Atoms Exchange Quantum States with Near-Total Stability over Distance

A new method for transferring quantum entanglement within a multi-giant-atom waveguide system has been achieved by Peng-Fei Wang of College of Physics and Electronic Engineering, and colleagues from Hainan Normal University. Perfect, unidirectional entanglement transfer was demonstrated by manipulating chiral spontaneous emission and dark-state dynamics, dynamically adjusting the entanglement length between atoms. The system maintains strong entanglement, even under challenging non-Markovian conditions, and offers a scalable approach to continuous, long-distance entanglement transport for future quantum networks, effectively mimicking braided architectures without their inherent limitations.

Persistent entanglement via chiral emission enables dynamic quantum state transfer

Researchers at Physics and Electronic Engineering and Hainan Normal University have demonstrated nearly lossless quantum state exchange between giant atoms, achieving a system where state exchange alternates back and forth with fidelity exceeding 99%. This represents a sharp improvement over conventional braided architectures, which suffer from propagation delays and spatial restrictions limiting long-distance entanglement. The team’s approach utilises chiral spontaneous emission and dark-state dynamics to enable persistent entanglement, even under challenging non-Markovian conditions where information is typically lost. This breakthrough allows for dynamic adjustment of entanglement length, enabling conversion between short-range and long-range entanglement during propagation, a capability previously unattainable without complex structural configurations.

Precise tuning of an additional phase applied to each atom’s coupling points demonstrated selective transfer of entanglement, not just between adjacent atoms but also between spatially separated ones. The system consistently converges towards a dark state, a condition protecting quantum information, guaranteeing high-fidelity directional transfer of quantum states. Stable, nearly lossless state exchange is achieved even when subjected to non-Markovian conditions, mimicking complex braided architectures without their inherent limitations. This dynamic adjustment enables switching between short and long-range entanglement during propagation.

Giant atom implementations for strong quantum entanglement distribution

Scientists have demonstrated a pathway for continuous long-distance entanglement transport and resilient state exchange in quantum networks. Giant atoms are quantum emitters interacting with their environment via multiple independent coupling points, giving rise to self-interference effects profoundly modifying atomic decay and coherence. These effects enable phenomena such as decoherence-free interactions, chiral spontaneous emission, non-Markovian retardation, and unconventional bound states.

Quantum entanglement is central to quantum information science, underpinning both fundamental physics and emerging technologies. Entanglement has been generated and manipulated across diverse platforms over the past decades. Giant atoms have been experimentally realised with superconducting qubits coupled to surface acoustic waves and microwave transmission lines, with other implementations proposed in dynamic optical lattices, coupled waveguide arrays, Rydberg atoms, synthetic photonic dimensions, and spin ensembles.

Waveguide quantum electrodynamics has emerged as a powerful platform for long-distance entanglement generation, scalable quantum networks and information processing architectures. However, state and entanglement transfer are often limited by dissipation and limited controllability in conventional atom-waveguide systems, leading to information loss. Giant atoms offer a compelling alternative: their low dissipation and multipoint coupling geometry naturally suppress information loss and enhance tunability, making them promising for high-fidelity quantum state and entanglement transfer.

In giant-atom systems, quantum state transfer is intimately related to the generation of entanglement. A common approach is the braided coupling configuration, enabling near-perfect state transfer via decoherence-free interactions under Markovian conditions. However, state transfer is often not strictly sequential in multi-atom systems, potentially leading to simultaneous entanglement generation. Information loss can also occur during transfers under non-Markovian conditions.

Building on previous work, a system of giant atoms coupled to a one-dimensional waveguide can realise perfect unidirectional sequential transfer of quantum states and their corresponding entanglement. This is achieved by engineering the atom-waveguide coupling coefficients to satisfy periodic time-reversal symmetry and by introducing additional phase modulations enabling chiral spontaneous emission and dark-state evolution. Under these conditions, the system supports strictly sequential entanglement propagation: the entangled pair is created, annihilated, and recreated between neighboring atoms along the chain, enabling directional entanglement flow.

By tuning the additional phase, selective transfer between non-adjacent atoms becomes accessible, and the entanglement length can be varied dynamically, allowing strong interconversion between long-range and short-range entanglement during propagation. Furthermore, a periodic piecewise phase modulation induces persistent, nearly lossless state exchange between distant giant atoms, sustaining stable entanglement even under non-Markovian dynamics. This behaviour mimics conventional braided giant-atom configurations but avoids their structural constraints and propagation-delay limitations.

Unlike conventional braided architectures, where long-distance state exchange is hindered by structural complexity and non-Markovian delays, this model requires only two giant atoms to achieve long-range, near-lossless quantum state transfer and generate stable entanglement under non-Markovian conditions. This scheme thus provides a scalable route towards continuous, long-distance entanglement transport and robust state exchange in quantum networks. The system spontaneously evolves into and remains in a dark state, further guaranteeing high-fidelity directional transfer.

Section II introduces the system model and equations of motion. Section III establishes the two key conditions for achieving near-perfect and stable quantum state transfer, chiral spontaneous emission and dark-state construction, and analyses their close connection to entanglement dynamics. Section IV demonstrates unidirectional sequential transfer of quantum states and entanglement, showing that selective transfer between non-adjacent atoms is accessible by tuning the additional phase.

Additionally, the entanglement length can be dynamically varied, enabling strong interconversion between long-range and short-range entanglement during propagation. Finally, Section V reveals the mechanism underlying sustained state exchange and steady entanglement under a periodic piecewise phase modulation, which reverses the chiral direction periodically and produces persistent, nearly lossless back-and-forth state exchange even under non-Markovian dynamics. Section VI concludes the paper.

The system consists of an array of N identical two-level giant atoms with transition frequency ωa coupled to an infinite one-dimensional lattice. Each lattice site has resonance frequency ω0, and η denotes the nearest-neighbour hopping rate. The l-th atom couples to the lattice sites n2l−1 and n2l with the time-dependent coupling coefficient gl(t), with a phase difference φl between the two coupling points breaking the time-reversal symmetry. The total Hamiltonian is H = Ha + Hw + Haw (ħ= 1), where Ha = N X l=1 ωaσ+ l σ− l, Hw = X j ω0a† jaj − X j η aja† j+1 + H.c., and Haw = N X l=1 gl(t) h σ− l a† n2l−1 + eiφla† n2l + H.c. i. Here, aj (a† j) annihilates (creates) a photon at site j, and σ− l = |g⟩ll⟨e| (σ+ l = |e⟩ll⟨g|) is the lowering (raising) operator of atom l with the ground state |g⟩l and the excited state |e⟩l. In the single-excitation subspace, the system state is |Ψ(t)⟩= X j cj(t)a† j + N X l=1 ul(t)σ+ l |G⟩, where cj(t) and ul(t) denote the excitation amplitudes of the j-th lattice site and the l-th atom at time t, respectively, and |G⟩= |g⟩⊗N⊗|∅⟩⊗∞(|∅⟩is the vacuum state of a lattice site.

A multi-giant-atom waveguide system enables perfect, unidirectional sequential transfer of quantum states and associated entanglement by tailoring chiral spontaneous emission and exploiting dark-state dynamics. The distance between entangled atoms, termed the entanglement length, can be dynamically adjusted, allowing conversion between long-range and short-range entanglement during propagation. The system converges to a dark state, guaranteeing high-fidelity directional transfer.

When the additional phase is modulated as a periodic piecewise function, spatially separated giant atoms exhibit stable, nearly lossless state exchange and maintain steady entanglement even under non-Markovian conditions. This behaviour mimics conventional braided architectures without propagation delays or spatial restrictions. This proposal offers a scalable pathway for continuous long-distance entanglement transport and resilient state exchange in quantum networks.

The group velocity, given by 2η sin(k) / 3, governs not only the speed of propagation but also its directionality. Analysis of the lattice energy band is performed relative to the giant-atom transition frequency. From the equation, the photon modes supported under this condition are left- and right-propagating waves with wave vectors kL = −π/2 and kR = π/2, respectively. Chiral spontaneous emission into a given direction requires coupling to the opposite mode to vanish while that to the desired mode remains finite.

Specifically, emission into the right-propagating mode and the complete suppression of left-propagating emission are achieved when −φl(kL) + φl = π + 2nπ and −φl(kR) + φl = π + 2nπ; conversely, emission into the left-propagating mode requires −φl(kR) + φl = π + 2nπ and −φl(kL) + φl = π + 2nπ. The jump operators associated with the right- and left- propagating modes are given by: JN L = N X l=1 eika(l−1)dsw q Γl L(t)σ− l, and JN R = N X l=1 eika(N−l)dsw q Γl R(t)σ− l, where ka = π/2, dsw = ds + dw, Γl R (t) = Γl (t) [1 + cos (−φl(kR) + φl)] /2, Γl L (t) = Γl (t) [1 + cos (−φl(kL) + φl)] /2, and Γl(t) = 4g2 l (t)/vg. When only right-propagating photons are present in the waveguide, JN L = 0. Under this condition, the propagation phase φl(kL) and the coupling phase φl must satisfy −φl(kL) + φl = π + 2nπ for some integer n. This phase-matching condition ensures that the dark-state evolution requires the right-propagating jump operator to satisfy JN R |Ψ(t)⟩= 0, which imposes the following constraint on the probability amplitudes: N X l=1 eiπ(N−l)dsw/2p Γl(t) |sin [φl (kR)]| ul(t) = 0. This equation simplifies when dsw = 4n with n an integer. For a two-atom system, setting ds = 3, dw = 1, and φl = −π/2, the equation reduces to p Γ1(t)u1(t) + p Γ2(t)u2(t) = 0. Perfect state transfer requires boundary conditions: |u1 | = |u2 (tc)| = 1, and |u1 (tc)| = |u2 | = 0. To simultaneously satisfy these equations, g1(t) = g2(t0 + τsw −t), where τsw = dsw/vg characterizes the time delay induced by non-Markovian effect. The coupling functions are chosen as g1(t) = g0 eα(t−t0 2 ) 2 −eα(t−t0 2 ) , 0 ⩽t

Dynamically adjustable entanglement offers a major route towards scalable quantum communication networks

The team’s demonstration of dynamic entanglement length adjustment and nearly lossless state exchange offers a potentially major approach to building quantum networks, systems where quantum information can be transmitted securely over vast distances. The researchers acknowledge a reliance on theoretical modelling, and while simulations suggest scalability, a vital gap remains in demonstrating physical realisation of this system. This work presents a significant advance in quantum network design.

The researchers have outlined a method for dynamically adjusting entanglement length, the distance over which two quantum particles remain linked, within a waveguide system. This adjustment allows for strong conversion between short and long-range entanglement during transmission, mirroring conventional architectures without their inherent delays. The team has demonstrated a method for sustaining entanglement between spatially separated quantum particles, termed giant atoms, within a waveguide system. This achievement bypasses limitations of traditional approaches, such as propagation delays inherent in braided architectures, by dynamically controlling the entanglement length. In particular, the system’s inherent convergence towards a dark state, a condition shielding quantum information, ensures high-fidelity transfer even under challenging, non-ideal conditions where signals typically degrade.

Researchers demonstrated perfect, unidirectional transfer of entanglement between giant atoms within a waveguide system. This is important because it provides a scalable method for transporting quantum information over long distances, potentially aiding the development of quantum networks. The team showed entanglement length could be dynamically adjusted, allowing conversion between short and long-range entanglement during propagation and maintaining stable state exchange even under non-ideal conditions. They suggest this approach replicates conventional architectures without the limitations of spatial restrictions or propagation delays.