Molecule-based coherent light-spin interfaces for quantum information processing -- optical spin state polarization in a binuclear Europium complex

The success of the emerging field of solid-state optical quantum information processing (QIP) critically depends on the access to resonant optical materials. Rare-earth ions (REIs) are suitable candidates for QIP protocols due to their extraordinary photo-physical and magnetic quantum properties such as long optical and spin coherence lifetimes ($T_2$). However, molecules incorporating REIs, despite having advantageous properties such as atomically exact quantum tunability, inherent scalability, and large portability, have not yet been studied for QIP applications. As a first testimony of the usefulness of REI molecules for optical QIP applications, we demonstrate in this study that narrow spectral holes can be burned in the inhomogeneously broadened $^5$D$_0\to^7$F$_0$ optical transition of a binuclear Eu(III) complex, rendering a homogeneous linewidth ($\Gamma_h$) = 22 $\pm$ 1 MHz, which translates as $T_2 = 14.5$ $\pm$ 0.7 ns at 1.4 K. Moreover, long-lived spectral holes are observed, demonstrating efficient polarization of Eu(III) ground state nuclear spins, a fundamental requirement for all-optical spin initialization and addressing. These results elucidate the usefulness of REI-based molecular complexes as versatile coherent light-spin interfaces for applications in quantum communications and processing.

applications, the coherent states must be isolated from the environmental fluctuations.
Optically active impurity systems, for example, colour centers in diamond 14 and rare-earth ions (REI) embedded in a suitable matrix 3,8,[15][16][17][18][19][20][21][22][23][24] , have been reported to act as ideal materials to achieve superposition states with long coherence lifetimes. Among the impurity systems studied, REIs are well-suited for QIP applications due to the following intrinsic properties, (i) long optical coherence lifetimes due to the well-shielded nature of the 4f-4f optical transitions from the surrounding environment by the outer 5s and 6p closed orbitals, and (ii) the presence of nuclear spins (I), which enables the creation of nuclear spin superposition states with long coherence lifetimes, useful for storing quantum states [25][26][27] . Importantly, the exceptionally good optical coherence lifetimes associated with the 4f-4f optical transitions, covering the whole visible and IR spectral range, allow for coherent optical addressing and manipulation of nuclear spin states, rendering REIs useful for QIP applications [28][29][30][31][32][33] .
Non-Kramers rare-earth ions with even number of f-electrons, for example, Eu(III), Pr(III), or Tm(III), embedded in a matrix with low average magnetic moments have been extensively studied for the implementation of QIP schemes 34 . The 5 D0 7 F0 transition of Eu(III) is of particular interest, because the 5 D0  7 F0 transition is an induced electric dipole transition 35 and is largely unaffected by the magnetic field fluctuations arising from the surrounding environment, thereby long optical coherence lifetimes are associated with the transition.
The QIP utility of Eu(III)-doped ceramics, powders, crystals, and nanoparticles-featuring 5 D0 7 F0 transition-has been elucidated in the literature 3,15,18,19,36,37 . However, it is difficult to tailor-make such systems with desirable optical properties by means of chemical and physical manipulations, limiting the utility of such materials for QIP applications. On the other hand, optical properties of molecular Eu(III) complexes can be easily tuned by ligand field-and molecular energy level engineering approaches. Further, by synthesizing 4 isotopically enriched nuclear spin-free ligands, minimization of multiphonon relaxation pathways could be realized, thereby high quantum efficiencies and narrow inhomogeneous broadening of 5 D0 7 F0 transition could be achieved. Importantly, Eu(III) complexes with isotopically pure emitting centers, for example, 151 Eu or 153 Eu, both with I = 5/2, can be synthesized via isotopologues coordination chemistry 38

Results and discussion
Preparation and X-ray structure analysis of [Eu2] The preparation of [Eu2] was performed by treating the commercially available EuCl3·6H2O and 4-picoline-N-Oxide (4-picNO) in 1:3 ratio in water followed by recrystallization of the crude reaction mixture from ethanol-ethyl acetate solvent mixture (Scheme S1). X-ray crystallographic analysis of the complex crystals revealed binuclear structure, as shown in   (Table S1) obtained from the indexing of the PXRD and SCXRD data 6 unambiguously prove the phase purity of the crystalline material utilized for photophysical and SHB studies.

Photophysical studies
The photoluminescence characteristics of the complex were studied in the solid-state by exciting the 4-picNO-based transition centerd at ~330 nm. Intense Eu(III)-based line-like emission bands corresponding to the 5 D0→ 7 FJ (J = 0-6) transitions were observed, as depicted in Fig. 2b and Fig. S6a. Remarkably, the 5 D0→ 7 F0 transition is sharp and nondegenerate (vide infra), thus indicating the presence of a single Eu(III) site, that is, the presence of the same spectroscopic site symmetry around the two Eu centers in the complex. Moreover, the occurrence of the 5 D0→ 7 F0 transition is a testimony of the lowsymmetric coordination environment around the Eu(III) ions in the complex (Fig. 2b). The near infra-red (NIR) 5 D0→ 7 F5,6 transitions were seen around 745 nm ( 5 D0→ 7 F5) and in the 801 nm to 836 nm ( 5 D0→ 7 F6) region (Fig. S6a). The 5 D0→ 7 F5 and 5 D0→ 7 F6 transitions amount to 3.3% and 7.5%, respectively, of the total emission intensity. Remarkably, the 5 D0→ 7 F4 transition centered around 700 nm accounts for 26% of the total emission. Overall, a deep red emission with chromaticity coordinates (x = 0.6615, y = 0.3382) on the commission internationale de l'éclairage (CIE) color space (Fig. S6b) was observed for the complex. 8

Fig. 2 | Photophysical properties of [Eu2Cl6(4-picNO)4(μ2-4-picNO)2]·2H2O in the solid-state.
(a) General mechanism of PL sensitization in Eu(III) complexes: The Eu(III)-based 5 D0 receiving level is populated after a series of excitation, intersystem crossing (ISC), and T1→ 5 D0 energy transfer (ET) processes. The radiative relaxation of 5 D0 level to ground 7 FJ (J = 0-6) crystal field levels manifests as line-like luminescence. Among the 5 D0→ 7 FJ transitions, the 5 D0→ 7 F0 transition is suited for QIP applications due to its narrow linewidth and long coherence lifetimes of the hyperfine states-±5/2, ±3/2, ±1/2 (I = 5/2 for 151  A strictly mono-exponential decay with luminescence lifetime (τobs) of 822 µs, upon monitoring the luminescence decay profiles at 616 nm, was observed at RT (Fig. 6c), confirming the presence of a single emitting Eu(III) species. A total emission quantum yield ( ) of 38 ± 6% (λexc = 330 nm) was determined in the solid-state using the absolute method. The total PL quantum yield, Qtot, can be represented as the product of the sensitization efficiency (ηsens) and the intrinsic quantum yield (QEu) of the europium emission from the 5 D0 level: Where τrad is the radiative lifetime of the 5 D0 level. The radiative lifetime is expressed as 42 Where A MD is the spontaneous emission probability for the 5 3b). Ions decaying back to the initial state will be immediately pumped back to the excited state. In contrast, those relaxing to a different nuclear spin level from the original one are no longer resonant with the excitation laser, therefore, population remains there until spin relaxation occurs (Fig. 3b). As the pumping proceeds, the original spin state is progressively emptied, and the population is transferred to the other spin level (Fig. 3b). Scanning the laser over the optical inhomogeneous line then reveals an increased transmission at the burning frequency, that is, a spectral hole. For an excitation laser linewidth much narrower compared to measured hole widths, the optical homogeneous linewidth of the transition can be derived from the hole width as h=hole/2. The SHB method is used for tailoring absorption profiles in several quantum storage protocols, and initialization of spin population 29,48 relies on the groundstate nuclear spin level with long population lifetimes, or at least, substantially longer than the time waited before probing the spectral hole.
A spectral hole burned in the 5 D0 7 F0 transition of Eu(III) is shown in Fig. 3c 51 . This mechanism is also to be considered here due to the direct coordination of nuclear spin containing chloride (Cl -) ligands and the presence of hydrogen atoms in the 4-picNO ligand skeleton.
To further confirm that the observed spectral holes result from population transfer to a different spin level, optical spin control manipulations were carried out. First, the The decay of the hole area was observed by increasing the delay between burning and readout pulses (Fig. 3d). This measurement provides insight into the relaxation constant (T1) for the nuclear spin levels of Eu(III), estimated as 2.1 s by exponential decay fit. As it is more than three orders of magnitude larger than the excited state lifetime, efficient spin population transfer can be achieved, enabling, for example, spin state initialization. We note that the spin T1 does not seem limited by spin flip-flops between neighboring Eu(III) ions 15 since the intramolecular flip-flop rate is expected between 10 -4 and 10 -5 s -1 53 , which is remarkably lower than the measured relaxation rate (T1 -1 ) of 0.5 s -1 .

Conclusion
Long-lived spectral holes were prepared in the inhomogeneously broadened 5  16

Methods
Experimental descriptions on the preparation of the complex, X-ray crystallography, and powder X-ray diffraction analysis of the complex are detailed in the supporting information associated with this article.

Steady state photoluminescence spectroscopy
Steady state emission spectra were recorded on a FLP920 spectrometer from Edinburgh