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arXiv:1802.00210 · Physical Review A

Generation of single- and two-mode multiphoton states in waveguide QED

Vanessa Paulisch, Harry J. Kimble, J. I. Cirac, Alejandro González-Tudela

Published May 22, 2018• 12 citations
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Abstract

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 [A. Gonz\'alez-Tudela et al., Phys. Rev. Lett. 118, 213601 (2017)], 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 them to generate two-mode multiphoton states, such as Yurke or NOON states.

DOI
10.1103/physreva.97.053831

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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 [A. Gonz'alez-Tudela et al., Phys. Rev. Lett. 118, 213601 (2017)], 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 them to generate two-mode multiphoton states, such as Yurke or NOON states.
Engineering quantum states of light is at the basis of many quantum technologies such as quantum cryptography, teleportation, or metrology among others. Though, single photons can be generated in many scenarios, the efficient and reliable generation of complex single-mode multiphoton states is still a long-standing goal in the field, as current methods either suffer from low fidelities or small probabilities. Here we discuss several protocols which harness the strong and long-range atomic interactions induced by waveguide QED to efficiently load excitations in a collection of atoms, which can then be triggered to produce the desired multiphoton state. In order to boost the success probability and fidelity of each excitation process, atoms are used to both generate the excitations in the rest, as well as to herald the successful generation. Furthermore, to overcome the exponential scaling of the probability of success with the number of excitations, we design a protocol to merge excitations that are present in different internal atomic levels with a polynomial scaling.
Waveguide QED offers the possibility of generating strong coherent atomic interactions either through appropriate atomic configurations in the dissipative regime or in the bandgap regime.In this work, we show how to harness these interactions in order to herald the generation of highly entangled atomic states, which afterwards can be mapped to generate single mode multi-photonic states with high fidelities.We introduce two protocols for the preparation of the atomic states, we discuss their performance and compare them to previous proposals.In particular, we show that one of them reaches high probability of success for systems with many atoms but low Purcell factors.The key resource of these protocols is the long-range dissipative coupling induced by the waveguide which enforces effective unitary dynamics through the quantum Zeno effect.In this work, we present two protocols that harness long-range coherent interactions induced by the guided modes to generate collective atomic excitations within an ensemble of atoms.• The first protocol ('double mirrors') is designed for emitters, whose resonance frequency corresponds to some guided mode in the band, see figure 1(a), and which is, e.g., well suited for optical fiber setups.In this case, the
Waveguide quantum electrodynamics (waveguide QED) describes the interaction between an electromagnetic field confined to a one-dimensional waveguide with atom-like quantum emitters close by. The characteristics of these kinds of systems are the possibility for strong and even ultrastrong interactions between the photonic and atom-like systems, and practically infinite range interactions between the emitters. These properties are valuable for a wide range of quantum optical applications, like quantum communication, quantum networks and quantum metrology. In this thesis we focus on two challenges in quantum optics, namely the generation and scattering of multiphoton states. In the first part of this thesis we demonstrate how waveguide QED systems can be exploited for the generation of multiphoton states, in particular of single-mode Fock states and superpositions thereof as well as multi-mode photonic states with metrological applications. The basic setup for this goal is an ensemble of quantum emitters coupled to a waveguide. In the so-called atomic mirror configuration symmetric Dicke states (or a superposition thereof) decay superradiantly to the ground state and emit the desired multiphoton state, which can be efficiently collected at the ends of the waveguide. We propose various protocols for the preparation of these Dicke states in waveguide QED systems and characterize the emitted photonic state. It turns out that in the low excitation regime, that is, if the number of photons is much lower than the ensemble size, the photonic state is emitted into a single mode. This single-mode structure is fundamental to current proposals for applications in quantum metrology with optical interferometers. Outside the low excitation regime, a multi-mode photonic state is generated, for which the metrological capabilities were unknown. We were able to show that these states still lead to quantum-enhanced optical interferometry. In the second part of this thesis we demonstrate how the scattering of multiphoton states on a single quantum emitter coupled to the waveguide can be used for testing the limits of the light-matter interaction strength. In particular, we investigate systems in the so-called ultrastrong coupling regime, where the coupling strength between the photonic and atom-like system is of the order of the emitter's transition energy. In this regime, many methods and approximations used in quantum optics, especially the Rotating Wave Approximation, break down and one needs to develop new analytical and numerical methods to study these systems. One approach is the so-called polaron Transformation. We show how this transformation can be applied for predicting the scattering amplitude of few photons scattering on the emitter. The comparison of these results with numerical simulations using matrix product states shows a good agreement for moderate coupling strengths. Both parts together show that waveguide QED systems are promising candidates for the generation of multiphoton states as well as for the investigation of fundamental limits probed through the scattering of multiphoton states. The latter also finds application in the implementation of photon-photon nonlinearities induced by the interaction with the quantum emitters. Apart from these and many other theoretical predictions, waveguide QED systems are also undergoing rapid progress in experiments. Therefore, we expect these kinds of systems to bring forth several advances in the field of quantum optics.
Waveguide QED offers the possibility of generating strong coherent atomic interactions either through appropriate atomic configurations in the dissipative regime or in the bandgap regime. In this work, we show how to harness these interactions in order to herald the generation of highly entangled atomic states, which afterwards can be mapped to generate single mode multi-photonic states with high fidelities. We introduce two protocols for the preparation of the atomic states, we discuss their performance and compare them to previous proposals. In particular, we show that one of them reaches high probability of success for systems with many atoms but low Purcell factors.
Entangled states of photons form the foundation of quantum communication, computation, and metrology. Yet their generation remains fundamentally constrained: in the absence of intrinsic photon-photon interactions, the generation of such states is inherently probabilistic rather than deterministic. The prevalent technique of post-selection verifies the creation of an entangled state by detecting and thus destroying it. Heralding offers a solution in which measuring ancillary photons in auxiliary modes signals the state generation without the need to measure it. Here, we introduce and experimentally demonstrate a scheme to generate a three-mode two-photon NOON state, where the detection of a single photon in one heralding mode signifies the presence of the state in three target modes. We validate the generated state by estimating a fidelity of 0.823 +/- 0.018 with respect to an ideal three-mode NOON state and certifying genuine multipartite entanglement. By virtue of the high success probability and small resource overhead of our scheme, our work provides a theoretical and experimental stepping stone for entangled multi-mode state generation, which is realizable with current technology. These multi-mode entangled states represent a key direction for linear optical quantum information that is complementary to multi-qubit state encoding.
We present the first experimental realisation of a heralded three-mode, two-photon NOON state—an essential ingredient for quantum metrology, quantum communication, and distributed quantum information protocols. Our approach is based on a linear-optical architecture that uses only three single-photon inputs interfaced with a four-mode interferometer, yet can theoretically reach a success probability of 25%. A heralding photon unambiguously signals the preparation of the desired state, thereby bypassing the major scalability bottlenecks inherent to conventional post-selection methods. The produced state exhibits a fidelity exceeding 80%, confirming genuine tripartite entanglement. Both the protocol and its experimental implementation constitute a substantial step forward for the fields of quantum optics and quantum information science.