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arXiv:1203.1402 · Physical Review A

Eigenmode description of Raman scattering in atomic vapors in the presence of decoherence

Jan Kołodyński, Jan Chwedeńczuk, Wojciech Wasilewski

Published Jul 13, 2012• 12 citations
arXivHTMLPDF

Abstract

A theoretical model describing the Raman scattering process in atomic vapors is constructed. The treatment investigates the low-excitation regime suitable for modern experimental applications. Despite the incorporated decoherence effects (possibly mode dependent) it allows for a direct separation of the time evolution from the spatial degrees of freedom. The impact of noise on the temporal properties of the process is examined. The model is applied in two experimentally relevant situations of ultracold and room-temperature atoms. The spatial eigenmodes of the Stokes photons and their coupling to atomic excitations are computed. Similarly, dynamics and the waveform of the collective atomic state are derived for quantum memory implementations.

DOI
10.1103/physreva.86.013818

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A theoretical model describing the Raman scattering process in atomic vapors is constructed. The treatment investigates the low-excitation regime suitable for modern experimental applications. Despite the incorporated decoherence effects (possibly mode dependent) it allows for a direct separation of the time evolution from the spatial degrees of freedom. The impact of noise on the temporal properties of the process is examined. The model is applied in two experimentally relevant situations of ultracold and room-temperature atoms. The spatial eigenmodes of the Stokes photons and their coupling to atomic excitations are computed. Similarly, dynamics and the waveform of the collective atomic state are derived for quantum memory implementations.
We apply collective Raman scattering to create, store and retrieve spatially multimode light in warm rubidium-87 vapors. The light is created in a spontaneous Stokes scattering process. This is accompanied by the creation of counterpart collective excitations in the atomic ensemble - the spin waves. After a certain storage time we coherently convert the spin waves into the light in deterministic anti-Stokes scattering. The whole process can be regarded as a delayed four-wave mixing which produces pairs of correlated, delayed random images. Storage of higher order spatial modes up to microseconds is possible owing to usage of a buffer gas. We study the performance of the Raman scattering, storage and retrieval of collective excitations focusing on spatial effects and the influence of decoherence caused by diffusion of rubidium atoms in different buffer gases. We quantify the number of modes created and retrieved by analyzing statistical correlations of intensity fluctuations between portions of the light scattered in the far field.
A quantum theory of stimulated Raman scattering is established that takes into account the time-dependence of pump laser pulse, two-photon detuning and atomic populations, allowing the general transient and spatial propagation study of Raman memory. Heisenberg–Langevin and Maxwell equations for the collective atomic operators are solved analytically under adiabatic condition , where the electric field envelopes and the collective atomic operators vary slowly. The analytical solution of Stokes/anti-Stokes signal electric field operator is obtained. The spatial–temporal intensity of quantum signal field is studied numerically and analytically for different two-photon detunings and initial populations.
Abstract Stimulated Raman scattering (SRS) is highly relevant to quantum memories involving Raman system. Using quantum Langevin equations with complete noise operators coupled to the quantum field propagation equation, we present a general theory of SRS for moving quantum particles where quantum Stokes pulse couples to both transitions (m1 and m3) while an arbitrary laser pulses couple to only one (m1) transition. Our coupled equations contain dynamical ac Stark shift due to laser pulses and Doppler shift, complete quantum noise operators and atomic coherences corresponding to all possible three transitions (not only the ground state coherence), quantum mechanical microscopic expressions for linear and nonlinear interactions with nonlocal (memory) or temporal dispersion effects. We obtain an analytical solution of the quantum Stokes field in laboratory spacetime with generalized quantum noise operators that include all initial atomic coherences and arbitrary initial and boundary quantum fields, valid for arbitrary laser pulses. The general solution provides a complete physical picture, composed of basically two parts: above and below the light line, t = z/c. This robust framework offers a powerful tool for optimizing Raman-based quantum information processes, particularly for modeling the spatial-temporal dynamics of quantum Stokes pulses in storage and retrieval stages of quantum memory.
We present an experimental demonstration of the Hamiltonian manipulation in light-atom interface in Raman-type warm rubidium-87 vapor atomic memory. By adjusting the detuning of the driving beam we varied the relative contributions of the Stokes and anti-Stokes scattering to the process of four-wave mixing which reads out a spatially multimode state of atomic memory. We measured the temporal evolution of the readout fields and the spatial intensity correlations between write-in and readout as a function of detuning with the use of an intensified camera. The correlation maps enabled us to resolve between the anti-Stokes and the Stokes scattering and to quantify their contributions. Our experimental results agree quantitatively with a simple, plane-wave theoretical model we provide. They allow for a simple interpretation of the coaction of the anti-Stokes and the Stokes scattering at the readout stage. The Stokes contribution yields additional, adjustable gain at the readout stage, albeit with inevitable extra noise. Here we provide a simple and useful framework to trace it and the results can be utilized in the existing atomic memories setups. Furthermore, the shown Hamiltonian manipulation offers a broad range of atom-light interfaces readily applicable in current and future quantum protocols with atomic ensembles.
We analyse the properties of a Raman quantum light-atom interface in long atomic ensemble and its applications as a quantum memory or two-mode squeezed state generator. We consider the weak-coupling regime and include both Stokes and anti-Stokes scattering and the effects of Doppler broadening in buffer gas assuming frequent velocity-averaging collisions. We find the Green functions describing multimode transformation from input to output fields of photons and atomic excitations. Proper mode basis is found via singular value decomposition for short interaction times. It reveals that triples of modes are coupled by a transformation equivalent to a combination of two beamsplitters and a two-mode squeezing operation. We analyse the possible transformations on an example of warm rubidium-87 vapour. The model we present bridges the gap between the Stokes only and anti-Stokes only interactions providing simple, universal description in a temporally and longitudinally multimode situation. Our results also provide an easy way to find an evolution of the states in a Schrödinger picture thus facilitating understanding and design.
The temperature effect on the resonance Raman scattering from molecules is investigated. Considering a total system consisting of a molecular system, a heat bath, and the weak radiation field, a general expression for the relaxation processes is derived utilizing the Liouville operator technique for the time evolution of the density matrix of the total system. By using the perturbation method with respect to the radiation and matter up to second order, rate constants for zero photon (radiationless processes), one-photon and two-photon processes are derived after taking the long time limit in the Markoff approximation. Assuming a weak interaction between the molecular system and heat bath, a temperature-dependent resonance Raman scattering cross section is formulated in the adiabatic basis set for the molecular systems. In the displaced harmonic oscillator model, we obtain an analytical expression for the temperature-dependent Raman scattering cross section for the multimode case, which is suitable for both weak coupling and strong coupling cases. Analytical expressions for the Stokes and anti-Stokes bands of the jth order vibrational transition in the one oscillator model can easily be obtained from the general expression for the resonance Raman scattering cross section derived. An approximate Stokes to anti-Stokes ratio is given up to the second order of the dimensionless displacement Δ. The resonance Raman scattering cross section and the excitation energy profiles are numerically calculated as a function of physical constant such as temperature, molecular vibrational frequency and Δ. It is shown that the excitation profiles of the anti-Stokes band of the jth order vibrational transition have the similar envelope of the corresponding Stokes band shifted by jh/ω. The inverse Raman effect which is closely related to the ordinary Raman effect is also discussed.