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European Quantum Electronics Conference (EQEC)

Giant interaction and entanglement of photons for deterministic optical quantum computation

David Petrosyan, Inbal Friedler, Gershon Kurizki

Published Jan 18, 2006• 0 citations
Publisher

Abstract

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.

DOI
10.1109/eqec.2005.1567485

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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.
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.
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.
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]
Mapping the strong interaction between Rydberg excitations in ultra-cold atomic ensembles onto single photons enables the realization of optical nonlinearities which can modify light on the level of individual photons.This novel approach forms the basis of a growing Rydberg quantum optics toolbox, which already contains photonic logic building-blocks such as single-photon sources, switches, transistors, and conditional π-phase shifts.This thesis reports on two experiments investigating strong photon-photon interactions mediated by Rydberg interactions.First, applying a ladder-type EIT scheme to Rydberg atoms in D-states with high principal quantum number results in the Rydberg interaction mediated nonlinearity accompanied by a time-dependent decay of transmission of probe light through the medium.In a joint experimental and theoretical analysis, this effect is attributed to the dephasing of propagating polaritons into stationary Rydberg excitations caused by the state mixing interaction occurring with Rydberg D-state atoms.Second, via a two-photon Raman excitation scheme Rydberg atoms are efficiently excited in a small atomic cloud.As the size of the Rydberg blockade exceeds the dimension of the medium, only a single Rydberg excitation can be present at a time.By fast engineered dephasing this Rydberg excitation is decoupled from the light field.Measurement of the transmitted light and the amount of excited Rydberg atoms gives evidence for the realization of a deterministic single-photon absorber.