Two photon conditional phase gate based on Rydberg slow light polaritons

Abstract

We analyze the fidelity of a deterministic quantum phase gate for two photons counterpropagating as polaritons through a cloud of Rydberg atoms under the condition of electromagnetically induced transparency (EIT). We provide analytical results for the phase shift of the quantum gate, and provide an estimation for all processes leading to a reduction to the gate fidelity. Especially, the influence of losses form the intermediate level, dispersion of the photon wave packet, scattering into additional polariton channels, finite lifetime of the Rydberg state, as well as effects of transverse size of the wave packets are accounted for. We show that the flatness of the effective interaction, caused by the blockade phenomena, suppresses the corrections due to the finite transversal size. This is a strength of Rydberg-EIT setup compared to other approaches. Finally, we provide the experimental requirements for the realization of a high fidelity quantum phase gate using Rydberg polaritons.

Singularities in nearly-uniform 1D condensates due to quantum diffusion

“…Dropping terms containing two and three derivatives, we find Eqs. ( 11) and (12) in the main text. Anticipating a solution where the density approaches a constant ρ 0 asymptotically and recalling ξ ≡ 1/mU ρ 0 , τ ≡ mξ 2 , c ≡ √ 2ξ/τ , these equations can be cast as The solution is valid only when v(z) is single-valued for all z (indicated by a green background).…”

“…Here we first derive the hydrodynamic equations in the main text, Eqs. ( 11) and (12), and then construct soliton solutions to them. For the derivation, we no longer assume ∆ρ ρ 0 but continue to make the long-wavelength approximation.…”

“…A prominent example is Rydberg systems, which have received much interest as a platform for quantum nonlinear optics [1][2][3] and quantum information processing/simulation [4][5][6][7][8][9][10][11][12]. The polaritons that form under the condition of electromagnetically-induced transparency (EIT) [13][14][15] undergo quantum diffusion, i.e., a one-body loss rate Γ k ∝ k 2 [2].…”

Variational analysis of driven-dissipative bosonic fields

“…Driven-dissipative systems of bosons arise in many different settings, ranging from semiconductor polaritonic systems [9], to cavity quantum electrodynamics arrays [10], to Rydberg polaritons in atomic quantum gases [11,12]. Especially for the latter, the development of efficient numerical descriptions is of great interest due to the applications of Rydberg polaritons in the context of strongly correlated photon states [13] and photonic quantum computing [14][15][16].…”

Exotic photonic molecules via Lennard-Jones-like potentials

“…An especially promising platform to achieve this goal are Rydberg polaritons, for which strong interactions between Rydberg states are mapped onto photons via electromagnetically induced transparency [8][9][10]. The effective interactions between photons are not only strong [11], but also saturate to a constant value [12][13][14] for distances shorter than the blockade radius r b ∼ 10 µm, which usually is much greater than the wavelength of the optical photons. These properties have enabled several theoretical proposals and experimental realizations related to quantum information processing, such as quantum gates [15,16], transistors [17][18][19], and nonclassical states of light [20][21][22].…”