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Physical Review A

Photon echoes from an atomic frequency comb affected by population relaxation

Devin Vega, Ming Tian

Published Nov 26, 2018• 1 citation
Publisher

Abstract

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.

DOI
10.1103/physreva.98.052340

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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.
Photon echoes in rare-earth-doped crystals are studied to understand the challenges of making broadband quantum memories using the atomic frequency comb (AFC) protocol in systems with hyperfine structure. The hyperfine structure of Pr 3+ poses an obstacle to this goal because frequencies associated with the hyperfine transitions change the simple picture of modulation at an externally imposed frequency. The current work focuses on the intermediate case where the hyperfine spacing is comparable to the comb spacing, a challenging regime that has recently been considered. Operating in this regime may facilitate storing quantum information over a larger spectral range in such systems. In this work, we prepare broadband AFCs using optical combs with tooth spacings ranging from 1 MHz to 16 MHz in fine steps, and measure transmission spectra and photon echoes for each. We predict the spectra and echoes theoretically using the optical combs as input to either a rate equation code or a density matrix code, which calculates the redistribution of populations. We then use the redistributed populations as input to a semiclassical theory using the frequency-dependent dielectric function. The two sets of predictions each give a good, but different account of the photon echoes.
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.
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.
Long-lived sub-levels of the electronic ground-state manifold of rare-earth ions in crystals can be used as atomic population reservoirs for photon echo-based quantum memories. We measure the dynamics of the Zeeman sub-levels of erbium ions that are doped into a lithium niobate waveguide, finding population lifetimes at cryogenic temperatures down to 0.7 K as long as seconds. Then, using these levels, we prepare and characterize atomic frequency combs (AFCs), which can serve as a memory for quantum light at 1532 nm wavelength. The results allow predicting a 0.1% memory efficiency, limited mainly by unwanted background absorption that we believe to be caused by excitation-induced erbium spin flips and frequency shifting due to two-level systems or non-equilibrium phonons. Hence, while it should be possible to create an AFC-based quantum memory in E r 3 + : T i 4 + : L i N b O 3 , improved crystal growth together with optimized AFC preparation will be required to make it suitable for applications in quantum communication.
Atomic frequency comb (AFC) quantum memory is a favorable protocol in long distance quantum communication. Putting the AFC inside an asymmetric optical cavity enhances the storage efficiency but makes the measurement of the comb properties challenging. We develop a theoretical model for cavity-enhanced AFC quantum memory that includes the effects of dispersion, and show a close alignment of the model with our own experimental results. Providing semi quantitative agreement for estimating the efficiency and a good description of how the efficiency changes as a function of detuning, it also captures certain qualitative features of the experimental reflectivity. For comparison, we show that a theoretical model without dispersion fails dramatically to predict the correct efficiencies. Our model is a step forward to accurately estimating the created comb properties, such as the optical depth inside the cavity, and so being able to make precise predictions of the performance of the prepared cavity-enhanced AFC quantum memory.
Lengthening of photon storage time has been an important issue in quantum memories for long distance quantum communications utilizing quantum repeaters. Atom population transfer into an auxiliary spin state has been adapted to increase photon storage time of photon echoes. In this population transfer process phase shift to the collective atoms is inevitable, where the phase recovery condition must be multiple of 2pi to satisfy rephasing mechanism. Recent adaptation of the population transfer method to atomic frequency comb (AFC) echoes [Afzelius et al., Phys. Rev. Lett. 104, 040503 (2010)], where the population transfer method is originated in a controlled reversible inhomogeneous broadening technique [Moiseev and Kroll, Phys. Rev. Lett. 87, 173601 (2001)], however, shows contradictory phenomenon violating the phase recovery condition. This contradiction in AFC is reviewed as a general case of optical locking applied to a dilute medium for an optical depth-dependent coherence leakage resulting in partial retrieval efficiency.