Transformations achievable by linear optical components allow to generate the whole unitary group only when restricted to the one-photon subspace of a multimode Fock space. In this paper, we address the more general problem of encoding quantum information by multiphoton states, and elaborating it via ancillary extensions, linear optical passive devices and photodetection. Our scheme stems in a natural way from the mathematical structures underlying the physics of linear optical passive devices. In particular, we analyze an economical procedure for mapping a fiducial 2-photon 2-mode state into an arbitrary 2-photon 2-mode state using ancillary resources and linear optical passive N-ports assisted by post-selection. We found that adding a single ancilla mode is enough to generate any desired target state. The effect of imperfect photodetection in post-selection is considered and a simple trade-off between success probability and fidelity is derived.
We present a review of theoretical and experimental aspects of multiphoton quantum optics. Multiphoton processes occur and are important for many aspects of matter-radiation interactions that include the efficient ionization of atoms and molecules, and, more generally, atomic transition mechanisms; system-environment couplings and dissipative quantum dynamics; laser physics, optical parametric processes, and interferometry. A single review cannot account for all aspects of such an enormously vast subject. Here we choose to concentrate our attention on parametric processes in nonlinear media, w…
It has been shown that there are not only transverse but also longitudinal couplings between microwave fields and a superconducting qubit with broken inversion symmetry of the potential energy. Using multiphoton processes induced by longitudinal coupling fields and frequency matching conditions, we design a universal algorithm to produce arbitrary superpositions of two-mode photon states of microwave fields in two separated transmission line resonators, which are coupled to a superconducting qubit. Based on our algorithm, we analyze the generation of evenly-populated states and NOON states. Co…
We examine an experimental setup implementing a family of quantum non-Gaussian filters. The filters can be applied to an arbitrary two-mode input state. We assume realistic photodetection in the filtering process and explore two different models of inefficient detection: a beam splitter of a small reflectivity located in front of a perfect detector and a Weierstrass transform applied to the unperturbed measurement outcomes. We explicitly give an operator which describes the coherent action of the filters in the realistic experimental conditions. The filtered states may find applications in qua…
Based on heralded interference on a six-port Mach-Zehnder interferometer, we propose protocols to generate a series of multiphoton states in primary output port, by injecting a coherent state in primary input port and two Fock states in two ancillary input ports, and measuring two Fock states in two ancillary output ports. Only manipulating at the single-photon level (i.e, |0> or |1>) in all ancillary ports, we generate sixteen types (six categories) of multiphoton nonclassical states, whose state vectors are unified as superposition of a new coherent state, a single-photon added coherent stat…
The quantum theory of electromagnetic radiation predicts characteristic statistical fluctuations for light sources as diverse as sunlight, laser radiation and molecule fluorescence. Indeed, these underlying statistical fluctuations of light are associated with the fundamental physical processes behind their generation. In this contribution, we demonstrate that the manipulation of the quantum electromagnetic fluctuations of a pair of vacuum states leads to a novel family of quantum-correlated multiphoton states with tunable mean photon numbers and degree of correlation. Our technique relies on …
We have developed a theory for accessing quantum coherences in mutually unbiased bases associated with generalized Pauli operators in multiphoton multimode linear optics networks (LONs). We show a way to construct complementary Pauli measurements in multiphoton LONs and establish a theory for evaluation of their photonic measurement statistics without dealing with the computational complexity of Boson samplings. This theory extends characterization of complementary properties in single-photon LONs to multiphoton LONs employing convex-roof extension. It allows us to detect quantum properties su…
We have examined both single and entangled two-mode multiphoton coherent states and shown how the `Janus-faced' properties between two partner states are mirrored in appropriate tomograms. Entropic squeezing, quadrature squeezing and higher-order squeezing properties for a wide range of nonclassical states are estimated directly from tomograms. We have demonstrated how squeezing properties of two-mode entangled states produced at the output port of a quantum beamsplitter are sensitive to the relative phase between the reflected and transmitted fields. This feature allows for the possibility of…
Single and two-mode multiphoton states are the cornerstone of many quantum technologies, e.g., metrology. In the optical regime these states are generally obtained combining heralded single-photons with linear optics tools and post-selection, leading to inherent low success probabilities. In a recent paper, we design several protocols that harness the long-range atomic interactions induced in waveguide QED to improve fidelities and protocols of single-mode multiphoton emission. Here, we give full details of these protocols, revisit them to simplify some of their requirements and also extend th…
We develop a theory for the interaction of multi-level atoms with multi-mode cavities yielding cavity-enhanced multi-photon resonances. The locations of the resonances are predicted from the use of effective two- and three-level Hamiltonians. As an application we show that quantum gates can be realised when photonic qubits are encoded on the cavity modes in arrangements where ancilla atoms transit the cavity. The fidelity of operations is increased by conditional measurements on the atom and by the use of a selected, dual-rail, Hilbert space. A universal set of gates is proposed, including the…
Determining an unknown quantum state from an ensemble of identical systems is a fundamental, yet experimentally demanding, task in quantum science. Here we study the number of measurement bases needed to fully characterize an arbitrary multi-mode state containing a definite number of photons, or an arbitrary mixture of such states. We show this task can be achieved using only linear optics and photon counting, which yield a practical though non-universal set of projective measurements. We derive the minimum number of measurement settings required and numerically show that this lower bound is s…
Multiphoton entanglement, as a quantum resource, plays an essential role in linear optical quantum information processing. Krenn et al. (Phys. Rev. Lett. 118, 080401 2017) proposed an innovative scheme that generating entanglement by path identity, in which two-photon interference (called Hong-Ou-Mandel effect) is not necessary in experiment. However, the experiments in this scheme have strict requirements in stability and scalability, which is difficult to be realized in bulk optics. To solve this problem, in this paper we first propose an on-chip scheme to generate multi-photon polarization …
Distributed Phase Sensing with Multiphoton States in Optical Interferometry
Politecnico di Bari（巴里理工大学）；Dipartimento Interateneo di Fisica, Politecnico di Bari（巴里理工大学联合物理系）；Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Bari（意大利国家核物理研究所（INFN）巴里分部）
We present a scheme, based only on linear optics and standard photon detection, that allows to generate heralded multiphoton entangled states of arbitrary photon number from spontaneous parametric downconversion (PDC) in the weak interaction regime. The scheme also works in the strong interaction regime, i.e., for the production of large photon numbers, when photon-number resolving detectors with nearly perfect quantum efficiency are used. In addition, the same setup can be used for quantum metrology as multiphoton interferometer with sensitivity at the Heisenberg limit.
Strong correlation of photons, particularly in the single-photon regime, has recently been exploited for various applications in quantum information processing. Existing correlation measurements, however, do not fully characterize multi-photon correlation in a relevant context and may pose limitations in practical situations. We propose a conceptually rigorous, but easy-to-implement, criterion for detecting correlated multi-photon emission out of a quantum optical system, drawn from the context of wavefunction collapse. We illustrate the robustness of our approach against experimental limitati…
Photon entanglement is an essential ingredient for linear optics quantum computing schemes, quantum cryptographic protocols and fundamental tests of quantum mechanics. Here we describe a setup that allows for the generation of polarisation-entangled N-photon states on demand. The photons are obtained by mapping the entangled state of N atoms, each of them trapped inside an optical cavity, onto the free radiation field. The required initial state can be prepared by performing postselective measurements on the collective emission from the cavities through a multiport beamsplitter.
The new process of quantum-injection into an optical parametric amplifier operating in entangled configuration is adopted to amplify into a large dimensionality spin 1/2 Hilbert space the quantum entanglement and superposition properties of the photon-couples generated by parametric down-conversion. The structure of the Wigner function and of the field's correlation functions shows a decoherence-free, multiphoton Schroedinger-cat behaviour of the emitted field which is largely detectable against the squeezed-vacuum noise. Furthermore, owing to its entanglement character, the system is found to…
Multiphoton entanglement is an important resource for linear optics quantum computing. Here we show that a wide range of highly entangled multiphoton states, including W-states, can be prepared by interfering single photons inside a Bell multiport beam splitter and using postselection. A successful state preparation is indicated by the collection of one photon per output port. An advantage of the Bell multiport beam splitter is that it redirects the photons without changing their inner degrees of freedom. The described setup can therefore be used to generate polarisation, time-bin and frequenc…
Multi-photon processes are the essence of nonlinear optics. Optical harmonics generation and multi-photon absorption, ionization, polymerization or spectroscopy are widely used in practical applications. Generally, the rate of an n-photon effect scales as the n-th order autocorrelation function of the incident light, which is high for light with strong photon-number fluctuations. Therefore `noisy' light sources are much more efficient for multi-photon effects than coherent sources with the same mean power, pulse duration and repetition rate. Here we generate optical harmonics of order 2-4 from…
Many recent experiments employ several parametric down conversion (PDC) sources to get multiphoton interference. Such interference has applications in quantum information. We study here how effects due to photon statistics, misalignment, and partial distinguishability of the PDC pairs originating from different sources may lower the interference contrast in the multiphoton experiments.
When an atom is strongly coupled to a cavity, the two systems can exchange a single photon through a coherent Rabi oscillation. This process enables precise quantum-state engineering and manipulation of atoms and photons in a cavity, which play a central role in quantum information and measurement. Recently, a new regime of cavity QED has been reached experimentally where the strength of the interaction between light and artificial atoms (qubits) becomes comparable to the atomic transition frequency or the resonance frequency of the cavity mode. Here we show that this regime can strongly modif…
A multiphoton collective phase is a multiphoton-scattering feature that cannot be reduced to a sequence of two-photon scattering events, and the three-photon "triad phas" is the smallest nontrivial example. Observing a higher-order collective phase is experimentally challenging, and only triad and four-photon tetrad collective phases have been observed. We introduce a scheme to make higher-order multiphoton collective-phase observations feasible by designing a sparse interferometer, which significantly reduces complexity compared with the current best scheme for observing a multiphoton collect…
We present the proposition of an experiment in which the multiphoton quantum superposition consisting of N= 10^5 particles generated by a quantum-injected optical parametric amplifier (QI-OPA), seeded by a single-photon belonging to an EPR entangled pair, is made to interact with a Mirror-BEC shaped as a Bragg interference structure. The overall process will realize a Macroscopic Quantum Superposition (MQS) involving a microscopic single-photon state of polarization entangled with the coherent macroscopic transfer of momentum to the BEC structure, acting in space-like separated distant places.
We consider a multiphoton Bell-type inequality to study nonlocality in four-mode continuous variable systems, which goes beyond two-photon states and can be applied to mixed as well as states with fluctuating photon number. We apply the inequality to a wide variety of states such as pure and mixed Gaussian states (including squeezed thermal states) and non-Gaussian states. We consider beam splitters as a model for leakage and show that the inequality is able to detect nonclassicality of noisy Gaussian states as well. Finally, we investigate nonlocality in pair-coherent states and entangled coh…
We propose a Bell measurement scheme by employing a logical qubit in Greenberger-Horne-Zeilinger (GHZ) entanglement with an arbitrary number of photons. Remarkably, the success probability of the Bell measurement as well as teleportation of the GHZ entanglement can be made arbitrarily high using only linear optics elements and photon on-off measurements as the number of photons increases. Our scheme outperforms previous proposals using single photon qubits when comparing the success probabilities in terms of the average photon usages. It has another important advantage for experimental feasibi…
Multiphoton quantum interference underpins fundamental tests of quantum mechanics and quantum technologies. Consequently, the detrimental effect of photon distinguishability in multiphoton interference experiments can be catastrophic. Here, we employ correlation measurements in the photonic inner modes, time or frequency, to restore quantum interference between photons differing in their colors or injection times in arbitrary linear optical networks, without the need for additional filtering or post selection. Interestingly, we demonstrate how harnessing the multiphoton inner-mode quantum info…
The estimation of high order correlation function values is an important problem in the field of quantum computation. We show that the problem can be reduced to preparation and measurement of optical quantum states resulting after annihilation of a set number of quanta from the original beam. We apply this approach to explore various photon bunching regimes in optical states with gamma-compounded Poisson photon number statistics. We prepare and perform measurement of the thermal quantum state as well as states produced by subtracting one to ten photons from it. Maximum likelihood estimation is…
The multiphoton Jaynes-Cummings model is investigated and applications in quantum information science are explored. Considering the strong atom-field coupling regime and an $N$-photon interaction, a nonlinear driving field can perform an arbitrary rotation in the Fock space of the cavity mode involving the vacuum and an $M$-Fock state, with $M<N$. Besides, driving the cavity mode with a linear coherent field (superposition of many Fock states), only the cavity states within the Fock subspace {$|0\rangle,|1\rangle,..., |N-1\rangle$} can be populated, i.e., we show how to implement a Fock state …
We propose a fruitful scheme for exploring multiphoton entangled states based on linear optics and weak nonlinearities. Compared with the previous schemes the present method is more feasible because there are only small phase shifts instead of a series of related functions of photon numbers in the process of interaction with Kerr nonlinearities. In the absence of decoherence we analyze the error probabilities induced by homodyne measurement and show that the maximal error probability can be made small enough even when the number of photons is large. This implies that the present scheme is quit…
Triggered single-photon sources produce the vacuum state with non-negligible probability, but produce a much smaller multiphoton component. It is therefore reasonable to approximate the output of these photon sources as a mixture of the vacuum and single-photon states. We show that it is impossible to increase the probability for a single photon using linear optics and photodetection on fewer than four modes. This impossibility is due to the incoherence of the inputs; if the inputs were pure-state superpositions, it would be possible to obtain a perfect single-photon output. In the more genera…
Engineering multiphoton states is an outstanding challenge with applications in multiple fields, such as quan- tum metrology, quantum lithography or even biological systems. State-of-the-art methods to obtain them rely on post-selection, multi-level systems or Rydberg atomic ensembles. Recently, it was shown that a strongly driven two-level system interacting with a detuned cavity mode can be engineered to continuously emit n-photon states. In the present work, we show that spectral filtering of its emission relaxes considerably the requirements on the system parameters even to the more access…
It was shown that using multiphoton qubits, a nearly deterministic Bell-state measurement can be performed with linear optics and on-off photodetectors [Phys. Rev. Lett. 114, 113603 (2015)]. However, multiphoton qubits are generally more fragile than single-photon qubits under a lossy environment. In this paper, we propose and analyze a scheme to teleport multiphoton-qubit information using hybrid entanglement with a loss-tolerant carrier qubit. We consider three candidates for the carrier qubit: a coherent-state qubit, a single-photon polarization qubit, and a vacuum-and-single-photon qubit. …
We introduce a formalism of nonlinear canonical transformations for general systems of multiphoton quantum optics. For single-mode systems the transformations depend on a tunable free parameter, the homodyne local oscillator angle; for n-mode systems they depend on n heterodyne mixing angles. The canonical formalism realizes nontrivial mixings of pairs of conjugate quadratures of the electromagnetic field in terms of homodyne variables for single-mode systems; and in terms of heterodyne variables for multimode systems. In the first instance the transformations yield nonquadratic model Hamilton…
We answer the question whether linear-optical processing of the states produced by one or multiple imperfect single-photon sources can improve the single-photon fidelity. This processing can include arbitrary interferometers, coherent states, feedforward, and conditioning on results of detections. We show that without introducing multiphoton components, the single-photon fraction in any of the single-mode states resulting from such processing cannot be made to exceed the efficiency of the best available photon source. If multiphoton components are allowed, the single-photon fidelity cannot be …
The quantum statistical fluctuations of the electromagnetic field establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broa…
We present an algorithm of quantum engineering of large-amplitude>5 high-fidelity>0.99 even/odd Schrodinger cat states (SCSs) using a single mode squeezed vacuum (SMSV) state as resource. Set of k beam splitters (BSs) with arbitrary transmittance and reflectance coefficients sequentially following each other acts as a hub that redirects a multiphoton state into the measuring modes simultaneously measured by photon number resolving (PNR) detectors. We show that the multiphoton state splitting guarantees significant increase of the success probability of the cat state generator compared to its i…
We investigate the multiphoton quantum dynamics of a leaking single-mode quantized cavity field coupled with a resonantly driven two-level system possessing permanent dipoles. The frequencies of the interacting subsystems are being considered very different, e.g., microwave ranges for the cavity and optical domains for the frequency of the two-level emitter, respectively. In this way, the emitter couples to the resonator mode via its diagonal dipole moments only. Furthermore, the generalized Rabi frequency resulting form the external coherent driving of the two-level subsystem is assumed as we…
In terms of the characteristic functions of the quantum states, we present a complete operator description of a lossy photon-subtraction scheme. Feeding a single-mode squeezed vacuum into a variable beam splitter and counting the photons in one of the output channels, a broad class of multiphoton-subtracted squeezed vacuum states (MSSVSs) can be generated in other channel. Here the losses are considered in the beginning and the end channels in the circuit. Indeed, this scheme has been discussed in Ref. [Phys. Rev. A 100, 022341 (2019)]. However, different from the above work, we give all the d…
We propose and analyze a multiphoton-state coherent transport protocol in a coupled-resonator quantum network. A multiphoton swap gate between two antipodes can be achieved with neither external modulation nor coupling strength engineering. Moreover, we extend this result to a coupled-resonator chain of arbitrary length with different coupling strengths. Effects of decoherence via quantum nondemolition interaction are studied with sources including vacuum quantum fluctuation and bath thermal excitations when the bath is in the thermal equilibrium state. These observations are helpful to unders…
Extending the scheme developed for a single mode of the electromagnetic field in the preceding paper ``Structure of multiphoton quantum optics. I. Canonical formalism and homodyne squeezed states'', we introduce two-mode nonlinear canonical transformations depending on two heterodyne mixing angles. They are defined in terms of hermitian nonlinear functions that realize heterodyne superpositions of conjugate quadratures of bipartite systems. The canonical transformations diagonalize a class of Hamiltonians describing non degenerate and degenerate multiphoton processes. We determine the coherent…
The absence of optical afterglow at some gamma-ray bursts (so called dark bursts) requires analyses of physical features of this phenomenon. It is shown that such singularity can be connected with multiphoton processes of frequencies summation in the Rayleigh- Jeans part of spectra, their pumping into higher frequencies. It can be registered most probably on young objects with still thin plasma coating, without further thermalization, i.e. soon after a prompt beginning of the explosive activity.
Multiphoton heralding generates large-amplitude squeezed Schrödinger cat states and parity-selective Fock superpositions from squeezed vacuum via an OPA
Single photons are a vital resource for optical quantum information processing. Efficient and deterministic single photon sources do not yet exist, however. To date, experimental demonstrations of quantum processing primitives have been implemented using non-deterministic sources combined with heralding and/or postselection. Unfortunately, even for eight photons, the data rates are already so low as to make most experiments impracticable. It is well known that quantum memories, capable of storing photons until they are needed, are a potential solution to this `scaling catastrophe'. Here, we an…
We investigate how multiphoton quantum states obtained through optical parametric amplification can be manipulated by performing a measurement on a small portion of the output light field. We study in detail how the macroqubit features are modified by varying the amount of extracted information and the strategy adopted at the final measurement stage. At last the obtained results are employed to investigate the possibility of performing a microscopic-macroscopic non-locality test free from auxiliary assumptions.
The efficient simulation of quantum systems is a primary motivating factor for developing controllable quantum machines. For addressing systems with underlying bosonic structure, it is advantageous to utilize a naturally bosonic platform. Optical photons passing through linear networks may be configured to perform quantum simulation tasks, but the efficient preparation and detection of multiphoton quantum states of light in linear optical systems are challenging. Here, we experimentally implement a boson sampling protocol for simulating molecular vibronic spectra [Nature Photonics $\textbf{9}$…
