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The Quantum Internet

H. J. Kimble

arXiv:0806.4195v1quant-ph

TL;DR

Realizing quantum networks requires reliable physical interfaces that connect quantum nodes by transporting quantum states and distributing entanglement. The paper surveys optical single-photon–atom processes for quantum interconnects and reports heralded entanglement between distant atomic ensembles, with inferred concurrence C = 0.9±0.3.

  • Problem

    Reliable physical processes are needed to translate quantum-network concepts into interconnected nodes that transport quantum states and distribute entanglement.

  • Method

    The paper surveys optical single-photon–atom processes that map quantum states between material systems and propagating optical fields, emphasizing cavity QED and atomic ensembles.

  • Results

    C = 0.9±0.3 was inferred for entanglement stored between atomic ensembles in distinct apparatuses separated by 3 m.

  • Takeaways & Limitations

    Optical quantum interconnects can provide quantum connectivity between nodes, including entanglement that supports quantum teleportation.

  • Takeaways & Limitations

    The paper is not exhaustive and focuses on basic physical implementation principles illustrated through selected quantum-optics examples.

Abstract

from arXiv · show

Quantum networks offer a unifying set of opportunities and challenges across exciting intellectual and technical frontiers, including for quantum computation, communication, and metrology. The realization of quantum networks composed of many nodes and channels requires new scientific capabilities for the generation and characterization of quantum coherence and entanglement. Fundamental to this endeavor are quantum interconnects that convert quantum states from one physical system to those of another in a reversible fashion. Such quantum connectivity for networks can be achieved by optical interactions of single photons and atoms, thereby enabling entanglement distribution and quantum teleportation between nodes.

INTRODUCTION

Quantum networks support quantum computation, communication, and metrology by linking nodes that generate, process, and store quantum information through quantum channels. Their realization depends on optical single-photon–atom processes, long-lived quantum memories, and efficient light–matter interfaces for transporting quantum states across complex networks.

  • Quantum networks: Quantum networks link nodes that locally generate, process, and store quantum information through channels that transport quantum states between sites.They are important both for formal analysis and for physical implementations of quantum computation, communication, and metrology.
  • Quantum connectivity: 2^kn is the state-space dimension of a fully quantum network with k nodes each containing n qubits, compared with k2^n for classical-channel connectivity.Quantum connectivity also offers a potential way to overcome size-scaling and error-correlation problems.
  • Physical realization: The physical realization of quantum networks requires reliable optical transport of quantum states across complex networks using single photons and atoms.This motivates examining the physical processes that translate abstract network architectures into functioning systems.
  • Physical realization: Strong coupling of single photons and atoms in cavity QED and quantum information processing with atomic ensembles are highlighted as two focus areas.Both rely on long-lived atomic quantum memories and efficient light–matter interfaces.
  • Research prospects: Many physical systems are being investigated, and it remains impossible to foresee which approaches will yield rudimentary or technologically significant quantum networks.The introduction explicitly acknowledges omissions of alternative approaches because the field is still in an early stage.

A QUANTUM INTERFACE BETWEEN LIGHT AND MATTER

Quantum networks require coherent single-photon control of light–matter interactions, enabling reversible quantum-state transfer that underpins quantum-optical interconnects. These interfaces can distribute coherence and entanglement between network nodes through controlled photon-mediated transfer.

  • The principal challenge is achieving coherent control of light–matter interactions at the single-photon level, where photon interaction cross-sections are typically too small for nontrivial dynamics.Atoms and electrons have relatively large long-range interactions for spin and charge degrees of freedom, unlike individual photons.
  • Theoretical cavity-QED protocols and later atomic-ensemble advances established reversible quantum-state mapping between atoms and photons as the basis for quantum-optical interconnects.This development began in the 1990s and expanded through important advances in the subsequent decade.
  • A generic quantum interface uses a time-dependent coupling χ(t) between an internal material system and the electromagnetic field, with ⟨H_int(t)⟩∼ℏχ(t).A stated design goal is user control of χ(t), for example through an auxiliary laser, to clock states to and from quantum memory.
  • One interface architecture traps single atoms in optical cavities at nodes A and B, using an optical fiber and externally controlled photons to transfer |ψ⟩ between the atoms.The quantum state stored in the atom at node A propagates to node B through photons.

CAVITY QUANTUM ELECTRODYNAMICS

Cavity quantum electrodynamics achieves strong, coherent interactions between single atoms and photons using electromagnetic resonators, enabling strong coupling in optical and microwave systems. This regime is characterized by g ≫ (γ, κ), with progress extending to photon and atom numbers below one.

  • Platforms: Cavity QED achieves strong coupling of single atoms and photons in optical and microwave electromagnetic resonators.Extensions include quantum dots in micropillars and photonic bandgap cavities, plus Cooper-pairs interacting with superconducting resonators.
  • Strong-coupling regime: Strong coupling requires g ≫ (γ, κ), where γ is atomic decay outside the cavity mode and κ is the cavity-mode decay rate.The coupling frequency g corresponds to half the one-photon Rabi frequency.
  • Strong-coupling regime: n0 ∼ γ2/g2 photons saturate the intracavity atom, while N0 ∼ κγ/g2 atoms appreciably affect the intracavity field.These quantities describe the departure of strong-coupling cavity QED from traditional optical physics.
  • Experimental progress: Microwave cavity QED advanced through Rydberg atoms and superconducting cavities with Q ∼ 1010, while optical systems use resonators with Q ∼ 107 − 1011.The reported cavity-Q ranges span both optical and microwave implementations.
  • Optical implementations: High-finesse optical resonators with F ∼ 105 − 106 and atomic transitions with oscillator strengths near unity have reached (n0, N0) ≪ 1.Reducing mode volume Vm increases the coupling g but makes atomic localization more stringent.

Coherence and entanglement in cavity QED

Cavity QED enables deterministic, control-shaped single-photon generation and reversible transfer of quantum states between atoms and optical fields. Extending these capabilities to polarization modes supports deterministic entangled-photon generation and entanglement distribution between network nodes.

  • Single-photon generation: Strong atom–cavity coupling and an external control field transfer one photon into the cavity and emit a collimated single-photon pulse with tailored amplitude and phase.The pulse is generated through the cavity output mirror as |φ1(t)⟩.
  • Single-photon generation: Experiments confirmed deterministic single-photon generation, including bit streams from single trapped atoms, while avoiding atomic excited-state population in the ideal adiabatic limit.These demonstrations constitute an initial step toward flying-photon quantum networks.
  • Reversible quantum-state transfer: A coherent optical field with mean photon number n̄ = 1.1 was mapped into a coherent superposition of Cesium-atom states and then coherently mapped back into a propagating field.The experiment implemented reversible mapping to and from internal states of a single trapped Cesium atom.
  • Entangled-photon generation: Using both cavity polarization eigenmodes, sequential control fields entangled atomic states with a first photon and produced a second photon, thereby generating entangled photons.The atom returned to its initial unentangled state after the second control field; the photon separation τ = t2 − t1 was limited by atomic transit time, while the protocol remained intrinsically deterministic and reversible.

QUANTUM NETWORKS WITH ATOMIC ENSEMBLES

Discrete-variable quantum networking with atomic ensembles builds on the DLCZ protocol, which uses single spin excitations and heralded optical detection to distribute entanglement between ensembles. The approach supports scalable networking despite propagation and detection losses and detector dark counts.

  • DLCZ protocol: The DLCZ protocol generates and retrieves single collective spin excitations in atomic ensembles, storing |1a⟩ and later converting it deterministically into propagating field 2.A write pulse creates the excitation, while a second pulse retrieves it from the atomic memory.
  • DLCZ protocol: Stable phase control is required because the entangled-state phase depends on the channel phase difference, η1 = βL −βR.The sign of the generated state is selected by whether detector D1 or D2 records the event.
  • DLCZ protocol: Indistinguishable detection of a photon from either ensemble probabilistically but heraldedly projects two ensembles into an entangled state sharing one collective spin excitation.The entanglement arises through quantum interference in the measurement process, and failed trials must be repeated because p ≪1.
  • Scalability and imperfections: The DLCZ scheme tolerates propagation and detection losses and detector dark counts, while incorporating built-in entanglement purification for efficient, scalable extension beyond two ensembles.The protocol is designed to remain resilient to these imperfections rather than relying on an idealized loss-free setting.
  • Experimental realization: A four-ensemble experiment formed functional quantum nodes L, R separated by 3 m, storing asynchronous entangled states and converting atomic excitations into photons that violated a Bell inequality.The setup used cylinders of 105 Cesium atoms at each site and operated under quantum control of single detection events.

Coherence and entanglement with atomic ensembles

Atomic ensembles enabled quantum correlations, efficient single-photon generation, and heralded entanglement stored in remote quantum memories. These capabilities supported quantum-repeater functionality, while EIT enabled deterministic light–ensemble state mapping and experiments characterized decoherence.

  • DLCZ protocol: 74% free-space and 84% cavity conditional readout efficiencies demonstrated transfer from a stored collective spin excitation to a single photon.The transfer used efficient mapping of collective atomic excitation to propagating wavepackets.
  • Heralded entanglement: Heralded entanglement was stored in two quantum memories located in distinct apparatuses separated by 3 m.The entanglement was later confirmed by mapping the atomic state to optical fields and measuring mutual coherence and photon statistics.
  • Scalable quantum networks: The DLCZ architecture used independent operations on parallel chains, with scalability relying on conditional control of states stored in remote quantum memories.An experiment achieved minimal functionality required for scalable quantum networks by creating heralded entanglement asynchronously between a qubit at a node and a remote system.
  • Deterministic mapping: Electromagnetically induced transparency enabled deterministic mapping of quantum states of light to and from atomic ensembles.Experiments progressed from storing and retrieving classical pulses to operating with single photons and entanglement between ensembles coupled to a cavity mode.
  • Decoherence characterization: Decoherence was characterized through decay of Bell-inequality violation, teleportation fidelity, and quantitative measurements of concurrence C(t).These measurements related the evolution of stored atomic excitation and entanglement to time.

EXTENDING ENTANGLEMENT FOR QUANTUM NETWORKS

Extending quantum networks beyond bipartite entanglement requires experimentally implementable verification protocols and practical ways to determine whether entanglement spans complex networks. Full density-matrix characterization scales exponentially, while algorithmic tests may fail below network-size thresholds, motivating physical many-body diagnostics.

  • Beyond bipartite entanglement: Existing cavity-QED and DLCZ experiments create bipartite entanglement, whereas shared entanglement among N > 2 systems remains an important research goal.Operational verification procedures are definitive for bipartite entanglement; protocols for more general states must be suitable for laboratory implementation.
  • Verification challenges: As quantum networks become moderately complex, quantitatively determining whether entanglement extends across the whole network becomes increasingly difficult.The challenge is framed as answering whether the network works and assessing its characteristics.
  • Verification challenges: Characterizing the network through its density matrix ρ(t) fails because ρ(t) grows exponentially with network size.The passage identifies exponential growth as the reason this physically motivated strategy is impractical.
  • Verification challenges: Testing a network with quantum algorithms is problematic because its quantum advantage may emerge only above a threshold network size.The approach aims to distinguish quantum capability from any classical counterpart but may not reveal an advantage below that threshold.
  • Many-body diagnostics: Many-body approaches instead examine physical characteristics such as pair-correlation scaling and multipartite entanglement, including behavior near quantum phase transitions.This perspective treats the quantum network as a quantum many-body system and builds on work in one-dimensional spin chains.

CONCLUSION

Realizing functional quantum networks still requires major theoretical and experimental advances, including reliable entanglement verification and scalable network components. The field is moving toward heterogeneous, complex systems while also advancing broader quantum science through controlled single-photon–atom interactions.

  • Conclusion: Functional quantum networks remain scientifically challenging, with current capabilities still primitive compared with robust, scalable network protocols.Needed advances include quantum memories, local quantum processing, quantum repeaters, and error correction.
  • Conclusion: Quantum networks are expected to evolve as heterogeneous entities combining cavity QED-based and DLCZ-based implementations.The same entanglement-generation protocol can connect atomic ensembles with an atom in a cavity.
  • Conclusion: Unambiguous entanglement verification is a critical, nontrivial task that has not always been performed correctly.The conclusion identifies verification procedures as essential for dependable quantum-network development.
  • Conclusion: Quantum-network research also advances quantum dynamical systems and creates new physics through controlled nonlinear interactions of single photons and atoms.The field is progressing from individual components such as a single atom-cavity system toward complex quantum systems.

BOX 1 - MAPPING QUANTUM STATES BETWEEN ATOMS AND PHOTONS

The section describes reversible atom–photon state transfer through coherent single-photon absorption and emission, enabling propagating optical-field states to be stored in and retrieved from a long-lived atomic quantum memory.

  • Atom–photon mapping: Reversible mappings |b⟩|1⟩→|a⟩|0⟩ and |a⟩|0⟩→|b⟩|1⟩ coherently absorb and emit single photons between atomic and cavity-field states.The atomic states |a⟩ and |b⟩ have long-lived coherence, while |0⟩ and |1⟩ denote zero- and one-excitation Fock states.
  • Atom–photon mapping: Adiabatically ramping control fields maps |b⟩ to |a⟩ during photon absorption and |a⟩ to |b⟩ during one-photon emission into the cavity mode.The ramp duration is slow compared with 1/g for absorption, with control-field direction determining the transfer.
  • Quantum-memory operation: The atomic states serve as a long-lived quantum memory, and a user-selected retrieval time t+τ is set by turning the second control field from off to on.The retrieved state is coherently mapped back to the flying field state β(t) = |φfield(t + τ)⟩.

BOX 2 - A NEW PARADIGM FOR CAVITY QED

Large-scale quantum networks require alternatives to conventional Fabry-Perot cavities, and microtoroidal resonators provide strong light–matter coupling with efficient, low-loss connectivity. Their integration and demonstrated atom–cavity interactions support scalable optical networks and nonclassical photon control.

  • Motivation: Large-scale quantum networks require interconnecting many quantum nodes over channels, but conventional Fabry-Perot configurations are ill suited, motivating alternative microcavity systems.Candidate systems include platforms for single atoms and atom-like systems such as nitrogen vacancy centers in diamond.
  • Microtoroidal resonators: Microtoroidal cavities support whispering gallery modes with evanescent external fields, while small mode volume and large quality factor enable strong atom–field coupling.The resonator is formed from fused silica (SiO2).
  • Network integration: Fabrication techniques enable integration of many microtoroidal resonators on silicon chips, forming optical networks with fiber-taper coupling.An illustrated implementation places a linear array of resonators within an ultrahigh-vacuum apparatus.
  • Performance: Q = 4×10^8 at λ = 1550 nm and Q ≃10^8 at λ = 850 nm have been realized, with prospects for improvement to Q ∼10^10.The resonators also support input-output coupling with small parasitic loss.
  • Performance: ϵ ∼0.99 −0.999 could be achieved for coupling quantum fields into and out of the resonator while remaining firmly in the strong-coupling regime.Such efficiency is identified as critical for complex quantum networks that distribute and process quantum information.
  • Demonstrations: Experiments demonstrated strong coupling between individual atoms and microtoroidal resonators, followed by a photon turnstile that regulated one-by-one photon transmission.The turnstile used a single atom to dynamically control photon transport through the resonator.

BOX 3 - WRITING AND READING SINGLE ATOMIC EXCITATIONS

The DLCZ protocol writes a probabilistic, collectively shared atomic excitation heralded by a detected photon, then reads it out after a delay as a propagating field excitation. The write and read processes provide reversible optical coupling between atomic and photonic states.

  • Writing single atomic excitations: The ensemble begins with Na identical atoms in a Λ-level configuration, all prepared in the metastable ground state |g⟩ with no excitation.The metastable states |g⟩ and |s⟩ can be atomic hyperfine ground states, supporting long-lived coherence.
  • Writing single atomic excitations: A weak off-resonant write pulse transfers one atom from |g⟩ to |s⟩ with amplitude √p while emitting a distinguishable photon into forward-scattered field 1.The emitted photon differs from the write field in frequency and/or polarization.
  • Writing single atomic excitations: For small excitation probability p ≪1, the write pulse usually produces no excitation, while the one-excitation component is a symmetric collective spin flip shared among Na atoms.The phase of the joint atomic-field state is determined by the write pulse and field 1 propagation phases.
  • Reading single atomic excitations: A field 1 detection event occurs with probability ∝p and heralds, with high probability, storage of a single atomic excitation |1a⟩ in the ensemble.Multiple atomic and field 1 excitations can occur, ideally with lowest-order probability p2.
  • Reading single atomic excitations: After a user-defined delay limited by quantum-memory lifetime, a strong read pulse converts |1a⟩ one-to-one into propagating field excitation |12⟩.For resonance on the |s⟩→|e⟩ transition, the read process uses electromagnetically induced transparency.
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