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arXiv:1902.01910 · Physical Review A

Quantum memory and quantum cloning in an atomic frequency comb

Ming Tian, Devin Vega

Published Oct 28, 2019• 2 citations
arXivHTMLPDF

Abstract

An atomic frequency comb (AFC) made of an ensemble of atoms with a periodic optical resonance was originally proposed as a viable approach for quantum memory for photons. In this paper we examine the quantum cloning capacity of an AFC in terms of the spectral distribution of the atomic populations in the energy levels associated with the optical transition. Expressions are derived for the memory readout efficiency, signal to noise ratio, and fidelity for an input at the single photon level. When applied to a square-toothed AFC, our analysis shows that there is a region where amplification from the excited state population results in greater than unit readout efficiency at a cost of fidelity being less than perfect, but still greater than the classical limit. The theory is developed under the assumption that both AFC and photon wave packets are spatially uniform. This can be regarded as a single spatial location inside an AFC and can be further expanded to study optically thick AFC with atomic population in both levels, which may find applications for quantum memory and quantum cloning machine.

DOI
10.1103/physreva.100.042328

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An atomic frequency comb (AFC) made of an ensemble of atoms with a periodic optical resonance was originally proposed as a viable approach for quantum memory for photons. In this paper we examine the quantum cloning capacity of an AFC in terms of the spectral distribution of the atomic populations in the energy levels associated with the optical transition. Expressions are derived for the memory readout efficiency, signal to noise ratio, and fidelity for an input at the single photon level. When applied to a square-toothed AFC, our analysis shows that there is a region where amplification from the excited state population results in greater than unit readout efficiency at a cost of fidelity being less than perfect, but still greater than the classical limit. The theory is developed under the assumption that both AFC and photon wave packets are spatially uniform. This can be regarded as a single spatial location inside an AFC and can be further expanded to study optically thick AFC with atomic population in both levels, which may find applications for quantum memory and quantum cloning machine.
Abstract Atomic frequency comb (AFC) quantum memories are a promising technology for quantum repeater networks because they enable multi-mode, long-time, and high-fidelity storage of photons with on-demand retrieval. The optimization of the retrieval efficiency of an AFC memory is important because it strongly impacts the entanglement distribution rate in quantum networks. Despite initial theoretical analyses and recent experimental demonstrations, a rigorous proof of the universally optimal configuration for the highest AFC retrieval efficiency has not been presented. In this paper we present a simple analytical proof which shows that the optimized square tooth offers the highest retrieval efficiency among all tooth shapes, under the physical constraint of finite optical depth of an atomic ensemble. The optimality still holds when the non-zero background absorption and the finite optical linewidth of atoms are considered. We further compare square, Lorentzian and Gaussian tooth shapes to reinforce the practical advantage of the square-tooth AFC in retrieval efficiency. Our proof lays rigorous foundation for the recipe of creating optimal AFC under realistic experimental conditions.
Quantum memories are used for storing the quantum mechanical states of photons and release identical photons at a later time. This has many applications within the field of quantum computing and is also essential in order to achieve long range quantum communication and cryptography. In this thesis Atomic frequency comb (AFC) quantum memories were investigated. In particular, three-level memory schemes were investigated in detail and a program for simulating these protocols was developed. These schemes make use of control pulses to transfer the population from the optically excited state to a ground state hyperfine level, as well as radio frequency fields to swap the population in the two ground state hyperfine levels. In this work control and RF pulses, tailored to give good transfer rates, are suggested and effects due to off resonant excitation was investigated. A memory protocol which could give efficiencies up to 60% for Praseodymium doped Yttrium Silicate based AFC memories is proposed. The main bottleneck for reaching higher efficiencies is that the AFC peak spacing needs to be small in order to give enough time to transfer the population to the spin state with the control pulses. With the control pulses suggested in this work and the current technology of tailoring AFC peaks in Pr-based memories, this gives a maximum finesse of 6 of the AFC structure.
The atomic frequency comb (AFC) is a promising approach for quantum memory, yet creating an ideal AFC only in the ground-state population remains a challenge. We studied an imperfect AFC initially created in the population inversion between the excited and ground states and redistributed due to population relaxation in a three-level system where a long-lived metastable state plays a crucial role. A theoretical model has been developed to treat the storage of a weak input pulse and retrieval in the form of a photon echo. By comparing theory with experimental results we have studied the echo efficiency and overall attenuation of an input pulse in the AFC affected by both its initial spectral structure and the population relaxation.
Photonic quantum memory, such as an atomic frequency comb (AFC), is essential to make photonic quantum computation and long distance quantum communication scalable and feasible. In standard AFC the frequency of different atoms must be stable relative to each other which presents difficulties in realizing the quantum memory. Here we propose a quantum memory using an intra-atomic frequency comb which does not require frequency stabilization. We show that the transitions between two degenerate energy levels of a single atom can be used to construct the frequency comb. The spacing between the teeth of the comb is controlled by applying an external magnetic field. Since the frequency comb is constructed from individual atoms, these atoms can be used alone or in ensembles to realize the quantum memory. Furthermore, the ensemble based quantum memory with intra-AFC is robust against Doppler broadening which makes it useful for high-temperature quantum memory. As an example, we numerically show the intra-AFC in cesium atoms and demonstrate a photon echo which is essential for quantum memory.
An efficient multimode quantum memory is a crucial resource for long-distance quantum communication based on quantum repeaters. We propose a quantum memory based on spectral shaping of an inhomogeneously broadened optical transition into an atomic frequency comb (AFC). The spectral width of the AFC allows efficient storage of multiple temporal modes without the need to increase the absorption depth of the storage material, in contrast to previously known quantum memories. Efficient readout is possible thanks to rephasing of the atomic dipoles due to the AFC structure. Long-time storage and on-demand readout is achieved by use of spin states in a lambda-type configuration. We show that an AFC quantum memory realized in solids doped with rare-earth-metal ions could store hundreds of modes or more with close to unit efficiency, for material parameters achievable today.
We demonstrate efficient and reversible mapping of a light field on to a thulium-doped crystal using an atomic frequency comb (AFC). Owing to an accurate spectral preparation of the sample, we reach an efficiency of nine per cent. Our interpretation of the data is based on an original spectral analysis of the AFC. By independently measuring the absorption spectrum, we show that the efficiency is limited by both the available optical thickness and the preparation procedure at large absorption depth for a given bandwidth. The experiment is repeated with less than one photon per pulse and single-photon counting detectors. We clearly observe that the AFC protocol is compatible with the noise level required for weak quantum field storage.