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Electromagnetically induced transparency in a mono-isotopic 167Er:7LiYF4 crystal below 1 Kelvin: microwave photonics approach

Nadezhda Kukharchyk, Dmitriy Sholokhov, Oleg Morozov, Stella L. Korableva, Alexey A. Kalachev, and Pavel A. Bushev

Open Access Open Access

Abstract

Electromagnetically induced transparency allows for the controllable change of absorption properties, which can be exploited in a number of applications including optical quantum memory. In this paper, we present a study of the electromagnetically induced transparency in a 167Er:7LiYF4 crystal at low magnetic fields and ultra-low temperatures. The experimental measurement scheme employs an optical vector network analysis that provides high precision measurement of amplitude, phase and group delay and paves the way towards full on-chip integration of optical quantum memory setups. We found that sub-Kelvin temperatures are the necessary requirement for observing electromagnetically induced transparency in this crystal at low fields. A good agreement between theory and experiment is achieved by taking into account the phonon bottleneck effect.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Figures (4)
Fig. 1.
Fig. 1. (a) Illustration of the experimental setup. MZ-IM stands for the Mach-Zehnder intensity modulator. DR is the dilution refrigerator. PD is the high-speed InGaAs photoreceiver. RF-VNA is the radio-frequency vector network analyser. SG is the RF signal generator. Both RF-VNA and SG are triggered by using a pulse generator. PC stands for the controlling computer. (b) Schematics of the energy-level structure indicating levels involved in the EIT measurement. (c) Measurement sequence for EIT consists of three steps: spectroscopy on the pump transition, background and EIT measurements.

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Fig. 2.
Fig. 2. (a) Absorption spectrum of the sample on the ${}^4I_{15/2}(0)-{}^4I_{13/2}(0)$ transition as a function of the longitudinal magnetic field and (b) absorption spectrum at the magnetic field of 20 mT. The frequency is given in detuning from the 196.888 THz of the main laser frequency. The absorption lines $|g\rangle \leftrightarrow |e\rangle$ and $|s\rangle \leftrightarrow |e\rangle$ form a symmetrical $\Lambda$-structure used for EIT. (c) Calculated hyperfine structure of the electronic ground state $^4I_{15/2}(0)$ as a function of the longitudinal magnetic field. The red arrow indicates the ZEFOZ point of spin transition between the states $|g\rangle$ and $|s\rangle$, which is observed at the magnetic field of 20 mT. (d) Measured transition frequency between the hyperfine states $|g\rangle$ and $|s\rangle$ as a function of the longitudinal magnetic field around the ZEFOZ point. The inset shows the modelled hyperfine transition frequency dependence on the longitudinal and transverse magnetic field detunings from the ZEFOZ point.

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Fig. 3.
Fig. 3. (a) Plot of EIT as a function of the couple frequency at 20 mT. The probe and couple frequencies are given in detunings from the 195.888 THz of the main laser frequency. Slices of the measured amplitude (b) and phase (c) of the EIT signal are shown for three temperatures: 0.1 K, 0.7 K and 1 K. The black line corresponds to the experimental signal, the red line shows the fit of the data to the OVNA model [32], Eqs. (5)–(6), with the spectral shape given by Eq. (7).

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Fig. 4.
Fig. 4. (i) VNA-measured (blue dots) and calculated (red circle) group delay. (ii) The EIT visibility derived with Eq. (11). (iii) Width of optical and spin transitions and EIT transparency window. Fit of the temperature dependence of $\Gamma_{\textrm{HF}}$ to the broadening from non-equilibrium phonons, Eq. (13), is shown with dash-dotted red line. From the NQP-model, $\Gamma_{\textrm{HF0}}$ is the guiding line for the minimal width of the spin transition at the ZEFOZ point.

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Equations (14)

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H = g ∥ μ B B z S z + g ⊥ μ B ( B x S x + B y S y ) + A I z S z + B ( I x S x + I y S y ) + P [ I z 2 − I ( I + 1 ) / 3 ] ,
| s ⟩ = 1 2 ( | − 1 / 2 , 7 / 2 ⟩ + | 1 / 2 , 5 / 2 ⟩ ) ,
| g ⟩ = 1 2 ( | − 1 / 2 , 7 / 2 ⟩ − | 1 / 2 , 5 / 2 ⟩ )
| e ⟩ = | 1 / 2 , 7 / 2 ⟩
α L ∝ ( 1 + ℑ [ χ ] 2 + 2 ℑ [ χ ] cos ⁡ ( ℜ [ χ ] ) 2 ) 1 2 ,
ϕ ∝ − ℑ [ χ ] sin ⁡ ( ℜ [ χ ] ) 1 + ℑ [ χ ] cos ⁡ ( ℜ [ χ ] ) .
χ = i λ α 0 2 π Γ ge ( Γ sg + i ( Δ ω ge − Δ ω se ) ) ( Γ ge + i Δ ω ge ) ( Γ sg + i ( Δ ω ge − Δ ω se ) ) + | Ω c 2 | 2 ,
Γ ge(sg) = 1 T 1 ge(sg) + 1 π T 2 ge(sg) + Γ inh ge(sg) = 1 2   Γ opt ( HF ) .
Γ HF ( Δ B ) = Γ HF0 + S 1 δ B + S 2 δ B 2 δ B 2 + 4 Δ B 2 ,
Γ EIT = Γ HF ( 1 + Ω c 2 Γ opt Γ HF )
V EIT = Ω c 2 Ω c 2 + Γ opt Γ HF .
Γ NQP = σ υ π 2 ω 2 Δ ω 2 π υ 3 coth ⁡ ( ℏ ω k B T ) 2 ,
Γ HF = Γ HF0 ( 1 + γ NQP coth ⁡ ( ℏ ω k B T eff ) 2 ) ,
T eff = T min ( 1 + T T min ) 1 2 ,
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