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arXiv:quant-ph/0503071 · Physical Review A

Long-range interactions and entanglement of slow single-photon pulses

Inbal Friedler, David Petrosyan, Michael Fleischhauer, Gershon Kurizki

Published Oct 5, 2005• 215 citations
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Abstract

We show that very large nonlocal nonlinear interactions between pairs of colliding slow-light pulses can be realized in atomic vapors in the regime of electromagnetically induced transparency. These nonlinearities are mediated by strong, long-range dipole-dipole interactions between Rydberg states of the multilevel atoms in a ladder configuration. In contrast to previously studied schemes, this mechanism can yield a homogeneous conditional phase shift of $\ensuremath{\pi}$ even for weakly focused single-photon pulses, thereby allowing a deterministic realization of the photonic phase gate.

DOI
10.1103/physreva.72.043803

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中国科学通报：英文版•Sep 8, 2026•0 citations
We show that very large nonlocal nonlinear interactions between pairs of colliding slow-light pulses can be realized in atomic vapors in the regime of electromagnetically induced transparency. These nonlinearities are mediated by strong, long-range dipole-dipole interactions between Rydberg states of the multilevel atoms in a ladder configuration. In contrast to previously studied schemes, this mechanism can yield a homogeneous conditional phase shift of \ensuremathπ\ensuremath{\pi}\ensuremathπ even for weakly focused single-photon pulses, thereby allowing a deterministic realization of the photonic phase gate.
We discuss electromagnetically induced transparency in a cold ensemble of atoms optically excited to the Rydberg states. Strong dipole-dipole or van der Waals interactions between the atomic Rydberg states translate into large nonlocal nonlinearities for a propagating probe field. In the case of weak quantum fields, this can be used to attain a conditional phase shift of π between pairs of single photons realizing a deterministic photonic phase gate. For stronger fields, long-range interactions between the atoms constrain the medium to behave as a collection of superatoms, each comprising a blockade volume that can accommodate at most one Rydberg excitation. The propagation of a probe field is affected by its two-photon correlations within the blockade distance, which are strongly damped due to low saturation threshold of the superatoms. Our calculations reproduce and interpret the results of recent experiments.
Hollow-core photonic-crystal waveguides filled with cold atoms can support giant optical nonlinearities through nondispersive propagation of light tightly confined in the transverse direction. Here we explore electromagnetically induced transparency is such structures, considering a pair of counterpropagating weak quantum fields in the medium of coherently driven atoms in the ladder configuration. Strong dipole-dipole interactions between optically excited, polarized Rydberg states of the atoms translate into a large dispersive interaction between the two fields. This can be used to attain a spatially homogeneous conditional phase shift of $\ensuremath{\pi}$ for two single-photon pulses, realizing a deterministic photonic phase gate, or to implement a quantum nondemolition measurement of the photon number in the signal pulse by a coherent probe, thereby achieving a heralded source of single- or few-photon pulses.
Rydberg atoms have emerged as a versatile platform for quantum optics due to their exaggerated properties, particularly their strong long-range interactions, which enable a new regime of light-matter interaction. By mapping the interactions between Rydberg atoms onto photons, effective photon-photon interactions can be realized at the single-photon level, thereby overcoming the intrinsic weakness of conventional optical nonlinearities. In this review, we first introduce the fundamental physical principles of Rydberg-mediated quantum optics, and then discuss some key developments, including single-photon engineering, photonic quantum gates, contactless nonlinear optics, and quantum entanglement, providing a comprehensive overview of the current state and prospects of this rapidly developing field.
Several novel schemes are studied which pave the way to deterministic quantum logic with photons. In one of such schemes, a weak (quantum) probe pulse, upon propagating through the medium, interacts with the forward and backward components of a weak signal pulse that is dynamically trapped in a photonic band-gap structure. In an alternative scheme, the two pulses propagate in the opposite directions in the EIT medium and interact with each other via strong, long-range dipole-dipole interaction between Rydberg states of the atoms. Both schemes are capable of implementing with high fidelity the conditional phase gate between two single-photon pulses, under physically realistic, experimentally accessible conditions.
We study the giant Kerr nonlinear interaction between two ultraweak optical fields in which the cross-phase-modulation is not accompanied by spectral broadening of the interacting pulses. This regime is realizable in atomic vapors, when a weak probe pulse, upon propagating through the electromagnetically induced transparency (EIT) medium, interacts with a signal pulse that is dynamically trapped in a photonic band gap created by spatially periodic modulation of its EIT resonance. We find that large conditional phase shifts and entanglement between the signal and probe fields can be obtained with this scheme. The attainable $\ensuremath{\pi}$ phase shift, accompanied by negligible absorption and quantum noise, is shown to allow a high-fidelity realization of the controlled-phase universal logic gate between two single-photon pulses.
Photons are ideal carriers of quantum information: they are fast, low-loss, and compatible with mature photonic infrastructure.Linear optical quantum computing exploits these properties but relies on probabilistic measurements and post-selection, incurring an exponential resource overhead that limits scalability [1].Circumventing this bottleneck requires deterministic quantum logic gates, which in turn demand strong, controllable interactions between individual photons.Photons do not interact in free space or in linear optical media.The standard route to attain effective photonphoton interactions is to hybridise photons with interacting matter excitations, forming polaritons.The matter component introduces an interaction-induced anharmonic level shift U into the ladder of polariton states: when one polariton occupies a mode, the next photon sees a shifted resonance (Fig. 1a).The key figure of merit is U/γ, where γ is the total polariton decoherence rate.For U/γ ≪ 1 the nonlinearity is classical; for U/γ ≳ 1 the system enters the quantum nonlinear regime, enabling photon blockade, large conditional phase shifts, and deterministic photonic gates.Atomic Rydberg systems have provided the clearest demonstration of this regime.Atoms excited to Rydberg states -electronic states with large principal quantum numbers n ≫ 1 -possess unique properties [2].Their lifetimes scale as 1/γ ∝ n 3 and transition dipole moments as µ ∝ n 2 , leading to strong dipole-dipole (U ∝ n 4 /r 3 ) or van der Waals (U ∝ n 11 /r 6 ) interactions over long distances r.These interactions can be imprinted onto photons via electromagnetically induced transparency (EIT) [3]: photons hybridise with collective atomic excitations to form slowly propagating Rydberg polaritons that strongly interact with each other over distances of up to tens of micrometres [4].This mechanism has produced photon blockade [5]