We report the generation of a type-I multimode two-photon state on a rubidium D$_2$ line (780 nm) using periodically poled KTiOPO$_4$ crystals. With a degenerate optical parametric oscillator far below threshold, we observe an oscillatory correlation function, the cross-correlation between two photons shows a cavity bandwidth of about 7.8 MHz. We also use a Fabry-P$\acute{\rm{e}}$rot etalon to filter its most longitudinal modes and observe its time correlation function. The experimental data are well fitted to theoretical curves. This system could be utilized for demonstrating storage and retrieval of narrowband photons in Rb atomic ensembles, which is important for long-distance quantum communication.
We apply collective Raman scattering to create, store and retrieve spatially multimode light in warm rubidium-87 vapors. The light is created in a spontaneous Stokes scattering process. This is accompanied by the creation of counterpart collective excitations in the atomic ensemble -- the spin waves. After a certain storage time we coherently convert the spin waves into the light in deterministic anti-Stokes scattering. The whole process can be regarded as a delayed four-wave mixing which produces pairs of correlated, delayed random images. Storage of higher order spatial modes up to microseco…
Diffusion is the main limitation of storage time in spatially multimode applications of warm atomic vapors. Precise knowledge of diffusional decoherence in the system is desired for designing most of vapor memory setups. Here we present a novel, efficient and direct method of measuring unbiased diffusional decoherence, clearly distinguished from all other decoherence sources. We found the normalized diffusion coefficients of rubidium atoms in noble gases to be as follows: neon 0.20 cm$^{2}$/s, krypton 0.068 cm$^{2}$/s and we are the first to give an experimental result for rubidium in xenon: 0…
We experimentally investigate the optical storage of perfect optical vortex (POV) and spatially multimode perfect optical vortex (MPOV) beams via electromagnetically induced transparency (EIT) in a hot vapor cell. In particular, we study the role that phase gradients and phase singularities play in reducing the blurring of the retrieved images due to atomic diffusion. Three kinds of manifestations are enumerated to demonstrate such effect. Firstly, the suppression of the ring width broadening is more prominent for POVs with larger orbital angular momentum (OAM). Secondly, the retrieved double-…
Quantum correlations and entanglement shared among multiple quantum modes are important for both fundamental science and the future development of quantum technologies. This development will also require an efficient quantum interface between multimode quantum light sources and atomic ensembles, which makes it necessary to implement multimode quantum light sources that match the atomic transitions. Here we report on such a source that provides a method for generating quantum correlated beams that can be extended to a large number of modes by using multiple four-wave mixing (FWM) processes in h…
We present the possibility of steering the direction of correlations between the off-resonant Raman scattered photons from the angularly multimode atomic memory based on warm rubidium vapors. Using acousto-optic deflectors (AOD) driven by different modulation frequencies we experimentally change the angle of incidence of the laser beams on the atomic ensemble. Performing correlations measurements for various deflection angles we verify that we can choose the anti-Stokes light propagation direction independently of the correlated Stokes scattered light in the continuous way. As a result we can …
We experimentally investigate electromagnetically-induced transparency (EIT) created on an inhomogeneously broadened 5S_1/2-5P_1/2 transition in rubidium vapor using a control field of a complex temporal shape. A comb-shaped transparency spectrum enhances the delay-bandwidth product and the light storage capacity for a matched probe pulse by a factor of about 50 compared to a single EIT line [D. D. Yavuz, Phys. Rev. A 75, 031801 (2007)]. If the temporal mode of the control field is slowly changed while the probe is propagating through the EIT medium, the probe will adiabatically follow, provid…
Nonlinear optical effects can be enhanced in tapered optical fibers with diameters less than the wavelength of the propagating light. Here we report on the observation of two-photon absorption using tapered fibers in rubidium vapor at power levels of less than 150 nW. Transit-time broadening produces two-photon absorption spectra with sharp peaks that are very different from conventional line shapes.
Using the process of cavity-enhanced spontaneous parametric down-conversion (SPDC), we generate a narrow-band polarization-entangled photon pair resonant on the rubidium (Rb) D1 line (795 nm). The degenerate single-mode photon pair is selected by multiple temperature controlled etalons. The linewidth of generated polarization-entangled photon pairs is 15 MHz which matches the typical atomic memory bandwidth. The measured Bell parameter for the polarization-entangled photons S=2.73+-0.04 which violates the Bell-CHSH inequality by ~18 standard deviations. The presented entangled photon pair sour…
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.
We experimentally find an interesting and unexpected thing: a rubidium cell with long decay time can not be used to generate a non-classical correlated photon pair via the D2 transition of $^{87}$Rb using four-wave mixing configuration [Opt. Express {\bf 16}, 21708 (2008)]. In this work, we give a detail theoretical analysis on the EIT of hot $^{87}$Rb with different ground decay time, which shows a probable reason why a rubidium cell with long decay time is not a useful candidate for preparation of a non-classical photon pair via the D2 transition. The simulations agree well with the experime…
An oscillatory correlation function has been observed by the coincidence counting of multimode two-photon pairs produced with a degenerate optical parametric oscillator far below threshold. The coherent superposition of the multimode two-photon pairs provides the oscillation in the intensity correlation function. The experimental data are well fitted to a theoretical curve.
We propose a photon echo quantum memory scheme using detuned Raman coupling to long lived ground states. In contrast to previous 3-level schemes based on controlled reversible inhomogeneous broadening that use sequences of $π$-pulses, the scheme does not require accurate control of the coupling dynamics to the ground states. We present a proof of principle experimental realization of our proposal using rubidium atoms in a warm vapour cell. The Raman resonance line is broadened using a magnetic field that varies linearly along the direction of light propagation. Inverting the magnetic field gra…
For one-mode and multimode light, the photon-number tomograms of Gaussian quantum states are explicitly calculated in terms of multivariable Hermite polynomials. Positivity of the tomograms is shown to be necessary condition for positivity of the density matrix.
We experimentally analyze the complete photon number statistics of parametric downconversion and ascertain the influence of multimode effects. Our results clearly reveal a difference between single mode theoretical description and the measured distributions. Further investigations assure the applicability of loss-tolerant photon number reconstruction and prove strict photon number correlation between signal and idler modes.
Particle distributions in squeezed states, even and odd coherent states are given in terms of multivariable Hermite polynomials. The Q--function and Wigner function for nonclassical field states are discussed.
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 address the reconstruction of the full photon distribution of multimode fields generated by seeded parametric down-conversion (PDC). Our scheme is based on on/off avalanche photodetection assisted by maximum-likelihood (MaxLik) estimation and does not involve photon counting. We present a novel constrained MaxLik method that incorporates the request of finite energy to improve the rate of convergence and, in turn, the overall accuracy of the reconstruction.
We consider theoretically how to extract mode dependent single photons from a time/frequency multimode non-classical beam. To achieve this task, we calculate the properties of sum frequency generation with a pulse shaped pump, taking into account both temporal and spatial degree of freedom. We show that using a non-collinear configuration it is possible to achieve a mode dependent weakly reflective beam splitter, with Schmidt number compatible with photon extraction for continuous variable regime tasks. We explicit the possible application to the degaussification of highly multimode squeezed f…
Advances in photonics require photon-number resolved simulations of quantum optical experiments with Gaussian states. We demonstrate a simple and versatile method to simulate the photon statistics of general multimode Gaussian states. The derived generating functions enable simulations of the photon number distribution, cumulative probabilities, moments, and factorial moments of the photon statistics of Gaussian states as well as of multimode photon-added and photon-subtracted Gaussian states. Numerical results are obtained by automatic differentiation of these generating functions by employin…
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.
We present a general model to account for the multimode nature of the quantum electromagnetic field in projective photon-counting measurements. We focus on photon-subtraction experiments, where non-gaussian states are produced conditionally. These are useful states for continuous-variable quantum information processing. We present a general method called mode reduction that reduces the multimode model to an effective two-mode problem. We apply this method to a multimode model describing broadband parametric downconversion, thereby improving the analysis of existing experimental results. The ma…
Genuine multimode entanglement in continuous variable systems can be quantified by exploring the geometry of the state-space, namely via the generalized geometric measure (GGM) which is defined as the shortest distance of a given multimode state from a nongenunely multimode entangled state. For multimode Gaussian states, we derive a closed form expression of GGM in terms of the symplectic invariants of the reduced states. Following that prescription, the characteristics of GGM for typical three- and four-mode Gaussian states are investigated. In the non-Gaussian paradigm, we compute GGM for ph…
We develop general tools to characterise and efficiently compute relevant observables of multimode $N$-photon states generated in non-linear decays in one-dimensional waveguides. We then consider optical interferometry in a Mach-Zender interferometer where a $d$-mode photonic state enters in each arm of the interferometer. We derive a simple expression for the Quantum Fisher Information in terms of the average photon number in each mode, and show that it can be saturated by number-resolved photon measurements that do not distinguish between the different $d$ modes.
We present a scheme to realize versatile quantum networks by cascading several four-wave mixing (FWM) processes in warm rubidium vapors. FWM is an efficient $χ^{(3)}$ nonlinear process, already used as a resource for multimode quantum state generation and which has been proved to be a promising candidate for applications to quantum information processing. We analyze theoretically the multimode output of cascaded FWM systems, derive its independent squeezed modes and show how, with phase controlled homodyne detection and digital post-processing, they can be turned into a versatile source of con…
The ability to coherently convert the frequency and temporal waveform of single and entangled photons will be crucial to interconnect the various elements of future quantum information networks. Of particular importance in this context is the quantum frequency conversion of photons emitted by material systems able to store quantum information, so called quantum memories. There have been significant efforts to implement quantum frequency conversion using non linear crystals, with non classical light from broadband photon pair sources and solid state emitters. However, so far, solid state quantu…
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…
Tomographic probability representation of multimode electromagnetic field states in the scheme of center-of-mass tomography is reviewed. Both connection of the field state Wigner function and observable Weyl symbols with the center-of-mass tomograms as well as connection of Grönewold kernel with the center-of-mass tomographic kernel determining the noncommutative product of the tomograms are obtained. The dual center-of-mass tomogram of the photon states are constructed and the dual tomographic kernel is obtained. The models of other generalised center-of-mass tomographies are discussed. Examp…
Spectro-temporal modes of light can be exploited for the generation of high-dimensional Gaussian quantum states. Such states are at the basis of continuous variable quantum information protocols where they have to support mode-selective non-Gaussian operations. We develop a general framework for single-photon addition on multimode states of light via parametric down conversion processes. We identify the analytical conditions for single-mode and mode-selective photon addition. We show that spectral mode selectivity can be achieved in the Type-II collinear down conversion, while single-mode cond…
We investigate the coupling efficiency of parametric downconversion light (PDC) into single and multi-mode optical fibers as a function of the pump beam diameter, crystal length and walk-off. We outline two different theoretical models for the preparation and collection of either single-mode or multi-mode PDC light (defined by, for instance, multi-mode fibers or apertures, corresponding to bucket detection). Moreover, we define the mode-matching collection efficiency, important for realizing a single-photon source based on PDC output into a well-defined single spatial mode. We also define a mu…
Quantum interfaces (QIs) that generate entanglement between a multimode atomic memory and a photon forms a multiplexed repeater node and hold promise to greatly improve quantum repeater rates. Recently, the temporal multimode spin-wave memory that is entangled with a photon has been demonstrated with cold atoms. However, due to additional noise generated in multimode operation, the fidelity of spin-wave-photon entanglement significantly decreases with the mode number. So far, the improvement on temporal-multimode entanglement fidelity via suppressing the additional noise remains unexplored. He…
Quantum correlations between long lived quantum memories and telecom photons that can propagate with low loss in optical fibers are an essential resource for the realization of large scale quantum information networks. Significant progress has been realized in this direction with atomic and solid state systems. Here, we demonstrate quantum correlations between a telecom photon and a multimode on-demand solid state quantum memory. This is achieved by mapping a correlated single photon onto a spin collective excitation in a Pr$^{3+}$:Y$_2$SiO$_5$ crystal for a controllable time. The stored singl…
We implement a direct detection scheme based on hybrid photodetectors to experimentally investigate high-order correlations for detected photons by means of quantities that can be experimentally accessed. We show their usefulness in fully characterizing a multimode twin-beam state in comparison with classical states and, in particular, we introduce a nonclassicality criterion based on a simple linear combination of high-order correlation functions. Our scheme is self-consistent, allowing the estimation of all the involved parameters (quantum efficiency, number of modes and average energy) dire…
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.
The sources, which generate atom-photon quantum correlations or entanglement based on quantum memory, are basic blocks for building quantum repeaters (QRs). For achieving highly entanglement-generation rates in ensemble-based QRs, spatial-, temporal- and spectral-multimode memories are needed. The previous temporal-multimode memories are based on rephrasing mechanisms in inhomogeneous-broadened media. Here, by applying a train of multi-direction write pulses into a homogeneous-broadened atomic ensemble to induce Duan-Lukin-Cirac-Zoller-like Raman processes, we prepare up to 19 pairs of modes, …
The generation and distribution of quantum correlations between photonic qubits is a key resource in quantum information science. For applications in quantum networks and quantum repeaters, it is required that these quantum correlations be stored in a quantum memory. In 2001, Duan, Lukin, Cirac, and Zoller (DLCZ) proposed a scheme combining a correlated photon-pair source and a quantum memory in atomic gases, which has enabled fast progress towards elementary quantum networks. In this letter, we demonstrate a solid state source of correlated photon pairs with embedded spin-wave quantum memory,…
We demonstrate two approaches for unbalanced interferometers as time-bin qubit analyzers for quantum communication, robust against mode distortions and polarization effects as expected from free-space quantum communication systems including wavefront deformations, path fluctuations, pointing errors, and optical elements. Despite strong spatial and temporal distortions of the optical mode of a time-bin qubit, entangled with a separate polarization qubit, we verify entanglement using the Negative Partial Transpose, with the measured visibility of up to 0.85$\pm$0.01. The robustness of the analyz…
We propose and theoretically study a method for the stochastic realization of arbitrary quantum channels on multimode single-photon qudits. In order for our method to be undemanding in its implementation, we restrict our analysis to linear-optical techniques, vacuum ancillary states and non-adaptive schemes, but we allow for random switching between different optical networks. With our method it is possible to deterministically implement random-unitary channels and to stochastically implement general, non-unital channels. We provide an expression for the optimal probability of success of our s…
We present a detailed analytic framework for studying multimode non-Gaussian states that are conditionally generated when few modes of a multimode Gaussian state are subject to photon-number-resolving detectors. From the output state Wigner function, we deduce that the state factorizes into a Gaussian gate applied to a finite Fock-superposition non-Gaussian state. The framework provides an approach to find the optimal strategy to generate a given target non-Gaussian state. We explore examples, such as the generation of cat states, weak cubic phase states, and bosonic code states, and achieve i…
Entanglement between photons at telecommunication wavelengths and long-lived quantum memories is one of the fundamental requirements of long-distance quantum communication. Quantum memories featuring on-demand read-out and multimode operation are additional precious assets that will benefit the communication rate. In this work we report the first demonstration of entanglement between a telecom photon and a collective spin excitation in a multimode solid-state quantum memory. Photon pairs are generated through widely non-degenerate parametric down-conversion, featuring energy-time entanglement …
We propose a universal scheme for the probabilistic generation of an arbitrary multimode entangled state of light with finite expansion in Fock basis. The suggested setup involves passive linear optics, single photon sources, strong coherent laser beams, and photodetectors with single-photon resolution. The efficiency of this setup may be greatly enhanced if, in addition, a quantum memory is available.
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.
Multiplexed quantum memories capable of storing and processing entangled photons are essential for the development of quantum networks. In this context, we demonstrate the simultaneous storage and retrieval of two entangled photons inside a solid-state quantum memory and measure a temporal multimode capacity of ten modes. This is achieved by producing two polarization entangled pairs from parametric down conversion and mapping one photon of each pair onto a rare-earth-ion doped (REID) crystal using the atomic frequency comb (AFC) protocol. We develop a concept of indirect entanglement witnesse…
The resonant interaction between two two-level atoms and m- electromagnetic modes in a cavity is considered. Entanglement dynamics between two atoms is examined. In particular we compare dynamical variations for different cavity modes as well as for different cavity photon numbers. The collapse and revival of entanglement is exhibited by varying the atom-photon interaction times.
The subtraction of a single photon from a multimode quantum field is analyzed as the conditional evolution of an open quantum system. We develop a theory describing different subtraction schemes in a unified approach and we introduce the concept of subtraction modes intrinsic to the process. The matching between the subtraction modes and the modes of the field defines different possible scenarios for the photon subtraction. In particular, our framework identifies: the conditions of pure photon subtraction, the quantum states of the field modes conditioned to the photon subtraction, the mode wi…
We investigate the entanglement patterns of photon-added and -subtracted four-mode squeezed vacuum states. Entanglements in different scenarios are analyzed by varying the number of photons added or subtracted in certain modes, which are referred to as the "player" modes, the others being "spectators." We find that the photon-subtracted state can give us higher entanglement than the photon-added state which is in contrast of the two-mode situation. We also study the logarithmic negativity of the two-mode reduced density matrix obtained from the four-mode state which again shows that the state …
The generation and distribution of entanglement are key resources in quantum repeater schemes. Temporally multiplexed systems offer time-bin encoding of quantum information which provides robustness against decoherence in fibers, crucial in long distance communication. Here we demonstrate the direct generation of entanglement in time between a photon and a collective spin excitation in a rare earth ion doped ensemble. We analyze the entanglement by mapping the atomic excitation onto a photonic qubit and by using time-bin qubits analyzers implemented with another doped crystal using the atomic …
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 an integrated silicon photonic chip, composed of several sub-wavelength ridge waveguides, and immersed in a micro-cell with rubidium vapor. Employing two-photon excitation, including a telecom wavelength, we observe that the waveguide transmission spectrum gets modified when the photonic mode is coupled to rubidium atoms through its evanescent tail. Due to the enhanced electric field in the waveguide cladding, the atomic transition can be saturated at a photon number $\approx$ 80 times less than a free-propagating beam case. The non-linearity of the atom-clad Si-waveguide is about 4 o…
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…
