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arXiv:1302.4839 · New Journal of Physics

Securing coherence rephasing with a pair of adiabatic rapid passages

M. F. Pascual-Winter, R.-C. Tongning, T. Chanelière, J.-L. Le Gouët

Published May 29, 2013• 16 citations
arXivHTMLPDF

Abstract

Coherence rephasing is an essential step in quantum storage protocols that use echo-based strategies. We present a thorough analysis on how two adiabatic rapid passages (ARPs) are able to rephase atomic coherences in an inhomogeneously broadened ensemble. We consider both optical and spin coherences, rephased by optical or radio-frequency (rf) ARPs, respectively. We show how a rephasing sequence consisting of two ARPs in a double-echo scheme is equivalent to the identity operator ( any state can be recovered), as long as certain conditions are fulfilled. Our mathematical treatment of the ARPs leads to a very simple geometrical interpretation within the Bloch sphere that permits a visual comprehension of the rephasing process. We also identify the conditions that ensure the rephasing, finding that the phase of the optical or rf ARP fields plays a key role in the ability of the sequence to preserve the phase of the superposition state. This settles a difference between optical and rf ARPs, since field phase control is not readily guaranteed in the former case. We also provide a quantitative comparison between π -pulse and ARP rephasing efficiencies, showing the superiority of the latter. We experimentally verify the conclusions of our analysis through rf ARP rephasing sequences performed on the rare-earth ion-doped crystal Tm 3+ :YAG, of interest in quantum memories.

DOI
10.1088/1367-2630/15/5/055024

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Coherence rephasing is an essential step in quantum storage protocols that use echo-based strategies. We present a thorough analysis on how two adiabatic rapid passages (ARPs) are able to rephase atomic coherences in an inhomogeneously broadened ensemble. We consider both optical and spin coherences, rephased by optical or radio-frequency (rf) ARPs, respectively. We show how a rephasing sequence consisting of two ARPs in a double-echo scheme is equivalent to the identity operator ( any state can be recovered), as long as certain conditions are fulfilled. Our mathematical treatment of the ARPs leads to a very simple geometrical interpretation within the Bloch sphere that permits a visual comprehension of the rephasing process. We also identify the conditions that ensure the rephasing, finding that the phase of the optical or rf ARP fields plays a key role in the ability of the sequence to preserve the phase of the superposition state. This settles a difference between optical and rf ARPs, since field phase control is not readily guaranteed in the former case. We also provide a quantitative comparison between π -pulse and ARP rephasing efficiencies, showing the superiority of the latter. We experimentally verify the conclusions of our analysis through rf ARP rephasing sequences performed on the rare-earth ion-doped crystal Tm 3+ :YAG, of interest in quantum memories.
Photon-echo-based quantum memories use inhomogeneously broadened, optically thick ensembles of absorbers to store a weak optical signal and employ various protocols to rephase the atomic coherences for information retrieval. We study the application of two consecutive, frequency-chirped control pulses for coherence rephasing in an ensemble with a ``natural'' inhomogeneous broadening. Although propagation effects distort the two control pulses differently, chirped pulses that drive adiabatic passage can rephase atomic coherences in an optically thick storage medium. Combined with spatial phase-mismatching techniques to prevent primary echo emission, coherences can be rephased around the ground state to achieve secondary echo emission with close to unit efficiency. Potential advantages over similar schemes working with $\ensuremath{\pi}$ pulses include greater potential signal fidelity, reduced noise due to spontaneous emission, and better capability for the storage of multiple memory channels.
This thesis explores the use of cryogenic rare earth ion doped solids for applications in quantum information science. A theoretical analysis of optically rephased memory protocols, namely the two pulse photon echo, is developed. This analysis is a fully quantum mechanical analysis. The two pulse photon echo suffers from collective amplified spontaneous emission in the output mode due to gain along the direction of propagation. This noise can be 'rephased' with a pi pulse, much like a two pulse photon echo, resulting in time separated nonclassical correlations. This thesis aims to characterize this noise and experimentally realize these nonclassical correlations. A theoretical analysis is presented for a hybrid photon echo rephasing protocol. The protocol uses strong optical rephasing pulses as well as external electric fields to rephase coherence in a two level ensemble of atoms. The Stark effect is utilized to reduce the collective spontaneous emission caused by inversion. We find that the protocol is noise free and has a theoretical maximum efficiency of 54% in the forward direction and 100% in the backward direction. The necessary task of laser frequency stabilization is presented in this thesis. The laser is locked using electronic and optical feedback, named the 'hybrid' lock. A theoretical analysis is presented as well as experimental results. The laser locking was sufficient for phase stable photon echo experiments to be conducted. Three experiments are presented in this thesis. The first experiment involved the characterization of the detection mode and the two pulse photon echo. Benchmark values are given to the photon echo efficiency, echo lifetime and Rabi frequency. The second experiment is the characterization of the amplified spontaneous emission from inverting a two level ensemble of cryogenic rare earth ions doped in a solid. These experiments were conducted on different optical depths on the inhomogeneous line of Tm:YAG. We find that indeed there is phase independent noise after the inversion with a bandwidth given by the Fourier width of the inverting pulse. It was seen that the noise measured increased exponentially with the optical depth, as expected from the theoretical analysis. The third experiment was the measurement of rephased amplified spontaneous emission and the nonclassical time separated correlation between the noise and the rephased noise. As outlined by the theory, the amplified spontaneous emission can be rephased with a pi pulse. This experiment is implemented on different optical depths on the inhomogeneously broadened line of Tm:YAG. For optical depths of 0.25 and greater, it was seen that the correlations were classical. For an optical depth of 0.046, the correlation was seen to violate the inseparability criterion. This violation of the criterion means that the ASE and RASE fields can not be described as a separable state. This correlation measurement was made with a confidence interval of 95.15%.
Photon-echo based optical quantum memory schemes often employ intermediate steps to transform optical coherences to spin coherences for longer storage times. We analyze a scheme that uses three identical chirped control pulses for coherence rephasing in an inhomogeneously broadened ensemble of three-level $\ensuremath{\Lambda}$ systems. The pulses induce a cyclic permutation of the atomic populations in the adiabatic regime. Optical coherences created by a signal pulse are stored as spin coherences at an intermediate time interval, and are rephased for echo emission when the ensemble is returned to the initial state. Echo emission during a possible partial rephasing when the medium is inverted can be suppressed with an appropriate choice of control pulse wave vectors. We demonstrate that the scheme works in an optically dense ensemble, despite control pulse distortions during propagation. It integrates conveniently the spin-wave storage step into memory schemes based on a second rephasing of the atomic coherences.
We report an experimental demonstration of composite adiabatic passage (CAP) for robust and efficient manipulation of two-level systems. The technique represents a altered version of rapid adiabatic passage (RAP), driven by composite sequences of radiation pulses with appropriately chosen phases. We implement CAP with radio-frequency pulses to invert (i.e., to rephase) optically prepared spin coherences in a Pr3+:Y2SiO5{\text{Pr}}^{3+}\text{:}{\text{Y}}_{2}{\text{SiO}}_{5}Pr3+:Y2​SiO5​ crystal. We perform systematic investigations of the efficiency of CAP and compare the results with conventional $\ensuremath{\pi}$ pulses and RAP. The data clearly demonstrate the superior features of CAP with regard to robustness and efficiency, even under conditions of weakly fulfilled adiabaticity. The experimental demonstration of composite sequences to support adiabatic passage is of significant relevance whenever a high efficiency or robustness of coherent excitation processes need to be maintained, e.g., as required in quantum information technology.
We present experimental investigations of rephasing optically driven atomic coherences, prepared by electromagnetically induced transparency in a Pr3+{}^{3+}3+:Y2{}_{2}2​SiO5{}_{5}\phantom{\rule{0.16em}{0ex}}5​ crystal. In particular, we systematically study rephasing based on rapid adiabatic passage and compare the performance of the latter with standard rephasing based on Hahn spin echoes. The data clearly demonstrate the superior performance of rapid adiabatic passage for any application of rephasing, which suffers from large inhomogeneous broadenings in the medium or inevitable fluctuations in the experimental parameters.
We consider in this paper a two-pulse photon echo sequence in the prospect of quantum light storage. We analyze the conditions where quantum storage could be realistically performed. We simply and analytically calculate the efficiency in that limit, and clarify the role of the exactly $\ensuremath{\pi}$-rephasing pulse in the sequence. Our physical interpretation of the process is well supported by its experimental implementation in a Tm3+{\text{Tm}}^{3+}Tm3+:yttrium aluminum garnet crystal thanks to an accurate control of the rephasing pulse area. We finally address independently the fundamental limitations of the quantum fidelity. Our work allows us to point out on one side the real drawbacks of this scheme for quantum storage and on the other side its specificities which can be a source of inspiration to conceive more promising procedures with rare-earth ion doped crystals.