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Optical Atomic Coherence at the 1-Second Time Scale

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Optical Atomic Coherence at the 1-Second Time Scale REPORTS optical trap (13), such that external motions do not Optical Atomic Coherence at the decohere the superposition of the two states. Using optically cooled 87Sr atoms in a zero-differential– Stark shift one-dimensional (1D) optical lattice and 1-Second Time Scale a cavity-stabilized probe laser with a sub-hertz spectral width, we have achieved probe-time– Martin M. Boyd, Tanya Zelevinsky, Andrew D. Ludlow, Seth M. Foreman, limited resonance linewidths of 1.8 Hz at the Sebastian Blatt, Tetsuya Ido,* Jun Ye† optical carrier frequency of 4.3 × 1014 Hz. The ratio of these frequencies, corresponding to a Q ≈ Highest-resolution laser spectroscopy has generally been limited to single trapped ion systems 14 because of the rapid decoherence that plagues neutral atom ensembles. Precision spectroscopy of 2.4 × 10 , is the highest obtained for any co- ultracold neutral atoms confined in a trapping potential now shows superior optical coherence herent spectral feature. without any deleterious effects from motional degrees of freedom, revealing optical resonance This ultrahigh spectral resolution allows us linewidths at the hertz level with a good signal-to-noise ratio. The resonance quality factor of to perform experiments in the optical domain 2.4 × 1014 is the highest ever recovered in any form of coherent spectroscopy. The spectral resolution analogous to radio-frequency nuclear magnetic 1 3 resonance (NMR) studies. Under a small mag- permits direct observation of the breaking of nuclear spin degeneracy for the S0 and P0 optical clock states of 87Sr under a small magnetic bias field. This optical approach for excitation of nuclear spin netic bias field, we make direct observations of 1 3 the magnetic sublevels associated with the states allows an accurate measurement of the differential Landé g factor between S0 and P0.The optical atomic coherence demonstrated for collective excitation of a large number of atoms will have a nuclear spin. Furthermore, we have precisely determined the differential Landé g factor be- strong impact on quantum measurement and precision frequency metrology. 1 3 tween S0 and P0 that arises from hyperfine 3 3 1 mixing of P0 with P1 and P1. This optical he relative rates of coherent interaction atomic clocks (14) benefit directly from the measurement approach uses only a small mag- and decoherence in a quantum system are enhanced signal size and the high resonance netic bias field, whereas traditional NMR ex- of fundamental importance for both quan- quality factor Q. Tests of atomic theory can be periments performed on a single state (either T 1 3 tum information science (1) and precision performed with increased precision. The availa- S0 or P0) would need large magnetic fields to metrology (2). Enhancing their ratio, which is ble spectral resolution also enables a direct induce splitting in the radio frequency range. 3 3 equivalent to improving spectral resolving optical manipulation of nuclear spins that are Because the state mixing between P0, P1, on August 20, 2008 1 power, characterizes much of the recent progress decoupled from the electronic angular momen- and P1 arises from both hyperfine interactions in these fields. Trapped ions have so far provided tum. Nuclear spins can have an exceedingly long and external fields, the use of a small field the best platform for research in this direction, relaxation time, making them a valuable alter- permits an accurate, unperturbed measurement resulting in a number of seminal achievements native for quantum information processing and of mixing effects. Optical manipulation of (3–8). The principal advantage of the ion system storage. Two ground-state nuclear spins can, for nuclear spins shielded by two spin-paired lies in the clean separation between the internal example, be entangled through dipolar interac- valence electrons, performed with a superior atomic state and the external center-of-mass tions when photoassociation channels to high- spatial and atomic state selectivity, may pro- 3 motion, leading to long coherence times asso- lying electronic states (such as P1) are excited vide an attractive choice for quantum infor- ciated with both internal and external degrees of (15). Combined with a quantum degenerate gas, mation science. www.sciencemag.org freedom. A large ensemble of neutral atoms the enhanced precision in measurement will Optical atomic clocks based on neutral atoms offers obvious benefits in the signal size and further strengthen the prospects of using optical benefit directly from a large signal-to-noise ratio scalability of a quantum system (9, 10). Multi- lattices to engineer condensed matter systems (S/N) and a superior line Q. Resolving nuclear atom collective effects can also dramatically (for example, allowing massively parallel quan- sublevels with optical spectroscopy permits enhance the coherent matter/field interaction tum measurements). improved measurements of systematic errors strength (11). However, systems based on Much of the recent interest in alkaline earth associated with the nuclear spin, such as linear neutral atoms normally suffer from decoher- atoms (and similar atoms and ions, such as Yb, Zeeman shifts, and tensor polarizability that ence resulting from coupling between their Hg, In+, and Al+) arises from the study of the manifests itself as nuclear spin–dependent trap Downloaded from internal and external degrees of freedom (12). forbidden optical transitions, both for metro- polarization sensitivity. Tensor polarizability of 3 In this article, we report a record-level spectral logical applications and as a means for quantum the P0 state is one of the important potential resolution in the optical domain based on a control, with an important achievement being systematic uncertainties for fermion-based clocks doubly forbidden transition in neutral atomic highly effective narrow line laser cooling (16–18). and is one of the primary motivations for recent 1 3 strontium. The atoms are confined in an optical The spin-forbidden S0- P1 transition has been proposals involving electromagnetically induced trapping potential engineered for accurate extensively studied as a potential optical frequen- transparency resonances or dc magnetic field– separation between these degrees of freedom cy standard in Mg (19), Ca (20), and Sr (21, 22) induced state mixing in bosonic isotopes (27–29). (13). The large number of quantum absorbers and has recently been explored as a tool for high- The work reported here has permitted control of − provides a dramatic enhancement in signal size resolution molecular spectroscopy through pho- these systematic effects to ~5 × 10 16 (30). Given for the recovered hertz-linewidth optical reso- toassociation in ultracold Sr (15). The doubly the superior S/N from the large number of 1 3 nance profile. forbidden S0- P0 transition is weakly allowed quantum absorbers, we expect this system to be The demonstrated neutral-atom coherence as a result of hyperfine-induced state mixing, competitive among the best performing clocks in properties will affect a number of research fields, yielding a linewidth of ~1 mHz for 87Sr with a terms of stability. Accuracy is already approach- 9 with some initial results reported here. Optical nuclear spin of =2. This transition is a particularly ing the level of the best atomic fountain clocks attractive candidate for optical domain exper- (31, 32), and absolute frequency measurement is JILA, National Institute of Standards and Technology and iments, where long coherence times are desirable, limited by the Cs clock–calibrated maser signal University of Colorado, and Department of Physics, and is currently being aggressively pursued for the available to us by means of a fiber link (33). An University of Colorado, Boulder, CO 80309–0440, USA. realization of an optical atomic clock (23–26). all-optical clock comparison is necessary to re- *Present address: National Institute of Information and Communications Technology, Koganei, Tokyo, Japan. Furthermore, because of the lack of electronic veal its greater potential. †To whom correspondence should be addressed. E-mail: angular momentum, the level shifts of the two To fully exploit the ultranarrow hyperfine- [email protected] states can be matched with high accuracy in an induced transition for high-precision spectrosco- 1430 1 DECEMBER 2006 VOL 314 SCIENCE www.sciencemag.org REPORTS py, it is critical to minimize decoherence from spread among ~100 lattice sites. The vacuum- nearly equal amplitudes, corresponds to the trap both fundamental and technical origins. The limited lattice lifetime is >1 s. The atoms are oscillation frequency in the transverse plane. ~100-s coherence time available from the 87Sr confined in the Lamb-Dicke regime along the With atoms confined in the lattice, the lin- atoms is not yet experimentally practical as a axis of the optical lattice. The Lamb-Dicke early polarized (parallel to the lattice polarization) result of environmental perturbations to the probe parameter, or the square root of the ratio of 698-nm laser drives the p transitions (Fig. 1B) for laser phase at long time scales, but atomic co- recoil frequency to trap oscillation frequency, is probe times between 0.08 and 1 s, depending on herence in the optical domain at 1 s can already ~0.3. Both the axial and radial trap frequencies the desired spectral resolution limited by the 1 3 greatly improve the current optical clock and are much larger than the S0- P0 transition Fourier transform of the probe time. The effect of quantum measurements. To achieve long atomic linewidth, leading to the spectral feature com- the probe laser is detected in two ways. First, after 3 coherence times, we trap atoms in an optical posed of a sharp optical carrier and two sets of some atoms are excited to the long-lived P0 state 1 lattice with a zero net ac Stark shift between the resolved motional sidebands. One pair of side- by the probe laser, the remaining S0 population 1 1 two clock states, enabling a large number of bands is observed ±40 kHz away from the is measured by exciting the strong S0- P1 neutral atoms to be interrogated free of pertur- carrier, corresponding to the axial oscillation transition with a resonant pulse at 461 nm.
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