Optical Measurement of the Effect of Electric Fields on the Nuclear Spin Coherence of Rare-Earth Ions in Solids R. M. Macfarlane, 1,* A. Arcangeli, 2,† A. Ferrier, 2,3 and Ph. Goldner 2,‡ 1 IBM Almaden Research Center, 650 Harry Road, San Jose, California 95120, USA 2 PSL Research University, Chimie ParisTech—CNRS, Institut de Recherche de Chimie Paris, 75005 Paris, France 3 Sorbonne Universités, UPMC Université Paris 06, 75005, Paris, France (Received 30 April 2014; published 7 October 2014) We show that the coherence properties of the nuclear spin states of rare-earth ions in solids can be manipulated by small applied electric fields. This was done by measuring the Stark effect on the nuclear quadrupole transitions of 151 Eu in Y 2 SiO 5 (YSO) using a combination of Raman heterodyne optical detection and Stark modulated quadrupole echoes to achieve high sensitivity. The measured Stark coefficients were 0.42 and 1.0 Hz cm=V for the two quadrupole transitions at 34.54 and 46.20 MHz, respectively. The long decoherence time of the nuclear spin states (25 ms) allowed us to make the measurements in very low electric fields of ∼10 V=cm, which produced 100% modulation of the nuclear spin echo, and to measure Stark shifts of ∼1 Hz or 20 ppm of the inhomogeneous linewidth. DOI: 10.1103/PhysRevLett.113.157603 PACS numbers: 76.60.Gv, 71.70.Ej, 76.30.Kg, 76.60.Lz Nuclear spin levels of rare-earth ions in solids are very attractive candidates for q-bits in quantum memories and other quantum information applications because of their long coherence times T 2 . Using nuclear spins in open shell ions with narrow optical resonances, such as rare earths (RE), introduces the possibility of using sensitive optical detection schemes to measure nuclear spin coherence and also of transferring coherence between nuclear and elec- tronic states. The importance of RE doped crystals for quantum information processing is shown by recent dem- onstrations of quantum memories for light [1–3], entangle- ment storage [4,5], light matter teleportation [6], as well as single ion detection [7] and coherent manipulation [8]. Moreover, it has been found that the coherence times of nuclear spin states can be greatly extended by the appli- cation of specific external magnetic fields or the application of specific rf pulse sequences [9–11]. We show here that it is also possible to exercise control over the coherence properties of RE nuclear spins with electric fields (Stark effect [12]). A combination of electric field induced spin- echo modulation and optical Raman heterodyne detection [13] was used to measure the Stark effect of the nuclear quadrupole levels of dilute Eu 3þ ions in Y 2 SiO 5 with high sensitivity using electric fields of only ∼10 V=cm. To the best of our knowledge this is the first observation of the Stark effect on nuclear levels of RE ions, and the first application of optical techniques to the measurement of the Stark effect of nuclear states. Our measurements combine Raman heterodyne detection of NQR with the exquisitely sensitive Stark echo modulation technique introduced by Mims [14] in the context of electron paramagnetic reso- nance. Subsequently the technique was used in nuclear quadrupole echo measurements [15]. The sensitivity of Stark echo modulation derives from the long decoherence times of quantum states. In the case of the quadrupole levels of 151 Eu these are 25 msec at 4 K. We were able to easily resolve Stark shifts of 0.6 Hz or ∼20 ppm of the inhomo- geneous linewidth of the transitions, and measure Stark coefficients of less than 1 Hz cm=V using electric fields of ∼10 V=cm. The mechanism for the nuclear Stark effect is coupling of the nuclear quadrupole moment to the change in the crystalline electric field gradient produced by the applied field [16,17]. We also used the Stark echo modu- lation technique to measure the optical Stark effect which is ∼10 4 × larger and measures the vector difference between the ground and excited electric dipole moments. Y 2 SiO 5 (YSO) is a monoclinic crystal with space group C 2h 6 and eight formula units per unit cell. The Eu 3þ ions substitute for Y 3þ ions on two crystallographic sites of C 1 symmetry. Europium has two isotopes: 151 Eu (44.77%) and 153 Eu (52.23%), with quadrupole moments of þ0.95ð10Þ eb and þ2.42ð20Þ eb, respectively [18]. The ratio of the quadrupole moments is known more precisely from laser ion-beam spectroscopy as 2.5516(6) [19]. The nuclear quadrupole levels of the 7 F 0 ground state of Eu 3þ are described by the Hamiltonian H ¼ðP þ P pq Þ½I 2 z − I ðI þ 1Þ=3 þðη=3ÞðI 2 x − I 2 y Þ. ð1Þ Here, I is the nuclear spin, P the pure quadrupole interaction between the nuclear quadrupole moment and the electric field gradient resulting from the distribution of lattice ions and the 4f electrons of the Eu 3þ ion and η is the asymmetry parameter. The pseudo-quadrupole interaction P pq [20] originates in the second order magnetic hyperfine interaction through the 7 F 1 level. Deviations of the ratio of the quadrupole splittings of the two isotopes ðP þ P pq Þ 153 = ðP þ P pq Þ 151 from the bare value of 2.5516 gives a measure PRL 113, 157603 (2014) PHYSICAL REVIEW LETTERS week ending 10 OCTOBER 2014 0031-9007=14=113(15)=157603(5) 157603-1 © 2014 American Physical Society