Recently, we have showed a mechanism that could provide a great transmission enhancement of the light waves passed through subwavelength aperture arrays in thin metal films not by the plasmon-polariton waves, but by the constructive interference of diffracted waves (beams generated by the apertures) at the detector placed in the far-field zone. We now present a quantum reformulation of the model. The Hamiltonian describing the interference-induced enhancement of the intensity and energy of a multimode quantum optical field is derived. Such a field can be produced, for instance, by a subwavelength array of coherent light sources.
The Hamiltonians describing the energy nonconservation in boson and fermion multimode fields under quantum interference have been derived. We show that violation of the energy conservation is accompanied by the nonconservation of momentum, number of particles and field charge. The phenomena could be observed in Young's double-slit subwavelength (nanometer-scale) setup.
Differing from the traditional method of achieving subwavelength interference, we have demonstrated the two-photon subwavelength interference effect of broadband chaotic light in a polarization-selective Michelson interferometer with an ultrafast two-photon absorption detector the first time, which is achieved by manipulating two-photon probability amplitudes involved in the interference. In theory, the two-photon polarization coherence matrix and probability amplitudes matrix are combined to develop polarized two-photon interference terms, which explains the experimental results well. In orde…
We demonstrate optomechanical interference in a multimode system, in which an optical mode couples to two mechanical modes. A phase-dependent excitation-coupling approach is developed, which enables the observation of constructive and destructive optomechanical interferences. The destructive interference prevents the coupling of the mechanical system to the optical mode, suppressing optically-induced mechanical damping. These studies establish optomechanical interference as an essential tool for controlling the interactions between light and mechanical oscillators.
We show that a thermal light random in transverse direction can perform subwavelength double slit interference in a joint-intensity measurement. This is the classical version of quantum lithography, and it can be explained with the correlation of rays instead of the entanglement of photons.
Two-photon interference of multimode two-photon pairs produced by an optical parametric oscillator has been observed for the first time with an unbalanced interferometer. The time correlation between the multimode two photons has a multi-peaked structure. This property of the multimode two-photon state induces two-photon interference depending on delay time. The nonclassicality of this interference is also discussed.
The two-photon Hong-Ou-Mandel (HOM) interference is a pure quantum effect which indicates the degree of indistinguishability of photons. The four-photon HOM interference exhibits richer dynamics in comparison to the two-photon interference and simultaneously is more sensitive to the input photon states. We demonstrate theoretically and experimentally an explicit dependency of the four-photon interference to the number of temporal modes, created in the process of parametric down-conversion. Moreover, we exploit the splitting ratio of the beam splitter to manipulate the interference between bunc…
The extended Dirac's principle describes the interference between different particles as an effect of the multiparticle system with itself. In this paper we present a novel example, based on the detection of particles emitted in multimode states by independent sources, which illustrates in a simple way the necessity of extending the original Dirac's criterion.
We report the first demonstration of quantum interference in multimode interference (MMI) devices and a new complete characterization technique that can be applied to any photonic device that removes the need for phase stable measurements. MMI devices provide a compact and robust realization of NxM optical circuits, which will dramatically reduce the complexity and increase the functionality of future generations of quantum photonic circuits.
We consider multimode two-photon interference at a beam splitter by photons created by spontaneous parametric down-conversion. The resulting interference pattern is shown to depend upon the transverse spatial symmetry of the pump beam. In an experiment, we employ the first-order Hermite-Gaussian modes in order to show that, by manipulating the pump beam, one can control the resulting two-photon interference behavior. We expect these results to play an important role in the engineering of quantum states of light for use in quantum information processing and quantum imaging.
We experimentally observe the two-photon interference of multimode photon pairs produced by an optical parametric oscillator far below threshold via a michelson interferometer, which shows a multipeaked structure. We find that the correlation function when the interferometer is unbalanced is clearly dependent on the path difference and phase between two interfering beams, but the shape of correlation function in balanced case is independent on the small path difference and phase beside the height. All experimental results are well agreed with the theoretical prediction.
The multimode interference technique is a simple way to study the interference patterns found in many quantum probability distributions. We demonstrate that this analysis not only explains the existence of so-called "quantum carpets," but can explain the spatial distribution of channels and ridges in the carpets. With an understanding of the factors that govern these channels and ridges we have a limited ability to produce a particular pattern of channels and ridges by carefully choosing the weighting coefficients c_{n} . We also use these results to demonstrate why fractional revivals of init…
We report measurements of two-photon interference using a cw-pumped type-II spontaneous parametric down-conversion source based on a multimode perodically poled potassium titanyl phosphate waveguide. We have used the recently demonstrated technique of controlling the spatial characteristics of the down-conversion process via intermodal dispersion to generate photon pairs in fundamental transverse modes, thus ensuring their spatial indistinguishability. Good spatial overlap of photon modes within pairs has been verified using the Hong-Ou-Mandel interferometer and the preparation of polarization…
Multimode two-particle systems show interference effects in one-particle detections when both particles have common modes. We explore the possibility of extending the usual concepts of distinguishability and visibility to these types of systems. Distinguishability will refer now to the balance between common and different modes of a two-particle system, instead of the standard definition concerning available alternatives for a one-particle system. On the other hand, the usual concept of visibility is not suitable for our problem and must be replaced with that of contrast, measuring the ratio o…
Field-Widened Multimode Interferometer with Long Time-Bin Delay Using a Multi-Pass Herriott Cell
National Research Council of Canada（加拿大国家研究委员会）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Department of Physics & Astronomy, University of Waterloo（滑铁卢大学物理与天文系）；Department of Physics, Simon Fraser University（西蒙菲莎大学物理系）
The method of defining quantum joint probabilities of two events is applied to a multimode system of trapped Bose-condensed atoms. The coherent modes are generated by modulating the trapping potential with an alternating field with a frequency in resonance with a transition frequency between two coherent modes. The system is subjected to nondestructive measurements randomly influencing the phase difference of the modes. The joint probability of observing two events, corresponding to the observation of two states, is calculated by employing the channel-state duality. The interference term in th…
We review some recent experiments based upon multimode two-photon interference of photon pairs created by spontaneous parametric down-conversion. The new element provided by these experiments is the inclusion of the transverse spatial profiles of the pump, signal and idler fields. We discuss multimode Hong-Ou-Mandel interference, and show that the transverse profile of the pump beam can be manipulated in order to control two-photon interference. We present the basic theory and experimental results as well as several applications to the field of quantum information.
We experimentally realize an optical fiber ring resonator that includes a tapered section with subwavelength-diameter waist. In this section, the guided light exhibits a significant evanescent field which allows for efficient interfacing with optical emitters. A commercial tunable fiber beam splitter provides simple and robust coupling to the resonator. Key parameters of the resonator such as its out-coupling rate, free spectral range, and birefringence can be adjusted. Thanks to the low taper- and coupling-losses, the resonator exhibits an unloaded finesse of F=75+/-1, sufficient for reaching…
The studies of mechanical resonators in the quantum regime not only provide insight into the fundamental nature of quantum mechanics of massive objects, but also introduce promising platforms for novel hybrid quantum technologies. Here we demonstrate a configurable interaction between a superconducting qubit and many acoustic modes in the quantum regime. Specifically, we show how consecutive Landau-Zener-Stückelberg (LZS) tunneling type of transitions, which take place when a system is tuned through an avoided crossing of the coupled energy levels, interfere in a multimode system. The work pro…
The challenging requirements of large scale quantum information processing using parametric heralded single photon sources involves maximising the interference visibility whilst maintaining an acceptable photon generation rate. By developing a general theoretical framework that allows us to include large numbers of spatial and spectral modes together with linear and non-linear optical elements, we investigate the combined effects of spectral and photon number impurity on the measured Hong--Ou--Mandel interference visibility of parametric photon sources, considering both threshold and number re…
Beam-splitter operations are widely used to process information encoded in bosonic modes. In hybrid quantum systems, however, it might be challenging to implement a reliable beam-splitter operation between two distinct bosonic modes. Without beam-splitters, some basic operations such as decoupling modes and swapping states between modes can become highly non-trivial or not feasible at all. In this work, we develop novel interference-based protocols for decoupling and swapping selected modes of a multimode bosonic system without requiring beam-splitters. Specifically, for a given generic couple…
Multi-photon propagation in connected structures - a quantum walk - offers the potential for simulating complex physical systems and provides a route to universal quantum computation. Increasing the complexity of quantum photonic networks where the walk occurs is essential for many applications. Here, we implement a quantum walk of indistinguishable photon pairs in a multimode fiber supporting 380 modes. Using wavefront shaping, we control the propagation of the two-photon state through the fiber in which all modes are coupled. Excitation of arbitrary output modes of the system is realized by …
All Reflective Field-widened Unbalanced Interferometer for Quantum Sensing and Communication Applications
University of Waterloo（滑铁卢大学）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）；Department of Physics and Astronomy, University of Waterloo（滑铁卢大学物理与天文学系）；National Research Council of Canada（加拿大国家研究委员会）；Department of Chemical Engineering, University of Waterloo（滑铁卢大学化学工程系）；Department of Physics, Simon Fraser University（西蒙菲莎大学物理系）
We introduce a novel physical mechanism for achieving giant quality factors ($Q$-factors) in finite-length periodic arrays of subwavelength optical resonators. The underlying physics is based on interference between the band-edge mode and another standing mode in the array, and the formation of spatially localized states with dramatically suppressed radiative losses. We demonstrate this concept for an array of $N$ dipoles with simultaneous cancellation of multipoles up to $N$-th order and the $Q$ factor growing as $Q \propto N^α$, where $α\gtrsim 6.88$. Based on this finding, we propose a real…
The 'Ghost' interference experiment is analyzed when the source of entangled photons is a multimode Optical Parametric Amplifier(OPA) whose weak limit is the two-photon Spontaneous Parametric Downconversion(SPDC) beam. The visibility of the double-slit pattern is calculated, taking the finite coincidence time window of the photon counting detectors into account. It is found that the coincidence window and the bandwidth of light reaching the detectors play a crucial role in the loss of visibility on coincidence detection, not only in the 'Ghost' interference experiment but in all experiments in…
Few-photon transport via waveguide-coupled local quantum systems has attracted extensive theoretical and experimental studies. Most of the study has focused on atomic or atomic-like local quantum systems due to their strong light-matter interaction useful for quantum applications. Here, we study few-photon transport via a waveguide-coupled multimode optical cavity with second-order bulk nonlinearity. We develop a Feynman diagram approach and compute the scattering matrix of the one- and two-photon transport. Based on the calculated scattering matrix, we show highly nonclassical photonic effect…
Quantum probabilities are defined for several important physical cases characterizing measurements with multimode quantum systems. These are the probabilities for operationally testable measurements, for operationally uncertain measurements, and for entangled composite events. The role of the prospect and state entanglement is emphasized. Numerical modeling is presented for a two-mode Bose-condensed system of trapped atoms. The interference factor is calculated by invoking the channel-state duality.
We propose an all-optical scheme to control the photon statistics using hybrid quantum plasmonic system. With the aid of dressed states assisted quantum interference effects, it is shown that the photon correlations of a signal field can be continuously modulated from bunching to antibunching under the control of a pump field. Apart from the exact multimode model, a single-mode model and an analytical treatment are also provided to help us identify the roles of multimode coupling and quantum interference between probability amplitudes. The proposed scheme, in contrast to the cavity quantum ele…
Particle indistinguishability is at the heart of quantum statistics that regulates fundamental phenomena such as the electronic band structure of solids, Bose-Einstein condensation and superconductivity. Moreover, it is necessary in practical applications such as linear optical quantum computation and simulation, in particular for Boson Sampling devices. It is thus crucial to develop tools to certify genuine multiphoton interference between multiple sources. Here we show that so-called Sylvester interferometers are near-optimal for the task of discriminating the behaviors of distinguishable an…
Integrated quantum optics has drastically reduced the size of table-top optical experiments to the chip-scale, allowing for demonstrations of large-scale quantum information processing and quantum simulation. However, despite these advances, practical implementations of quantum photonic circuits remain limited because they consist of large networks of waveguide interferometers that path encode information which do not easily scale. Increasing the dimensionality of current quantum systems using higher degrees of freedom such as transverse spatial field distribution, polarization, time, and freq…
We study beating of a probe field with a time-varying susceptibility in a coherently prepared Raman medium. We consider the general case of an arbitrary variation of susceptibility, which corresponds to a superposition of an arbitrary number of excited Raman transitions. We derive a general analytical solution and conservation relations for this process. We show that the interference between Raman polarizations may substantially affect frequency modulation and pulse compression for the probe field.
One of the greatest challenges in utilizing multimode optical fibers is mode-mixing and inter-modal interference, which scramble the information delivered by the fiber. A common approach for canceling these effects is to tailor the optical field at the input of the fiber to obtain a desired field at its output. In this work, we present a new approach which relies on modulating the transmission matrix of the fiber rather than the incident light. We apply computer-controlled mechanical perturbations to the fiber to obtain a desired intensity pattern at its output. Using an all-fiber apparatus, w…
We study theoretically the dynamics of multiple mechanical oscillators coupled to a single cavity field mode via linear or quadratic optomechanical interactions. We focus specifically on the strong coupling regime where the cavity decays much faster than the mechanical modes, and the optomechanical coupling is comparable to or larger than the mechanical frequency, so that both the optical and mechanical systems operate in the deep quantum regime. Using the examples of one and two mechanical oscillators we show that the system can classically exhibit bistability and bifurcations, and we explore…
Quantum memory is a fundamental building block for large-scale quantum networks. On-demand optical storage with a large bandwidth, a high multimode capacity and an integrated structure simultaneously is crucial for practical application. However, this has not been demonstrated yet. Here, we fabricate an on-chip waveguide in a $\mathrm {^{151}Eu^{3+}:Y_2SiO_5}$ crystal with insertion losses of 0.2 dB, and propose a novel pumping scheme to enable spin-wave atomic frequency comb (AFC) storage with a bandwidth of 11 MHz inside the waveguide. Based on this, we demonstrate the storage of 200 tempora…
We bring together a cavity-enhanced light-matter interface with a multimode interferometer (MMI) integrated onto a photonic chip and demonstrate the potential of such hybrid systems to tailor distributed entanglement in a quantum network. The MMI is operated with pairs of narrowband photons produced a priori deterministically from a single 87Rb atom strongly coupled to a high-finesse optical cavity. Non-classical coincidences between photon detection events show no loss of coherence when interfering pairs of these photons through the MMI in comparison to the two-photon visibility directly meas…
We report on coherent and multi-temporal mode storage of light using the full atomic frequency comb memory scheme. The scheme involves the transfer of optical atomic excitations in Pr3+:Y2SiO5 to spin-waves in the hyperfine levels using strong single-frequency transfer pulses. Using this scheme, a total of 5 temporal modes are stored and recalled on-demand from the memory. The coherence of the storage and retrieval is characterized using a time-bin interference measurement resulting in visibilities higher than 80%, independent of the storage time. This coherent and multimode spin-wave memory i…
Exploiting multiple modes in a quantum acoustic device could enable applications in quantum information in a hardware-efficient setup, including quantum simulation in a synthetic dimension and continuous-variable quantum computing with cluster states.We develop a multimode surface acoustic wave (SAW) resonator with a superconducting quantum interference device (SQUID) integrated in one of the Bragg reflectors. The interaction with the SQUID-shunted mirror gives rise to coupling between the more than 20 accessible resonator modes. We exploit this coupling to demonstrate two-mode squeezing of SA…
We study the non-equilibrium dynamics of a coherently split one-dimensional (1d) Bose gas by measuring the full probability distribution functions of matter-wave interference. Observing the system on different length scales allows us to probe the dynamics of excitations on different energy scales, revealing two distinct length-scale dependent regimes of relaxation. We measure the crossover length-scale separating these two regimes and identify it with the prethermalized phase-correlation length of the system. Our approach enables a direct observation of the multimode dynamics characterizing on…
We measure the joint Q-function of a multi-spatial-mode field using a charge-coupled device array detector in an unbalanced heterodyne configuration. The intensity pattern formed by interference between a weak signal field and a strong local oscillator is resolved using Fourier analysis and used to reconstruct quadrature amplitude statistics for 22 spatial modes simultaneously. The local oscillator and signal propagate at an angle of 12 mrad thus shifting the classical noise to modes that do not overlap with the signal. In this configuration, balanced detection is not necessary.
We discuss characterization of single-photon wave packets by measuring Hong-Ou-Mandel interference with a weak coherent pulse. A complete multimode calculation is presented and effects of multiphoton terms in the coherent field as well as the impact of source and detection imperfections are discussed.
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…
We theoretically investigate quantum interference of two single photons at a lossy asymmetric beam splitter, the most general passive 2$\times$2 optical circuit. The losses in the circuit result in a non-unitary scattering matrix with a non-trivial set of constraints on the elements of the scattering matrix. Our analysis using the noise operator formalism shows that the loss allows tunability of quantum interference to an extent not possible with a lossless beam splitter. Our theoretical studies support the experimental demonstrations of programmable quantum interference in highly multimodal s…
The problem of defining quantum probabilities of composite events is considered. This problem is of high importance for the theory of quantum measurements and for quantum decision theory that is a part of measurement theory. We show that the Luders probability of consecutive measurements is a transition probability between two quantum states and that this probability cannot be treated as a quantum extension of the classical conditional probability. The Wigner distribution is shown to be a weighted transition probability that cannot be accepted as a quantum extension of the classical joint prob…
Quantum Schrodinger cat states are of great interest in quantum communications and quantum optics. These states are used in various scientific fields such as quantum computing, quantum error correction and high-precision measurements. The analysis of the Schrodinger cat states coherence is an important task for their complete practical application. Our developed approach makes it possible to estimate the coherence of the quantum Schrodinger cat state of arbitrary dimension, as well as to find the interference visibility of the state - an important optical characteristic. The obtained simple qu…
Coherent temporal filtering of multimode parametric down-conversion using a quantum pulse gate
Integrated Quantum Optics Group, Institute for Photonic Quantum Systems (PhoQS), Paderborn University（帕德博恩大学光子量子系统研究所）；School of Mathematics and Physics, University of Queensland（昆士兰大学数学与物理学院）
We study a driven-dissipative array of coupled nonlinear optical resonators by numerically solving the Von Neumann equation for the density matrix. We demonstrate that quantum correlated states of many photons can be generated also in the limit where the nonlinearity is much smaller than the losses, contrarily to common expectations. Quantum correlations in this case arise from interference between different pathways that the system can follow in the Hilbert space to reach its steady state under the effect of coherent driving fields. We characterize in particular two systems: a linear chain of…
We study the possibility of creating spatial patterns having subwavelength size by using the so-called dark states formed by the interaction between atoms and optical fields. These optical fields have a specified spatial distribution. Our experiments in Rb vapor display spatial patterns that are smaller than the length determined by the diffraction limit of the optical system used in the experiment. This approach may have applications to interference lithography and might be used in coherent Raman spectroscopy to create patterns with subwavelength spatial resolution.
Optical cavity QED provides a platform with which to explore quantum many-body physics in driven-dissipative systems. Single-mode cavities provide strong, infinite-range photon-mediated interactions among intracavity atoms. However, these global all-to-all couplings are limiting from the perspective of exploring quantum many-body physics beyond the mean-field approximation. The present work demonstrates that local couplings can be created using multimode cavity QED. This is established through measurements of the threshold of a superradiant, self-organization phase transition versus atomic pos…
High-visibility interference of photon echoes generated in spatially separated solid-state atomic ensembles is demonstrated. The solid state ensembles were LiNbO$_3$ waveguides doped with Erbium ions absorbing at 1.53 $μ$m. Bright coherent states of light in several temporal modes (up to 3) are stored and retrieved from the optical memories using two-pulse photon echoes. The stored and retrieved optical pulses, when combined at a beam splitter, show almost perfect interference, which demonstrates both phase preserving storage and indistinguishability of photon echoes from separate optical memo…
In this thesis we present a direct scheme for measuring quasidistribution functions of light. This scheme, based on photon counting, is derived from a simple relation linking the Wigner function with photon statistics. We develop a full multimode theory of the scheme, and show that the principle of the measurement can be straightforwardly generalized to the detection of the multimode radiation. We also discuss practical aspects of the scheme, including statistical error, non-unit detection efficiency, and imperfect interference visibility. Next, we report experimental realization of the scheme…
