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

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 multi-level atoms in a ladder configuration. In contrast to previously studied schemes, this mechanism can yield a homogeneous conditional phase shift of π even for weakly focused singlephoton pulses, thereby allowing a deterministic realization of the photonic phase gate.PACS numbers: 42.50.Gy, 03.67.LxWhether or not quantum information processing and quantum computing [1] become practical technologies crucially depends on the ability to implement highfidelity quantum logic gates in a scalable way [2]. Among alternative routes to this challenging goal, are of particular interest the schemes operating with photons as qubits [3,4], since photons are ideal carriers of quantum information in terms of transfer rates, distances and scalability. A current trend makes use of linear optical elements and photodetectors for the implementation of key components of quantum communications and information processing in a probabilistic way [4]. The desirable objective though is a deterministic realization of entangling operations between individual photons, which require sufficiently strong nonlinearities or long interaction times. These are achievable, at the single-photon level, by tight spatial confinement of the photons, in the very demanding regime of strong atom-field coupling in high-Q cavities [5].A promising alternative is to enhance both the nonlinear susceptibility and interaction time, by employing the ultra-slow light propagation in resonant media subject to electromagnetically induced transparency (EIT) [6,7,8]. In a pioneering work, Schmidt and Imamoglu have suggested the possibility of enhanced, non-absorptive, crossphase modulation of two weak fields in the EIT regime [9], provided their interaction time is long enough. However, upon entering the EIT medium light pulses become spatially compressed by the ratio of group velocity v to the vacuum speed of light c [10], so that the interaction time of two colliding pulses is a constant independent of v. In order to maximize this time, copropagating pulses with nearly matched group velocities have been proposed [11,12]. The essential drawback of such an approach is the spatial inhomogeneity of the conditional phase shift, causing spectral broadening of the interacting pulses, thereby preventing the realization of a highfidelity quantum phase gate. Alternative approaches free of spectral broadening have been suggested [13,14,15]. In all of them, however, a rather tight transverse confinement through waveguiding or focusing of the pulses, close to the diffraction limit of λ 2 , is needed in order to attain a phase shift of π, which is technically challenging.When the light pulses enter EIT media, photonic excitations are temporarily transferred to atomic excitations ...

Quantum nonlinear optics — photon by photon

“…In the simplest case of resonant Rydberg EIT (both lasers resonant with their respective transitions, Fig. 4), the strong interaction between two Rydberg atoms tunes the two-photon transition out of resonance, thereby destroying the transparency and leading to absorption 22,58,59,[62][63][64] for two or more photons. The quantum nonlinearity in this case arises from the Rydberg excitation blockade 61 , which precludes the simultaneous excitation of two Rydberg atoms that are separated by less than the blockade radius r b (Fig.…”

“…An alternative approach that does not require the use of optical resonators exploits strong atom-atom interactions in the metastable state |rñ of an EIT scheme [58][59][60][61] (Fig. 4).…”

Photon-photon gate via the interaction between two collective Rydberg excitations

“…There is a significant body of work studying the effects of mapping photons onto collective atomic Rydberg excitations [14][15][16][17][18][19][20]. Most proposals for photon-photon gates involve propagating Rydberg excitations (polaritons), either using blockade [21,22] or two excitations [23][24][25][26].…”

“…Achieving blockade conditions can be challenging since both photons have to be localized within the blockade volume. Following [6,7,[23][24][25][26], we here propose a storage-based scheme that instead relies on the interaction between two stationary Rydberg excitations.The main challenge for two-excitation based Rydberg gates in atomic ensembles arises from the fact that the interaction is strongly distance-dependent and thus not uniform over the profiles of the two stored photons. We show that this a priori reduces the gate's fidelity by displacing the collective excitations in momentum space and by entangling their quantum states.…”

“…Achieving blockade conditions can be challenging since both photons have to be localized within the blockade volume. Following [6,7,[23][24][25][26], we here propose a storage-based scheme that instead relies on the interaction between two stationary Rydberg excitations.…”