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arXiv:1304.3761 · Physical Review Letters

Excitation of a Single Atom with Exponentially Rising Light Pulses

Syed Abdullah Aljunid, Gleb Maslennikov, Yimin Wang, Hoang Lan Dao, Valerio Scarani, Christian Kurtsiefer

Published Sep 3, 2013• 71 citations
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Abstract

We investigate the interaction between a single atom and optical pulses in a coherent state with a controlled temporal envelope. In a comparison between a rising exponential and a square envelope, we show that the rising exponential envelope leads to a higher excitation probability for fixed low average photon numbers, in accordance with a time-reversed Weisskopf-Wigner model. We characterize the atomic transition dynamics for a wide range of the average photon numbers and are able to saturate the optical transition of a single atom with ≈50 photons in a pulse by a strong focusing technique.

DOI
10.1103/physrevlett.111.103001

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•Jan 1, 2013•0 citations
We investigate the interaction between a single atom and optical pulses in a coherent state with a controlled temporal envelope. In a comparison between a rising exponential and a square envelope, we show that the rising exponential envelope leads to a higher excitation probability for fixed low average photon numbers, in accordance with a time-reversed Weisskopf-Wigner model. We characterize the atomic transition dynamics for a wide range of the average photon numbers and are able to saturate the optical transition of a single atom with ≈50 photons in a pulse by a strong focusing technique.
We investigate the interaction between a single87Rb atom and optical pulses with a controlled temporal envelope. In our experiment an atom is coupled to the light field by high numerical aperture aspheric lens that focuses a Gaussian beam to an atom and fixes the spatial overlap with a field. The frequency/temporal overlap can be changed by shaping the temporal envelope of an attenuated coherent pulse with fast modulators [3]. The excitation probability Peis measured by detecting atomic fluorescence with high temporal resolution and normalizing the acquired rates by optical losses (Fig. 1).
Scattering of light by matter has been studied extensively in the past. Yet, the most fundamental process, the scattering of a single photon by a single atom, is largely unexplored. One prominent prediction of quantum optics is the deterministic absorption of a travelling photon by a single atom, provided the photon waveform matches spatially and temporally the time-reversed version of a spontaneously emitted photon. Here we experimentally address this prediction and investigate the influence of the photon's temporal profile on the scattering dynamics using a single trapped atom and heralded single photons. In a time-resolved measurement of atomic excitation we find a 56(11)% increase of the peak excitation by photons with an exponentially rising profile compared with a decaying one. However, the overall scattering probability remains unchanged within the experimental uncertainties. Our results demonstrate that envelope tailoring of single photons enables precise control of the photon-atom interaction.
Summary form only given. Is an atom more likely to scatter a photon with an exponentially rising or decaying temporal profile? We try to answer this question experimentally and investigate the scattering of heralded photons from a single atom in free-space. We use a single Rubidium atom trapped in optical tweezers and prepared in the groundstate of a cyclic dipole transition as a textbook-like two-level system. A time-ordered photon pair source, in conjunction with an asymmetric cavity, generates heralded single photons with an exponentially decaying or rising temporal profile. The heralded photons are resonant with the atomic transition and have a bandwidth comparable to the atomic linewidth. The photons are strongly focused onto the atom by a large numerical aperture lens. We study the scattering dynamics by measuring the atomic emission and the reduction in the number of transmitted photons. We perform the scattering experiment for photons with exponentially decaying and rising temporal envelopes and find that the atomic dynamics depend on the temporal profile of the photon. The atomic absorption is shorter but has a higher maximum for the rising photon than for the the decaying one. Interestingly, the overall probability that the photon is scattered by the atom is similar for decaying and rising photons.
We report on a simple method to prepare optical pulses with exponentially rising envelope on the time scale of a few ns. The scheme is based on the exponential transfer function of a fast transistor, which generates an exponentially rising envelope that is transferred first on a radio frequency carrier, and then on a coherent cw laser beam with an electro-optical phase modulator. The temporally shaped sideband is then extracted with an optical resonator and can be used to efficiently excite a single (87)Rb atom.
We investigate the dynamics of a single two-level atom, which interacts with pulses propagating in two spatial modes (right and left) and frequency continuum. Using Heisenberg equations of motion, we present the explicit analytical derivations and general formalisms for atomic excitation with two-spatial-mode multiphoton pulses in both the Fock and coherent states. Based on those formalisms, we show that perfect atomic excitation by a single-photon Fock state pulse can only be realized when it is rising exponentially shaped in the even mode, a balanced superposition of the two spatial modes. A single photon from a single spatial mode can only give half of the maximal atomic excitation probability. We also show that the maximum atomic excitation probability with multiphoton pulses in the even mode is a monotonic function of the average photon number for the coherent state, but not for the Fock states. Furthermore, we demonstrate that the atomic dynamics can be controlled by the initial relative phase between the two counterpropagating coherent state pulses incident on the atom, which is not the case with the two Fock state pulses.
Quantum information processing tasks have been implemented in various physical platforms. In this thesis, we consider two specific implementations: Part I presents a detailed study of the interaction of a single atom with a light pulse. Part II examines the case of a quantum controlled-phase gate in circuit quantum electrodynamics in the ultrastrong coupling regime. They are both actively pursued by many research groups. In Part I, we first present the framework for a single two-level atom interacting with the quantized electromagnetic field. The effect of temporal and spectral properties of the pulses on atomic excitation is studied for both Fock state and coherent state pulse. The detailed analysis of atomic excited state population is provided for single photon pulse with various temporal shapes. The work is then extended to a more general case with two spatial-modes and multi-photon pulses. The difference between Fock state and coherent state pulse on atomic excitation is further investigated. We find that at few photon levels, the maximum atomic excitation probability is a monotonic function of photon number for the coherent state pulse, but not for the Fock state pulse. Furthermore, we show that the atomic dynamics can be controlled by the initial relative phase between the two counter-propagating coherent state pulses incident on the atom, which is not the case with two Fock state pulses. The theoretical prediction is then compared with an experiment, where a single trapped 87Rb atom interacts with coherent state pulses engineered in temporal shape of rising exponential and rectangular form. Next, we propose a quantum memory setup based on a single two-level atom in a half cavity with a moving mirror. The efficiency of the quantum storage process is studied analytically and