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arXiv:1809.09863 · Laser Physics

Stark shift in Y 2 SiO 5 :Er 3+ by the photon echo beating method

V N Lisin, A M Shegeda, V V Samartsev, S A Kutovoi, Yu. D. Zavartsev

Published Nov 22, 2018• 3 citations
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Abstract

Abstract The coefficient of a linear Stark shift of the 4 F 9/2 – 4 I 15/2 transition of Er 3+ ion in Y 2 SiO 5 is measured (14.3 kHz V −1 cm) by splitting the upper and lower levels of the transition by a pulsed electric field and measuring the splitting frequency from the period of beatings of the temporal form of a photon echo signal (stark photon echo beating method). The linear Stark coefficients of Er 3+ transitions in Y 2 SiO 5 have not been measured before, and this is a valuable result for a number of applications such as gradient echo memory, group velocity control via spectral hole burning, etc.

DOI
10.1088/1555-6611/aae59a

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Precise Measurement of the Stark Effect with Sub-homogeneous Linewidth Resolution in Eu3+:YAIO3

Alfred Johann Meixner, C. Michael Jefferson, R. M. Macfarlane

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.

Spectral Hole-Burning and Related Spectroscopies: Science and Applications•Jan 1, 1992•0 citations
Abstract The coefficient of a linear Stark shift of the 4 F 9/2 – 4 I 15/2 transition of Er 3+ ion in Y 2 SiO 5 is measured (14.3 kHz V −1 cm) by splitting the upper and lower levels of the transition by a pulsed electric field and measuring the splitting frequency from the period of beatings of the temporal form of a photon echo signal (stark photon echo beating method). The linear Stark coefficients of Er 3+ transitions in Y 2 SiO 5 have not been measured before, and this is a valuable result for a number of applications such as gradient echo memory, group velocity control via spectral hole burning, etc.
We describe and demonstrate a method for performing ultrahigh-resolution optical spectroscopy in the time domain which utilizes modulations in the intensity of the two-pulse photon echo in the presence of a perturbation that splits the optical transition frequencies of two or more subgroups of ions. The method is applied to a measurement of the pseudo-Stark effect in alexandrite and YAlO3{\mathrm{YAlO}}_{3}YAlO3​:Er3+{\mathrm{Er}}^{3+}Er3+. Stark shifts of \ensuremath{\simeq}100 kHz are observed, but the technique is capable of resolutions 10 kHz in some systems.
A relative phase shift between the different groups of excited dipoles, which appears as result of its frequency splitting due to action of a pulse of electric or magnetic fields, depends on a time, if the pulse overlaps in time with echo-pulse. As а consequence, the echo waveform is changed. The echo time form is modulated. The inverse modulation period well enough approximates Zeeman and pseudo-Stark splitting in the cases of magnetic and, therefore, electrical fields. Thus the g-factors of ground 4I15/2 and excited 4F9/2 optical states of Er3+ ion in LuLiF4 and YLiF4 have been measured and pseudo-Stark shift of R1 line in ruby has been determined.
Effect of a hybrid transition moment on Stark-modulated photon echoes in Er3+^{3+}3+:Y2_22​SiO5_55​
The 1538 nm 4{}^44I15/2_{15/2}15/2​ - 4{}^44I13/2_{13/2}13/2​ transition of Er3+^{3+}3+ has an unusual hybrid electric-magnetic dipole character, and signatures of the hybrid moment can be expected in coherent transient measurements. Here, we investigate the effect of the hybrid moment in both sites of Er3+^{3+}3+:Y2_22​SiO5_55​ on Stark-modulated photon echo measurements, showing that it results in a reduction of visibility of the modulated signal as well as phase and polarization shifts. We interpret these effects using a simple optical Bloch equation model, showing that site 1 has a strongly mixed moment and site 2 is predominantly magnetic dipole. We discuss the implications of the hybrid moment for quantum information applications of quantum memories. We also use the echo measurements to extract the Stark shift of the optical transition along three orthogonal directions, finding values between 10.50 and 11.93 kHz/(V/cm) for site 1 and 1.61 and 15.35 kHz/(V/cm) for site 2. We observe a modification of the Zeeman shift by the electric field in both sites and discuss how this may be used to electrically control Er3+^{3+}3+ spin qubits.
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.