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Journal of the Optical Society of America B

Chirped excitation of optically dense inhomogeneously broadened media using Eu^3+:Y_2SiO_5

Todd L. Harris, Ming Tian, W. Randall Babbitt, Geoffrey W. Burr, John A. Hoffnagle, Michael Jefferson

Published Apr 1, 2004• 5 citations
Publisher

Abstract

We describe experimentally accessible diagnostics for the excitation of optically dense frequency-selective media by linear frequency-chirped pulses using a sensitive pump–probe technique on the 7F0 to 5D0 transitions of 1.0% Eu3+:Y2SiO5. Distinct features within a transmitted cw probe pulse are used to identify the combination of linear chirp rate and optical power needed to produce an average Bloch-vector rotation of 90°. The resulting superposition state is thus an equal mixture of the ground and excited states on average. We find experimentally a linear relationship between the applied chirp-pulse intensity and chirp rate required to produce this half-inversion, a conclusion supported by both analytical calculations made using a Landau–Zener approach, and detailed computer simulations using the Maxwell–Bloch model. The numerical simulations predict experimentally observed phenomena such as the reshaping of probe pulses by stimulated emission or absorption. Finally, we quantify the relationship between chirp rate and optical power for half-inversion as a function of the optical density of the medium. The pump–probe experimental techniques and simulation analysis techniques developed here can be extended to produce an arbitrary mixture of ground and excited states, on average, in media spanning a wide range of optical density. Preparation of such media by chirped pulses for applications in quantum computing, photon-echo-based time-domain storage, and signal processing will be aided by these techniques.

DOI
10.1364/josab.21.000811

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Eu-doped yttrium orthosilicate (Eu(3+) : Y2SiO5) had been a subject being investigated for coherent time-domain optical memory and information processing applications since its ultraslow optical dephasing was discovered several years ago. In this crystal the weakly allowed (7)F0 - (5)D0 transition of europium ions exhibits a sufficient long dephasing time and no spectral difli.usion on a time scale of several hours at low temperature, thus an information pattern or data can be stored as a population grating in the ground state hyperfine levels. On the other hand, the study on photon-echo relaxation shows that the dephasing time T2 of Eu (3+) and other rare-earth ions doped YAG, YAlO3 strongly depends on the intensity of the excitation pulses. In Eu (3+) :YAlO3, an exponential decay of photon-echo with T2 = 53 microseconds if the excitation pulses are weak (5 vJ/pulse) was observed. However, when the excitation pulses are strong (80 pJ/pulse) they observed a much shortened T2 with a highly nonexponential decay pattern. The conclusion they derived is that the intensity-dependent dephasing rate effects are quite general, and it depends on how much the excitation intensity varies. In this paper we use transient grating formation technique showing that a temporal lattice distortion may only occur along crystal c axis, caused by EU (3+) excitation. At high excitation level the produced exciton in conduction band may also couple to the dynamical lattice relaxation process, giving rise to an apparently much shortened dephasing time.

NASA University Research Centers Technical Advances in Aeronautics, Space Sciences and Technology, Earth Systems Sciences, Global Hydrology, and Education•Feb 22, 1998•0 citations
We describe experimentally accessible diagnostics for the excitation of optically dense frequency-selective media by linear frequency-chirped pulses using a sensitive pump–probe technique on the 7F0 to 5D0 transitions of 1.0% Eu3+:Y2SiO5. Distinct features within a transmitted cw probe pulse are used to identify the combination of linear chirp rate and optical power needed to produce an average Bloch-vector rotation of 90°. The resulting superposition state is thus an equal mixture of the ground and excited states on average. We find experimentally a linear relationship between the applied chirp-pulse intensity and chirp rate required to produce this half-inversion, a conclusion supported by both analytical calculations made using a Landau–Zener approach, and detailed computer simulations using the Maxwell–Bloch model. The numerical simulations predict experimentally observed phenomena such as the reshaping of probe pulses by stimulated emission or absorption. Finally, we quantify the relationship between chirp rate and optical power for half-inversion as a function of the optical density of the medium. The pump–probe experimental techniques and simulation analysis techniques developed here can be extended to produce an arbitrary mixture of ground and excited states, on average, in media spanning a wide range of optical density. Preparation of such media by chirped pulses for applications in quantum computing, photon-echo-based time-domain storage, and signal processing will be aided by these techniques.
Linear- and nonlinear-optical properties of Eu3+:Y2SiO5 have been investigated. All the energy levels of the7F0,1,2,… ground-state manifold and the 5D0,1,2 excited-state manifold were identified, and they were found to be doubly structured because of the two inequivalent optical sites. Two absorption lines of the 7F0–5D0 transition were studied in detail by using nonlinear spectroscopic techniques, photon-echo and stimulated-photon-echo methods. It was found by the photon-echo measurement that the optical dephasing time for one site is extremely long and is excitation-intensity dependent. With the smallest possible intensity we observed the longest ever dephasing time in a solid, 822 μs, or a 387-Hz homogeneous linewidth. From the stimulated-photon-echo measurement, the linewidth was found to be constant over a wide range of time scales, implying the absence of spectral diffusion in this crystal. These quite advantageous properties of this crystal were used for the demonstration of two novel types of time-domain optical data readout: time- and frequency-domain hybrid optical memory and spectrally programmed coherent transients.
Summary form only given. We study the interaction between intense (50 MW peak power), shaped ultrafast laser pulses and optically dense samples of Rb vapor. In particular, we concentrate our attention on laser pulses with a the complex hyperbolic secant envelope, or equivalently, a sech electric field envelope with a tanh frequency sweep. In order to produce and characterize the shaped laser pulses used in our experiments, we exploited several new technologies: amplified, shaped laser pulses were generated using an acousto-optic modulator-based system combined with a chirped-pulse regenerative amplifier. The amplitude and phase of these pulses were then characterized by the STRUT (spectrally and temporally resolved upconversion technique). The STRUT was used to measure the laser pulses both before and after propagating through Rb vapor. Examples of such experimental STRUT images are presented. The complex sech pulse was selected because, in optically thin media, only it and rectangular pulses give complete analytical solutions to the Bloch equations. This shape has been found to generate complete population inversion over a well-defined and amplitude-insensitive bandwidth. In optically dense samples the excited state dynamics are not so straightforward. We have found, both in experiments and theoretically, that the extent and character of the population inversion is related to the frequency sweep of the laser pulses as does the amount of residual excited population after the pulse and any subsequent stimulated emission.
A technique is proposed to manipulate atomic population in an inhomogeneously broadened medium, which can set an arbitrary absorption spectrum to a uniform transparency (erasure) or to a nearly complete inversion. These reconfigurations of atomic spectral distribution are achieved through excitation of electronic transitions using a laser pulse with chirped frequency, which precisely affects selected spectral regions while leaving the rest of the spectrum unperturbed. An erasure operation sets the final atomic population inversion to zero and the inversion operation flips the population between the ground and the excited states, regardless of the previously existing population distribution. This technique finds important applications both in optical signal processing, where fast, recursive processing and high dynamic range are desirable and in quantum memory and quantum computing, which both require high efficiency and high fidelity in quantum state preparation of atomic ensembles. Proof-of-concept demonstrations were performed in a rare-earth doped crystal.
A technique for the numerical simulation of coherent optical responses of the photon echo type formed in resonance media with strong inhomogeneous broadening under the action of femtosecond laser pulses is developed. This approach is based on solving the Maxwell-Bloch equations using the finite-difference time-domain (FDTD) method without application of a fast rotating field and slowly varying envelope approximations. The method can be used to simulate coherent responses in different resonance media with a complex structure of energy levels. The technique was validated using the example of describing experiments on narrowing a photon echo pulse and femtosecond echo processing.
The photon echo is often the best technique for measuring ultra narrow homogeneous linewidths of an inhomogeneously broadened optical transition for which a higher spectral resolution than the laser bandwidth is required. Homogenous linewidths on the order of one kHz have been measured for Eu3+ and Pr3+ in different host materials at liquid helium temperature from the echo intensity as a function of the delay between the two excitation pulses. These linewidths arc three orders of magnitude narrower than the long term jitter bandwidth of the laser which was used for excitation.1 Here we present a novel spectroscopic method based on the modulation of a 2-pulsc photon echo or a stimulated echo by an externally applied field, for the accurate measurement of frequency shifting perturbations with sub-homogeneous linewidth resolution. This is illustrated by the Stark effect on the 7F0→5D0 transition of Eu3+:YAIO3. The basic idea is that two coherent preparation pulses create an excited state population grating in the frequency domain of an inhomogeneously broadened line, which then gives rise to the echo in the course of the free induction decay of the coherently prepared ions. Since the photon echo can be observed for pulse separations much larger than T2, it is possible to generate frequency gratings which have a periodic spacing smaller than the homogeneous linewidth.2 In the case of a centrosymmetric crystal there are two groups of ions with equal and opposite dipole moments. An applied electric field Es shifts the ground and excited state energy levels through interaction with the electric dipole moments of these states and hence leads to a linear frequency shift, Ω=δμ⇀⋅E⇀s/ℏ, for the two sets of ions in opposite directions, where δμ⇀ is the difference between the ground and excited state dipole moments. If the electric field is applied after the first pulse, the two sets of ions accumulate equal and opposite phase shifts Φ = ± Ωt during the time interval, t. The result of the second pulse is that an excited state population grating is created in the frequency domain with a period (t + τ)-1 where t is the time interval between the pulses and τ is the duration of one pulse. Since there arc two sets of ions with opposite phase shifts, we formally get two population gratings, one with the phase Φ = + Ωt and one with the phase Φ = − Ωt. with respect to the population grating that is caused without an applied field.
Eu-doped yttrium orthosilicate (Eu(3+) : Y2SiO5) had been a subject being investigated for coherent time-domain optical memory and information processing applications since its ultraslow optical dephasing was discovered several years ago. In this crystal the weakly allowed (7)F0 - (5)D0 transition of europium ions exhibits a sufficient long dephasing time and no spectral difli.usion on a time scale of several hours at low temperature, thus an information pattern or data can be stored as a population grating in the ground state hyperfine levels. On the other hand, the study on photon-echo relaxation shows that the dephasing time T2 of Eu (3+) and other rare-earth ions doped YAG, YAlO3 strongly depends on the intensity of the excitation pulses. In Eu (3+) :YAlO3, an exponential decay of photon-echo with T2 = 53 microseconds if the excitation pulses are weak (5 vJ/pulse) was observed. However, when the excitation pulses are strong (80 pJ/pulse) they observed a much shortened T2 with a highly nonexponential decay pattern. The conclusion they derived is that the intensity-dependent dephasing rate effects are quite general, and it depends on how much the excitation intensity varies. In this paper we use transient grating formation technique showing that a temporal lattice distortion may only occur along crystal c axis, caused by EU (3+) excitation. At high excitation level the produced exciton in conduction band may also couple to the dynamical lattice relaxation process, giving rise to an apparently much shortened dephasing time.