Multiphoton Interference Research Articles

Optically induced currents in dielectrics and semiconductors as a nonlinear optical effect

We demonstrate theoretically that when well-below-the-bandgap femtosecond optical pulses propagate through a dielectric or semiconductor, DC current and charges are produced even though no real carriers are excited in the bands. The photoinduced current is a new ultrafast nonlinear optical effect based on multiphoton quantum interference and the creation of an asymmetric distribution of virtual carriers in the conduction and valence bands. We establish an unambiguous connection between the nonlinear optical conductivity responsible for the photoinduced DC currents and charges and the odd-order nonlinear optical susceptibilities of the material. We then apply our results to the recent experiments [Nature493, 70 (2013)10.1038/nature11567NATUAS0028-0836] in which photoinduced charges were observed in SiO2 irradiated by below-the-gap ultrashort optical pulses. Using a single well-known measured value of the third-order susceptibility (nonlinear index) of SiO2, we obtain excellent agreement with all the experimental data of [Nature493, 70 (2013)10.1038/nature11567NATUAS0028-0836]. A clear physical picture of the origin of the photoinduced currents and charges shows that the versatility of ultrafast (virtual) nonlinear optical phenomena extends even further than had been previously thought.

Generalized Multiphoton Quantum Interference

Non-classical interference of photons lies at the heart of optical quantum information processing. This effect is exploited in universal quantum gates as well as in purpose-built quantum computers that solve the BosonSampling problem. Although non-classical interference is often associated with perfectly indistinguishable photons this only represents the degenerate case, hard to achieve under realistic experimental conditions. Here we exploit tunable distinguishability to reveal the full spectrum of multi-photon non-classical interference. This we investigate in theory and experiment by controlling the delay times of three photons injected into an integrated interferometric network. We derive the entire coincidence landscape and identify transition matrix immanants as ideally suited functions to describe the generalized case of input photons with arbitrary distinguishability. We introduce a compact description by utilizing a natural basis which decouples the input state from the interferometric network, thereby providing a useful tool for even larger photon numbers.

Phase-dependent light switching in triple-Λ system

We theoretically studied a triple-Λ system comprising three pairs of coupling-probe fields. Three probe fields were phase-dependently switched with a switching depth above 80%, at which the group-velocity matching of all probe pulses was available under slow light-propagation conditions. We considered the probe susceptibility as the superposition of three-photon transitions to systematically understand the multi-photon interference in a triple-Λ system, which can be applied to systems with N−Λ (N≥1). This helped us to tailor the probe susceptibility by adjusting the detuning and phases of the coupling and probe fields. This work can be applied to all-optical switching gates for triple-photons and can enhance the speed of processing optical information.

Coherently stimulated parametric down-conversion, phase effects, and quantum-optical interferometry

We re-examine the properties of the states produced by nondegenerate coherently stimulated parametric down-conversion wherein the signal and idler modes are seeded with coherent states of light and where the nonlinear crystal is driven by a strong classical field as described by the parametric approximation. The states produced are the two-mode squeezed coherent states defined with a specific ordering of operators, namely, the displacement operators of the two modes acting on the double vacuum state followed by the action of the two-mode squeeze operator representing the down-conversion process. Though mathematically equivalent to the reverse ordering of operators, but with different displacement parameters, the ordering we consider is closely related to what could most easily be implemented in the laboratory. The statistical properties of the state are studied with an emphasis on how they, and its average photon number, are affected by the various controllable phases, namely, those of the classical pump field of the two input coherent states. We then consider the multiphoton interference effects that arise if the two beams are overlapped on a 50:50 beam splitter, investigating the role of the phases in controlling the statistical properties of the output states. Finally, we study the prospects for the application of the states to quantum-optical interferometry to obtain sensitivities in phase-shift measurements beyond the standard quantum limit.

Space-Time Quantum Imaging

We report on an experimental and theoretical investigation of quantum imaging where the images are stored in both space and time. Ghost images of remote objects are produced with either one or two beams of chaotic laser light generated by a rotating ground glass and two sensors measuring the reference field and bucket field at different space-time points. We further observe that the ghost images translate depending on the time delay between the sensor measurements. The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results. The theoretical model includes certain phase factors of the rotating ground glass. These experiments demonstrated a means to investigate the time and space aspects of ghost imaging and showed that ghost imaging contains more information per measured photon than was previously recognized where multiple ghost images are stored within the same ghost imaging data sets. This suggests new pathways to explore quantum information stored not only in multi-photon coincidence information but also in time delayed multi-photon interference. The research is applicable to making enhanced space-time quantum images and videos of moving objects where the images are stored in both space and time.

Vibrational noise removal method for the multi-photon interferometer of an optical loop system

Multi-photon interference effects of the optical loop in a double-Λ/V system aid coherent photon control, especially all-optical switching between single photons. In the multi-photon interference, phase fluctuations induced by the mechanical vibration of the optical components should be removed to observe the high fidelity of photon controls. We solved this problem by overlapping coupling and probe beams that have opposite phase shifts in the optical loop system to cancel out phase fluctuation induced by mechanical vibration. We used two independent laser sources to generate two pairs of coupling-probe fields that are resonant on a double-Λ system. The removal of vibrational phase fluctuation was confirmed by comparison with a normal phase-dependent light-switching experiment.

Charge-flux qubit coupled to a tank circuit in a strong low-frequency electromagnetic field

A superconducting charge-flux qubit coupled to a high-Q tank circuit was studied in a low-frequency electric field. A fine structure of the multiphoton resonance lines and quantum interference effects associated with the excitation of a quasi-two-level system due to the Landau–Zener–Stückelberg tunneling was observed. The results obtained for multiphoton resonant excitations and low-frequency oscillations of the average occupation of quantum levels were compared using different parameters of the measuring circuit. The mechanism responsible for the fine structure of resonance lines was considered. The method to measure the impedance arising in the tank circuit due to the oscillations of the superconducting current in the qubit and the main sources of decoherence were discussed.

Four-Photon Imaging with Thermal Light

In a near-field four-photon correlation measurement, ghost imaging with classical incoherent light is investigated. By applying the Klyshko advanced-wave picture, we consider the properties of four-photon spatial correlation and find that the fourth-order spatial correlation function can be decomposed into multiple lower-order correlation functions. On the basis of the spatial correlation properties, a proof-of-principle four-photon ghost imaging is proposed, and the effect of each part in a fourth-order correlation function on imaging is also analyzed. In addition, the similarities and differences among ghost imaging by fourth-, second-, and third-order correlations are also discussed. It is shown that the contrast and visibility of fourth-order correlated imaging are improved significantly, while the resolution is unchanged. Such studies can be very useful in better understanding multi photon interference and multi-channel correlation imaging.

Increased time resolution with multiphoton interference beating

I investigate a variation of Hong–Ou–Mandel interference where two interference filters with different central frequencies are placed in the two output-ports of a beam splitter. Taking photons as wavepackets in the time domain, we get a general analytic formula for the probability that N photons emerge in each output-port after interference. The probability is shown to oscillate as a cosine function modulated by a dip and the oscillation period is inversely proportional to N which indicates a better time resolution with multiphoton beating.

Experimental validation of photonic boson sampling

A boson sampling device is a specialised quantum computer that solves a problem which is strongly believed to be computationally hard for classical computers. Recently a number of small-scale implementations have been reported, all based on multi-photon interference in multimode interferometers. In the hard-to-simulate regime, even validating the device's functioning may pose a problem . In a recent paper, Gogolin et al. showed that so-called symmetric algorithms would be unable to distinguish the experimental distribution from the trivial, uniform distribution. Here we report new boson sampling experiments on larger photonic chips, and analyse the data using a scalable statistical test recently proposed by Aaronson and Arkhipov. We show the test successfully validates small experimental data samples against the hypothesis that they are uniformly distributed. We also show how to discriminate data arising from either indistinguishable or distinguishable photons. Our results pave the way towards larger boson sampling experiments whose functioning, despite being non-trivial to simulate, can be certified against alternative hypotheses.

Compression of ultrashort laser pulses via gated multiphoton intrapulse interference phase scans

Delivering femtosecond laser light in the focal plane of a high numerical aperture microscope objective is still a challenge, despite significant developments in the generation of ultrashort pulses. One of the most popular techniques, used to correct phase distortions resulting from propagation through transparent media, is the multiphoton intrapulse interference phase scan (MIIPS). The accuracy of MIIPS however is limited when higher order phase distortions are present. Here we introduce an improvement, called Gated-MIIPS, which avoids shortcomings of MIIPS, reduces the influence of higher order phase terms, and can be used to more efficiently compress broad band laser pulses even with a simple 4f pulse shaper setup. In this work we present analytical formulas for MIIPS and Gated-MIIPS valid for chirped Gaussian pulses; we show an approximated analytic expression for Gated-MIIPS valid for arbitrary pulse shapes; finally we demonstrate the increased accuracy of Gated-MIIPS via experiment and numerical simulation.

Visualization of high-order dispersion for compression of few-cycle pulses

We present a visually intuitive method for higher-order dispersion compensation based on multi-photon interpulse interference pulse scans. The dispersion values obtained from these scans are fed back as a correction to an acousto-optical programmable dispersive filter to compensate residual higher-order dispersions up to fifth order. This method is applied to the dispersion management of a non-collinear optical parametric chirped-pulse amplifier. A grism-pair stretcher is designed based on a global dispersion balance which provides a large stretching factor and supports a spectral bandwidth of up to 320 nm. It is implemented in a two-stage three-pass non-collinear optical parametric chirped-pulse amplifier and stretches 6-fs seed pulses to about 80 ps from 700 to 1,000 nm. The amplified pulses are compressed by material dispersion. Pulses of less than 10-fs duration with a pulse energy of 125 μJ are obtained at 20-kHz repetition rate.

Indistinguishability and correlations of photons generated by quantum emitters undergoing spectral diffusion

Photon-based quantum information processing is based on manipulating multi photon interference. We focus on the Hong-Ou-Mandel (HOM) dip in the photon coincidence rate which provides a direct measure of interference of indistinguishable photons linked to their Bose statistics. The effect has been first observed with entangled photons generated by parametric down conversion and then extended to independent emitters. Fluctuations caused by coupling between emitters and a bath can erode the interference which causes the dip. Here we show how the magnitude and shape of the HOM dip is affected by spectral diffusion induced by coupling to a brownian oscillator bath. Conditions for maintaining and controlling the interference are specified.

Real-time single-shot measurement and correction of pulse phase and amplitude for ultrafast lasers

The transition of femtosecond lasers from the laboratory to commercial applications requires real-time automated pulse compression, ensuring optimum performance without assistance. Single-shot phase measure- ments together with closed-loop optimization based on real-time multiphoton intrapulse interference phase scan are demonstrated. On-the-fly correction of amplitude, as well as second- and third-order phase distortions based on the real-time measurements, is accomplished by a pulse shaper.© 2014 Society of Photo-Optical Instrumentation Engineers

Spectral phase measurement and compensation of femtosecond laser pulse based on multi-photon intra-pulse interference phase scan

In this paper, we develop a system that can be used to measure and compensate spectral phase of femtosecond laser pulses based on the multi-photon intra-pulse interference phase scan (MIIPS). In the system, a liquid crystal spatial light modulator (LC-SLM) is used to impose phase scan on the femtosecond laser pulse, while a spectrometer is used to record the MIIPS trace. Both the LC-SLM and the spectrometer are driven by home-developed LabVIEW programs. By analyzing the MIIPS trace, we obtain the spectral phase of the pre-chirped femtosecond laser pulse with only 3-times iteration. The femtosecond laser pulse is centered at 810 nm and has a repetition of 1 kHz. The accuracy of our measurement is less than ±0.1 rad. The measured phases are compensated by the LC-SLM, then we obtain a femtosecond laser pulse which is almost in the transform limit state. The device will be useful in many fields, for example, multi-photon microscopy, pulse shaping, and femtosecond laser spectroscopy etc.

Non-monotonic projection probabilities as a function of distinguishability

Typically, quantum superpositions, and thus measurement projections of quantum states involving interference, decrease (or increase) monotonically as a function of increased distinguishability. Distinguishability, in turn, can be a consequence of decoherence, for example caused by the (simultaneous) loss of excitation or due to inadequate mode matching (either deliberate or indeliberate). It is known that for some cases of multi-photon interference a non-monotonic decay of projection probabilities occurs, which has so far been attributed to interference between four or more photons. We show that such a non-monotonic behavior of projection probabilities is not unnatural, and can also occur for single-photon and even semiclassical states. Thus, while the effect traces its roots from indistinguishability and thus interference, the states for which this can be observed do not need to have particular quantum features.

Two-photon quantum interference in integrated multi-mode interference devices

Multi-mode interference (MMI) devices fabricated in silicon oxynitride (SiON) with a refractive index contrast of 2.4% provide a highly compact and stable platform for multi-photon non-classical interference. MMI devices can introduce which-path information for photons propagating in the multi-mode section which can result in degradation of this non-classical interference. We theoretically derive the visibility of quantum interference of two photons injected in a MMI device and predict near unity visibility for compact SiON devices. We complement the theoretical results by experimentally demonstrating visibilities of up to 97.7% in 2×2 MMI devices without the requirement of narrow-band photons.

Observation of detection-dependent multi-photon coherence times

The coherence time constitutes one of the most critical parameters that determines whether or not interference is observed in an experiment. For photons, it is traditionally determined by the effective spectral bandwidth of the photon. Here we report on multi-photon interference experiments in which the multi-photon coherence time, defined by the width of the interference signal, depends on the number of interfering photons and on the measurement scheme chosen to detect the particles. A theoretical analysis reveals that all multi-photon interferences with more than two particles feature this dependence, which can be attributed to higher-order effects in the mutual indistinguishability of the particles. As a striking consequence, a single, well-defined many-particle quantum state can exhibit qualitatively different degrees of interference, depending on the chosen observable. Therefore, optimal sensitivity in many-particle quantum interferometry can only be achieved by choosing a suitable detection scheme.

Integrated multimode interferometers with arbitrary designs for photonic boson sampling

The evolution of bosons undergoing arbitrary linear unitary transformations quickly becomes hard to predict using classical computers as we increase the number of particles and modes. Photons propagating in a multiport interferometer naturally solve this so-called boson sampling problem1, thereby motivating the development of technologies that enable precise control of multiphoton interference in large interferometers2,3,4. Here, we use novel three-dimensional manufacturing techniques to achieve simultaneous control of all the parameters describing an arbitrary interferometer. We implement a small instance of the boson sampling problem by studying three-photon interference in a five-mode integrated interferometer, confirming the quantum-mechanical predictions. Scaled-up versions of this set-up are a promising way to demonstrate the computational advantage of quantum systems over classical computers. The possibility of implementing arbitrary linear-optical interferometers may also find applications in high-precision measurements and quantum communication5.

Multiphoton quantum interference with high visibility using multiport beam splitters

Multiphoton states can be produced in multiple parametric down-conversion (PDC) processes. The nonlinear crystal in such a case is pumped with high power. In theory, the more populated these states are, the deeper is the conflict with local realistic description. However, the interference contrast in multiphoton PDC experiments can be quite low for high pumping. We show how the contrast can be improved. The idea employs currently accessible optical devices, the multiport beam splitters. They are capable of splitting the incoming light in one input mode to $M$ output modes. Our scheme works as a positive operator-valued measure filter. It may provide a feasible Clauser-Horne-Shimony-Holt-Bell inequality test, and thus can be useful in, e.g., schemes reducing communication complexity.