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.
In this Letter, we demonstrate the generation of multimode entangled states of propagating microwaves. The entangled states are generated by parametrically pumping a multimode superconducting cavity. By combining different pump frequencies, applied simultaneously to the device, we can produce different entanglement structures in a programable fashion. The Gaussian output states are fully characterized by measuring the full covariance matrices of the modes. The covariance matrices are absolutely calibrated using an in situ microwave calibration source, a shot noise tunnel junction. Applying a v…
In this work we analyse the structure of highly-entangled multimode squeezed states, such as those generated by broadband pulses undergoing type-II parametric down-conversion (PDC). Such down-conversion has previously been touted as a natural and efficient means of cluster-state generation, and therefore a viable future pathway to quantum computation. We first detail how broadband PDC processes lead directly to a series of orthogonal supermodes that are linear combinations of the original frequency modes. We then calculate the total squeezing of the multimode entangled states when they are ass…
We investigate the systematic use of the Schwinger representation, by virtue of which two boson fields are equivalent to an effective spin, for casting multimode squeezed states into multipartite spin entangled states. The motivation for this endeavor is the following established fact: finitely squeezed, two-mode entangled states can be recast into maximally entangled bipartite spin states, irrespective of their level of squeezing (in the lossless case). This work explores the generalization of this interesting property to multipartite entanglement. While we found that the generalization of mu…
Entangled coherent states for multiple bosonic modes, also referred to as multimode cat states, not only are of fundamental interest, but also have practical applications. The nonclassical correlation among these modes is well characterized by the violation of the Mermin-Klyshko inequality. We here study Mermin-Klyshko inequality violations for such multi-mode entangled states with rotated quantum-number parity operators. Our results show that the Mermin-Klyshko signal obtained with these operators can approach the maximal value even when the average quantum number in each mode is only 1, and …
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…
We address the intrinsic multimode nature of the quantum state of light obtained by pulsed spontaneous parametric downconversion and develop a theoretical model based only on experimentally accessible quantities. We exploit the pairwise entanglement as a resource for conditional multimode measurements and derive closed formulas for the detection probability and the density matrix of the conditional states. We present a set of experiments performed to validate our model in different conditions that are in excellent agreement with experimental data. Finally, we evaluate nonGaussianity of the con…
We numerically demonstrate that "mode-entangled states" based on the transverse modes of classical optical fields in multimode waveguides violate Bell's inequality. Numerically simulating the correlation measurement scheme of Bell's inequality, we obtain the normalized correlation functions of the intensity fluctuations for the two entangled classical fields. By using the correlation functions, the maximum violations of Bell's inequality are obtained. This implies that the two classical fields in the mode-entangled states, although spatially separated, present a nonlocal correlation.
We present a detailed analysis of the multimode quantum state embedded in an optical frequency comb generated by a Synchronously Pumped Optical Parametric Oscillator (SPOPO). The full covariance matrix of the state is obtained with homodyne detection where the local oscillator is spectrally controlled with pulse shaping techniques. The resulting matrix reveals genuine multipartite entanglement. Additionally, the beam is comprised of several independent eigenmodes that correspond to specific pulse shapes. The experimental data is confirmed with numerical simulations. Finally, the potential to c…
Entanglement between large numbers of quantum modes is the quintessential resource for future technologies such as the quantum internet. Conventionally the generation of multimode entanglement in optics requires complex layouts of beam-splitters and phase shifters in order to transform the input modes in to entangled modes. These networks need substantial modification for every new set of entangled modes to be generated. Here we report on the highly versatile and efficient generation of various multimode entangled states with the ability to switch between different linear optics networks in re…
Even though Gaussian quantum states of multimode light are promising quantum resources due to their scalability, non-Gaussianity is indispensable for quantum technologies, in particular to reach quantum computational advantage. However, embodying non-Gaussianity in a multimode Gaussian state remains a challenge as controllable non-Gaussian operations are hard to implement in a multimode scenario. Here, we report the first generation of non-Gaussian quantum states of a multimode light field by subtracting a photon in a desired mode from multimode Gaussian states, and observe negativity of the W…
Schemes for generation and protocols for network teleportation of multimode entangled cat-states are proposed. Explicit expressions for probability of successful teleportation are derived for both symmetric and asymmetric networks.
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…
We discuss mode-entangled states based on the optical transverse modes of the optical field propagating in multi-mode waveguides, which are classical analogs of the quantum entangled states. The analogs are discussed in detail, including the violation of the Bell inequality and the correlation properties of optical pulses' group delays. The research on these analogs may be important, for it not only provides useful insights into fundamental features of quantum entanglement, but also yields new insights into quantum computation and quantum communication.
We show that the light generated via spontaneous four-wave mixing or parametric down conversion in multiple, coupled, lossy cavities is a multimode squeezed thermal state. Requiring this state to be the solution of the Lindblad master equation results in a set of coupled first-order differential equations for the time-dependent squeezing parameters and thermal photon numbers of the state. The benefit of this semi-analytic approach is that the number of coupled equations scales linearly with the number of modes but is independent of the number of photons generated. With this analytic form of th…
We propose a Raman quantum memory scheme that uses several atomic ensembles to store and retrieve the multimode highly entangled state of an optical quantum frequency comb, such as the one produced by parametric down-conversion of a pump frequency comb. We analyse the efficiency and the fidelity of such a quantum memory. Results show that our proposal may be helpful to multimode information processing using the different frequency bands of an optical frequency comb.
We analyze theoretically spontaneous parametric down-conversion in a multimode nonlinear waveguide as a source of entangled pairs of spatial qubits, realized as superpositions of a photon in two orthogonal transverse modes of the waveguide. It is shown that by exploiting intermodal dispersion, down-conversion into the relevant pairs of spatial modes can be selected by spectral filtering, which also provides means to fine-tune the properties of the generated entangled state. We also discuss an inverting interferometer detecting the spatial parity of the input beam as a versatile tool to charact…
We develop an operator-based description of two types of multimode-entangled single-neutron quantum optical devices: Wollaston prisms and radio-frequency spin flippers in inclined magnetic field gradients. This treatment is similar to the approach used in quantum optics, and is convenient for the analysis of quantum contextuality measurements in certain types of neutron interferometers. We describe operationally the way multimode-entangled single-neutron states evolve in these devices, and provide expressions for the associated operators describing the dynamics, in the limit in which the neutr…
We present a protocol for the teleportation of the quantum state of a pulse of light onto the collective spin state of an atomic ensemble. The entangled state of light and atoms employed as a resource in this protocol is created by probing the collective atomic spin, Larmor precessing in an external magnetic field, off resonantly with a coherent pulse of light. We take here for the first time full account of the effects of Larmor precession and show that it gives rise to a qualitatively new type of multimode entangled state of light and atoms. The protocol is shown to be robust against the dom…
We report on the the experimental realization of hyper-entangled two photon states, entangled in polarization and momentum. These states are produced by a high brilliance parametric source of entangled photon pairs with peculiar characteristics of flexibility in terms of state generation. The quality of the entanglement in the two degrees of freedom has been tested by multimode Hong-Ou-Mandel interferometry.
We propose a novel interferometer by using optical transverse modes in multimode waveguide that can beat the standard quantum limit. In the scheme, the classical simulation of $N$-partical quantum entangled states is generated by using $N$ independent classical fields and linear optical elements. Similar to the quantum-enhanced measurements, the classical simulation can also achieve $\sqrt{N}$ enhancement over the precision of the measurement $N$ times for independent fields. Due to only using classical fields and linear optical elements, the scheme can be realized much more easily.
We present a multimode treatment of the optical parametric oscillator, which is valid for both pulsed and continuous-wave pump fields. The two-time correlation functions of the output field are derived, and we apply the theory to analyze a scheme for heralded production of non-classical field states that may be subsequently stored in an atomic quantum memory.
Continuous-variable encoding of quantum information in the optical domain has recently yielded large temporal and spectral entangled states instrumental for quantum computing and quantum communication. We introduce a protocol for the generation of spatial multipartite entanglement based on phase-matching of a propagation eigenmode in a monolithic photonic device: the array of quadratic nonlinear waveguides. We theoretically demonstrate in the spontaneous parametric downconversion regime the generation of large multipartite entangled states useful for multimode quantum networks. Our protocol is…
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.
We present a consistent multimode theory that describes the coupling of single photons generated by collinear Type-I parametric down-conversion into single-mode optical fibers. We have calculated an analytic expression for the fiber diameter which maximizes the pair photon count rate. For a given focal length and wavelength, a lower limit of the fiber diameter for satisfactory coupling is obtained.
We present a method for computing the action of conditional linear optical transformations, conditioned on photon counting, for arbitrary signal states. The method is based on the Q-function, a quasi probability distribution for anti normally ordered moments. We treat an arbitrary number of signal and ancilla modes. The ancilla modes are prepared in an arbitrary product number state. We construct the conditional, non unitary, signal transformations for an arbitrary photon number count on each of the ancilla modes.
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…
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…
Using continuous wave superposition of spatial modes, we demonstrate experimentally displacement measurement of a light beam below the standard quantum limit. Multimode squeezed light is obtained by mixing a vacuum squeezed beam and a coherent beam that are spatially orthogonal. Although the resultant beam is not squeezed, it is shown to have strong internal spatial correlations. We show that the position of such a light beam can be measured using a split detector with an increased precision compared to a classical beam. This method can be used to improve the sensitivity of small displacement …
Multimode Gaussian quantum light, including multimode squeezed and/or multipartite quadrature entangled light, is a very general and powerful quantum resource with promising applications to quantum information processing and metrology involving continuous variables. In this paper, we determine the ultimate sensitivity in the estimation of any parameter when the information about this parameter is encoded in such Gaussian light, irrespective of the exact information extraction protocol used in the estimation. We then show that, for a given set of available quantum resources, the most economical…
We report on the observation of multimode strong coupling of a small ensemble of atoms interacting with the field of a 30-m long fiber resonator containing a nanofiber section. The collective light--matter coupling strength exceeds the free spectral range and the atoms couple to consecutive longitudinal resonator modes. The measured transmission spectra of the coupled atom-resonator system provide evidence of this regime, realized with a few hundred atoms with an intrinsic single-atom cooperativity of 0.26. These results are the starting point for studies in a new setting of light-matter inter…
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 propose quantum dense coding protocol for optical images. This protocol extends the earlier proposed dense coding scheme for continuous variables [S.L.Braunstein and H.J.Kimble, Phys.Rev.A 61, 042302 (2000)] to an essentially multimode in space and time optical quantum communication channel. This new scheme allows, in particular, for parallel dense coding of non-stationary optical images. Similar to some other quantum dense coding protocols, our scheme exploits the possibility of sending a classical message through only one of the two entangled spatially-multimode beams, using the other one…
We develop a universal approach enabling the study of any multimode quantum optical system evolving under a quadratic Hamiltonian. Our strategy generalizes the standard symplectic analysis and permits the treatment of multimode systems even in situations where traditional theoretical methods cannot be applied. This enables the description and investigation of a broad variety of key-resources for experimental quantum optics, ranging from optical parametric oscillators, to silicon-based micro-ring resonator, as well as opto-mechanical systems.
The recent surface plasmon entanglement experiment [E. Altewischer et al., Nature (London) 418, 304 (2002)] is theoretically analyzed. The entanglement preservation upon transmission in the non-focused case is found to provide information about the interaction of the biphoton and the metallic film. The entanglement degradation in the focused case is explained in the framework of a fully multimode model. This phenomenon is a consequence of the polarization-selective filtering behavior of the metallic nanostructured film.
We present a scheme for generating and manipulating three-mode squeezed states with genuine tripartite entanglement by injecting single-mode squeezed light into an array of coupled optical waveguides. We explore the possibility to selectively generate single-mode squeezing or multimode squeezing at the output of an elliptical waveguides array, determined solely by the input light polarization. We study the effect of losses in the waveguides array and show that quantum correlations and squeezing are preserved for realistic parameters. Our results show that arrays of optical waveguides are suita…
We report on a novel pseudothermal light source based on laser light coupled into an optical multimode fiber. The setup is simple, of low cost, exhibits inherently high directional light emission and allows for a flexible arrangement. By measuring the photon statistics and spatial two point intensity correlations in the far field we show that the setup exhibits all characteristics of a gaussian random source.
General solutions to the quantum Rabi model involve subspaces with unbounded number of photons. However, for the multiqubit multimode case, we find special solutions with at most one photon for arbitrary number of qubits and photon modes. Unlike the Juddian solution, ours exists for arbitrary single qubit-photon coupling strength with constant eigenenergy. This corresponds to a horizontal line in the spectrum, while still being a qubit-photon entangled state. As a possible application, we propose an adiabatic scheme for the fast generation of arbitrary single-photon multimode W states with non…
Multimode nonclassical states of light are an essential resource in quantum computation with continuous variables, for example in cluster state computation. They can be generated either by mixing different squeezed light sources using linear optical operations, or directly in a multimode optical device. In parallel, frequency combs are perfect tools for high precision metrological applications and for quantum time transfer. Synchronously Pumped Optical Parametric Oscillators (SPOPOs) have been theoretically shown to produce multimode non-classical frequency combs. In this paper, we present the…
We demonstrate the coherent transduction of quantum noise reduction, or squeezed light, by Ag localized surface plasmons (LSPs). Squeezed light, generated through four-wave-mixing in Rb vapor, is coupled to a Ag nanohole array designed to exhibit LSP-mediated extraordinary-optical transmission (EOT) spectrally coincident with the squeezed light source at 795 nm. We demonstrate that quantum noise reduction as a function of transmission is found to match closely with linear attenuation models, thus demonstrating that the photon-LSP-photon transduction process is coherent near the LSP resonance.
We examine the properties of an atom laser produced by outcoupling from a Bose-Einstein condensate with squeezed light. We model the multimode dynamics of the output field and show that a significant amount of squeezing can be transfered from an optical mode to a propagating atom laser beam. We use this to demonstrate that two-mode squeezing can be used to produce twin atom laser beams with continuous variable entanglement in amplitude and phase.
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 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…
To manipulate cold atoms in spatially constrained quantum engineering platforms, we developed a lensless optical system with a $\sim$1 $μ$m resolution and a transverse size of only 225 $μ$m. We use a multimode optical fiber with a high numerical aperture, which directly guides light inside the ultra-high-vacuum system. Spatial light modulators allow us to generate control beams at the in-vacuum fiber end by digital optical phase conjugation. As a demonstration, we use this system to optically transport cold atoms towards the in-vacuum fiber end, to load them in optical microtraps and to re-coo…
