source of radiation is classical or quantum. Supporting this point, we present a ghost imaging type of second-order spatial correlation experiment of chaotic light to show that the classical understanding based on the concept of statistical intensity fluctuations does not give a correct interpretation for the observation. From a practical point of view, this experiment demonstrates the possibility of having high contrast lensless two-photon imaging with chaotic light, suggesting imaging applications for radiations for which no effective lens is available.

Experimental demonstration of continuous variable quantum erasing

We experimentally demonstrate the concept of continuous variable quantum erasing. The amplitude quadrature of the signal state is labeled to another state via a quantum nondemolition interaction, leading to a large uncertainty in the determination of the phase quadrature due to the inextricable complementarity of the two observables. We show that by erasing the amplitude quadrature information we are able to recover the phase quadrature information of the signal state.

Mode-locked two-photon states

The concept of mode locking in laser is applied to a two-photon state with frequency entanglement. Cavity enhanced parametric down conversion is found to produce exactly such a state. The mode-locked two-photon state exhibits a comblike correlation function. An unbalanced Hong-Ou-Mandel type interferometer is used to measure the correlation function. A revival of the typical interference dip is observed. We will discuss a scheme for engineering of quantum states in time domain.

Demonstration of nondeterministic quantum logic operations using linear optical elements

Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)] recently showed that nondeterministic quantum logic operations could be performed using linear optical elements, additional photons (ancilla), and postselection based on the output of single-photon detectors. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT (CNOT) gate and a quantum parity check. These two devices can be combined with a pair of entangled photons to implement a conventional (nondestructive) CNOT that succeeds with a probability of 1/4.

Time-resolved diffraction and interference: Young's interference with photons of different energy as revealed by time resolution

We present time-resolved diffraction and two-slit interference experiments using a streak camera as a detector for femtosecond pulses of photons. These experiments show how the diffraction pattern is built by adding frames of a few photons to each frame. It is estimated that after 300 photons the diffraction pattern emerges. With time resolution we can check the speed of light and put an upper limit of 2 ps at our resolution to the time for wave function collapse in the quantum measurement process. We then produce interference experiments with photons of different energies impinging on the slits, i.e. we know which photon impinges on each slit. We show that for poor time resolution, no interference is observed, but for high time resolution, we have interference that is revealed as beats of 100 GHz frequency. The condition for interference is that the two pulses should overlap spatially at the detector, even if the pulses have different energies but are generated from the same pulse of the laser. The interference seems to be in agreement with classical theory at first sight. However, closer study and analysis of the data show deviations in the visibility of the interference fringes and of their phase. These experiments are discussed in connection with quantum mechanics and it may be concluded that the time resolution provides new data for understanding the longstanding and continuing arguments on wave-particle duality initiated by Newton, Young, Fresnel, Planck and others. A thought experiment is presented in the appendix to try to distinguish the photons at the detector by making it sensitive to colour.

Generating entangled two-photon states with coincident frequencies

It is shown that parametric down-conversion, 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.

Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit

Classical optical lithography is diffraction limited to writing features of a size lambda/2 or greater, where lambda is the optical wavelength. Using nonclassical photon-number states, entangled N at a time, we show that it is possible to write features of minimum size lambda/(2N) in an N-photon absorbing substrate. This result allows one to write a factor of N2 more elements on a semiconductor chip. A factor of N = 2 can be achieved easily with entangled photon pairs generated from optical parametric down-conversion. It is shown how to write arbitrary 2D patterns by using this method.

Delayed "Choice" quantum eraser

We report a delayed "choice" quantum eraser experiment of the type proposed by Scully and Druhl (where the "choice" is made randomly by a photon at a beam splitter). The experimental results demonstrate the possibility of delayed determination of particlelike or wavelike behavior via quantum entanglement. The which-path or both-path information of a quantum can be marked or erased by its entangled twin even after the registration of the quantum.