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arXiv:2401.03934 · Physical Review Letters

Long-Lived Coherence on a μ Hz Scale Optical Magnetic Quadrupole Transition

V. Klüsener, Sebastian Pucher, Dimitry Yankelev, Jan Trautmann, F. Spriestersbach, Dmytro Filin, S. G. Porsev, Marianna S. Safronova, Immanuel Bloch, Sebastian Blatt

Published Jun 20, 2024• 16 citations
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Abstract

We report on the coherent excitation of the ultranarrow ^{1}S_{0}-^{3}P_{2} magnetic quadrupole transition in ^{88}Sr. By confining atoms in a state insensitive optical lattice, we achieve excitation fractions of 97(1)% and observe linewidths as narrow as 58(1) Hz. With Ramsey spectroscopy, we find coherence times of 14(1) ms, which can be extended to 266(36) ms using a spin-echo sequence. We determine the lifetime of the ^{3}P_{2} level for spontaneous emission of magnetic quadrupole radiation to be 110(31) min, confirming long-standing theoretical predictions. These results establish an additional clock transition in strontium and pave the way for applications of the metastable ^{3}P_{2} state in quantum computing and quantum simulations.

DOI
10.1103/physrevlett.132.253201

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Optical lattice clocks based on the narrow ( 5 s 2 ) S 0 1 − ( 5 s 5 p ) P 0 3 transition in neutral strontium (Sr) are among the most precise and accurate measurement devices in existence. Although this transition is completely forbidden by selection rules, state mixing from the hyperfine interaction in Sr 87 provides a weakly allowed transition that can be coherently driven with practical clock laser intensities. While the coherent interrogation times of optical clocks are typically set by the linewidth of the probe laser, this limitation can be overcome in synchronous differential comparisons between ensembles. In such measurements the natural lifetime of the S 0 1 – P 0 3 clock transition becomes the fundamental limiting factor to the duration of a single run of the experiment. However, a direct measurement of the decay rate of the clock excited state is quite challenging due to the competing effects of other loss channels such as Raman scattering, inelastic collisions, and atom loss due to background gas. In this work, we monitor the decay of Sr atoms trapped in an optical lattice and initialized in the P 0 3 state. By making measurements of high and low density ensembles of both Sr 87 and Sr 88 across varying lattice trap depths, we isolate radiative decay, which accounts for a significant fraction of the observed decays at low depths. We obtain a natural radiative decay lifetime of 167 − 40 + 79 s for the P 0 3 clock state in Sr 87 , a value that is consistent with previously reported measurements and theoretical predictions. We also introduce an additional measurement scheme that involves repeated measurements of the ground-state population within a single experimental sequence, validating our model and the consistency of the measured rates. We expect that the techniques introduced in this work are applicable to lifetime measurements of long-lived metastable states in other atoms and ions used for clocks and quantum computing. The results presented in this work inform performance estimates of proposed gravitational wave detectors and long-baseline atom interferometers making use of Sr 87 .

arXiv:2505.06440•Physical Review A•Jul 29, 2025•4 citations
We report on the coherent excitation of the ultranarrow ^{1}S_{0}-^{3}P_{2} magnetic quadrupole transition in ^{88}Sr. By confining atoms in a state insensitive optical lattice, we achieve excitation fractions of 97(1)% and observe linewidths as narrow as 58(1) Hz. With Ramsey spectroscopy, we find coherence times of 14(1) ms, which can be extended to 266(36) ms using a spin-echo sequence. We determine the lifetime of the ^{3}P_{2} level for spontaneous emission of magnetic quadrupole radiation to be 110(31) min, confirming long-standing theoretical predictions. These results establish an additional clock transition in strontium and pave the way for applications of the metastable ^{3}P_{2} state in quantum computing and quantum simulations.
We demonstrate coherent control of the fine-structure qubit in neutral strontium atoms. This qubit is encoded in the metastable ^{3}P_{2} and ^{3}P_{0} states, coupled by a Raman transition. Using a magnetic quadrupole transition, we demonstrate coherent state initialization of this THz qubit. We show Rabi oscillations with more than 60 coherent cycles and single-qubit rotations on the μs scale. With spin echo, we demonstrate coherence times of tens of ms. Our results pave the way for fast quantum information processors and highly tunable quantum simulators with two-electron atoms.
We present a detailed investigation of the ultranarrow magnetic-quadrupole $^{1}\mathrm{S}_{0}\text{\ensuremath{-}}^{3}\mathrm{P}_{2}$ transition in neutral strontium and show how it can be made accessible for quantum simulation and quantum computation. By engineering the light shift in a one-dimensional optical lattice, we perform high-resolution spectroscopy and observe the characteristic absorption patterns for a magnetic quadrupole transition. We measure an absolute transition frequency of 446,647,242,704(2)446,647,242,704(2)446,647,242,704(2) kHz in 88Sr^{88}\mathrm{Sr}88Sr and an $^{88}\mathrm{Sr}\text{\ensuremath{-}}^{87}\mathrm{Sr}$ isotope shift of +62.91(4)+62.91(4)+62.91(4) MHz. In a proof-of-principle experiment, we use this transition to demonstrate local addressing in an optical lattice with 532 nm spacing with a Rayleigh-criterion resolution of 494(45)494(45)494(45) nm. Our results pave the way for applications of the magnetic quadrupole transition as an optical qubit and for single-site addressing in optical lattices.
We demonstrate a spin-polarized clock transition spectrum of the 87Sr optical lattice clock. The clock transition 5s2 1S05s5p 3P0 of isotope 87Sr has a hyperfine structure due to non-zero nuclear spin, inducing ten -polarized transitions from each individual mF state under the condition of a bias magnetic field along the probing polarization axis. In this experiment, atoms are driven to a certain mF state by a circular-polarization pump light to maximize the atomic population, which is beneficial to the stability and uncertainty evaluation of the optical lattice clock. After two stages cooling and trapping, about 3.5106 atoms are trapped in the red magneto-optical trap with a temperature of 3.9 K. A grating-feedback external cavity diode laser with a tapered amplifier is used to build the optical lattice with a magic-wavelength of 813.426 nm. Both waists of the counter-propagating lattice beam along the horizontal direction are overlapped to form a one-dimensional (1D) optical lattice. The lifetime of the atoms trapped in the 1D optical lattice is 1600 ms. The clock laser at 698 nm is a grating-feedback diode laser, which is locked to an ultra-low expansion cavity by the Pound-Drever-Hall technique to stabilize the frequency and phase. As a result, the linewidth of clock laser is narrowed to Hz level. By the normalized shelving method, we obtain a resolved sideband spectrum of 87Sr 5s2 1S05s5p 3P0 transition. According to the spectrum, the lattice temperature along the longitudinal direction is approximately 4.2 K. After that a linewidth of 6.7 Hz of the degenerate clock transition is obtained at a probing time of 150 ms by utilizing a three-dimensional (3D) bias magnetic field, which is used to eliminate the stray magnetic fields. Then a small bias magnetic field of 300 mGs is applied along the polarization axis of the lattice light to achieve the spectrum of Zeeman magnetic sublevels of the clock transition. Furthermore, the mF=+9/2 and mF=-9/2 magnetic sublevels are picked to be respectively pumped by the +-polarized and --polarized light at 689 nm, a variable liquid crystal wave plate is employed to switch on both polarizations. Finally, the spin polarized clock transition spectrum is obtained at the interrogating pulse of 150 ms, and the linewidths of the mF=+9/2, mF=-9/2 magnetic sublevel transitions are 6.8 Hz and 6.2 Hz respectively.
Cavity-QED determination of the natural linewidth of the 87^{87}87Sr millihertz clock transition with 30μ\muμHz resolution
We present a new method for determining the intrinsic natural linewidth or lifetime of exceptionally long-lived optical excited states. Such transitions are key to the performance of state-of-the-art atomic clocks, have potential applications in searches for fundamental physics and gravitational wave detectors, as well as novel quantum many-body phenomena. With longer lifetime optical transitions, sensitivity is increased, but so far it has proved challenging to determine the natural lifetime of many of these long lived optical excited states because standard population decay detection techniques become experimentally difficult. Here, we determine the ratio of a poorly known ultranarrow linewidth transition (3^33P0_00​ to 1^11S0_00​ in 87^{87}87Sr) to that of another narrow well known transition (3^33P1_11​ to 1^11S0_00​) by coupling the two transitions to a single optical cavity and performing interleaved nondestructive measurements of the interaction strengths of the atoms with cavity modes near each transition frequency. We use this approach to determine the natural linewidth of the clock transition 3^33P0_00​ to 1^11S0_00​ in 87^{87}87Sr to be γ0/(2π)=1.35(3) \gamma_0/(2\pi) = 1.35(3)~γ0​/(2π)=1.35(3) mHz or τ=118(3) \tau= 118(3)~τ=118(3) s. The 30 μ~\mu μHz resolution implies that we could detect states with lifetimes just below 2 hours, and with straightforward future improvements, we could detect states with lifetimes up to 15 hours, using measurement trials that last only a few hundred milliseconds, eliminating the need for long storage times in optical potentials.
We report our observation of the spin polarized 1 S 0 → 3 P 0 clock transition spectrum in an optical lattice clock based on fermionic 87 Sr. The atoms are trapped and pre-cooled to about 2 μK with two stages of laser cooling at 461 nm and 689 nm, respectively. Then the atoms are loaded into an optical lattice formed by the interference of counter-propagating laser beams at 813 nm. An external cavity diode laser at 698 nm, which is stabilized to a high finesse cavity with a linewidth of about 5 Hz and a drift rate of less than 0.2 Hz/s, is used to excite the atoms to the 3 P 0 state. The π-polarized clock transition spectrum of resolvable m F states is obtained by applying a small bias magnetic field along the polarization axis of the probe beam. A spin polarized clock transition spectrum as narrow as 10 Hz with an 80 ms probe pulse is obtained.
Optical lattice clocks based on the narrow ( 5 s 2 ) S 0 1 − ( 5 s 5 p ) P 0 3 transition in neutral strontium (Sr) are among the most precise and accurate measurement devices in existence. Although this transition is completely forbidden by selection rules, state mixing from the hyperfine interaction in Sr 87 provides a weakly allowed transition that can be coherently driven with practical clock laser intensities. While the coherent interrogation times of optical clocks are typically set by the linewidth of the probe laser, this limitation can be overcome in synchronous differential comparisons between ensembles. In such measurements the natural lifetime of the S 0 1 – P 0 3 clock transition becomes the fundamental limiting factor to the duration of a single run of the experiment. However, a direct measurement of the decay rate of the clock excited state is quite challenging due to the competing effects of other loss channels such as Raman scattering, inelastic collisions, and atom loss due to background gas. In this work, we monitor the decay of Sr atoms trapped in an optical lattice and initialized in the P 0 3 state. By making measurements of high and low density ensembles of both Sr 87 and Sr 88 across varying lattice trap depths, we isolate radiative decay, which accounts for a significant fraction of the observed decays at low depths. We obtain a natural radiative decay lifetime of 167 − 40 + 79 s for the P 0 3 clock state in Sr 87 , a value that is consistent with previously reported measurements and theoretical predictions. We also introduce an additional measurement scheme that involves repeated measurements of the ground-state population within a single experimental sequence, validating our model and the consistency of the measured rates. We expect that the techniques introduced in this work are applicable to lifetime measurements of long-lived metastable states in other atoms and ions used for clocks and quantum computing. The results presented in this work inform performance estimates of proposed gravitational wave detectors and long-baseline atom interferometers making use of Sr 87 .