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arXiv:2306.12007

Effect of a hybrid transition moment on Stark-modulated photon echoes in Er$^{3+}$:Y$_2$SiO$_5$

Rose L. Ahlefeldt, Alexey Lyasota, Smith, Jodie, Jinliang Ren, Matthew J. Sellars

Published Jun 21, 2023• 0 citations
arXivHTMLPDF

Abstract

The 1538 nm ${}^4$I$_{15/2}$ - ${}^4$I$_{13/2}$ transition of Er$^{3+}$ 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 Er$^{3+}$:Y$_2$SiO$_5$ 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 Er$^{3+}$ spin qubits.

DOI
10.48550/arxiv.2306.12007

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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.

EPJ Web of Conferences•Jan 1, 2015•2 citations
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 1538-nm ${}^{4}{\mathrm{I}}_{15/2} \ensuremath{\rightarrow} {}^{4}{\mathrm{I}}_{13/2}$ transition of Er3+{\mathrm{Er}}^{3+}Er3+ 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+{\mathrm{Er}}^{3+}Er3+:Y2SiO5{\mathrm{Y}}_{2}{\mathrm{SiO}}_{5}Y2​SiO5​ 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 $11.93\phantom{\rule{4pt}{0ex}}\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ for site 1 and 1.61 and $15.35\phantom{\rule{4pt}{0ex}}\mathrm{kHz}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\mathrm{cm}$ for site 2, dependent on the direction of the electric field. 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+{\mathrm{Er}}^{3+}Er3+ spin qubits.
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.
The influence of the anisotropic Zeeman effect on optical decoherence was studied for the 1.54 μm telecom transition in Er3+:Y2SiO5 using photon echo spectroscopy as a function of applied magnetic field orientation and strength. The decoherence strongly correlates with the Zeeman energy splittings described by the ground- and excited-state g factor variations for all inequivalent Er3+ sites, with the observed decoherence times arising from the combined effects of the magnetic dipole-dipole coupling strength and the ground- and excited-state spin-flip rates, along with the natural lifetime of the upper level. The decoherence time was maximized along a preferred magnetic field orientation that minimized the effects of spectral diffusion and that enabled the measurement of an exceptionally narrow optical resonance in a solid—demonstrating a homogeneous linewidth as narrow as 73 Hz.
The dependence of the magnetic fluctuations and the spin coherence time T2hypT_2^{\rm hyp}T2hyp​ of the lowest Stark states 4I15/2 (Z1)^4I_{15/2}\ (Z_1)4I15/2​ (Z1​) in 167^{167}167Er3+^{3+}3+:Y2_22​SiO5_55​ under zero magnetic field on Er concentration is numerically investigated in the range of 10 to 100 parts per million (ppm). We investigate two primary sources of magnetic fluctuation limiting spin coherence: a constant contribution from host Y nuclei and a concentration-dependent component from dipole-dipole interactions among Er ions. Due to these two components, the Er-concentration dependence of T2hypT_2^{\rm hyp}T2hyp​ at the zero first-order Zeeman (ZEFOZ) points saturates for crystals with Er concentration below 10 ppm and no extension of the T2hypT_2^{\rm hyp}T2hyp​ is expected without an external magnetic field. Under a magnetic field, the longest T2hypT_2^{\rm hyp}T2hyp​ at a particular ZEFOZ point is expected to be over 170 s (90 s) for site 1 (site 2), which is more than 10410^4104 times longer than that at zero field for 10-ppm 167^{167}167Er3+^{3+}3+:Y2_22​SiO5_55​. Remarkably, these optimal ZEFOZ points form striking geometric patterns: a line for site 1 and a plane for site 2. This trend, which is favorable for experiments, can be explained by the anisotropy of the effective spin Hamiltonian parameters. Finally, the tolerance of the ZEFOZ point at each site with the longest T2hypT_2^{\rm hyp}T2hyp​ against the errors in the applied magnetic field vector is evaluated.
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.