We demonstrate a set of tools for microscopic control of neutral strontium atoms. We report single-atom loading into an array of sub-wavelength scale optical tweezers, light-shift free control of a narrow-linewidth optical transition, three-dimensional ground-state cooling, and high-fidelity nondestructive imaging of single atoms on sub-wavelength spatial scales. Extending the microscopic control currently achievable in single-valence-electron atoms to species with more complex internal structure, like strontium, unlocks a wealth of opportunities in quantum information science, including tweezer-based metrology, new quantum computing architectures, and new paths to low-entropy many-body physics.

Collective measurements can project a system into an entangled state with enhanced sensitivity for measuring a quantum phase, but measurement backaction has limited previous efforts to only modest improvements. Here we use a collective measurement to produce and directly observe, with no background subtraction, an entangled, spin-squeezed state with phase resolution improved in variance by a factor of 10.5(1.5), or 10.2(6) dB, compared to the initially unentangled ensemble of N = 4.8 × 10 5 87 Rb atoms. The measurement uses a cavity-enhanced probe of an optical cycling transition to mitigate back-action associated with state-changing transitions induced by the probe. This work establishes collective measurements as a powerful technique for generating entanglement for precision measurement, with potential impacts in biological sensing, communication, navigation, and tests of fundamental physics.A defining characteristic of quantum mechanics is the ability of a measurement to change the state of the system being measured. For example, a measurement of a system in a super-1 arXiv:1310.3177v1 [quant-ph] 11 Oct 2013 position of two states causes the system to project, or collapse, into one of the two discrete states. Measurements performed on an ensemble, however, can project the ensemble into an entangled state when only collective quantities are measured. For instance, here we measure a cavity field that is entangled with the total number of spin-1/2 atoms in spin up (Fig. 1A). Any information about the spin-state of a single atom that leaks to the environment due to imperfections in the collective measurement reduces entanglement due to collapse of individual atoms.Such collective or joint measurements arise in a wide range of applications, including quantum teleportation (1), quantum information protocols (2), studies of strongly-correlated quantum systems (3), Dicke superradiance (4), and entanglement generation in optical (5), solid state (6) and atomic systems (7).Entanglement generated by a collective measurement can be used to overcome the fundamental quantum randomness that limits a diverse set of precision measurements (8). Atomic sensors in particular are nearly or already limited by quantum noise, so entanglement-enhanced metrology would improve some of the most precise measurements of external fields (9), rotations (10), and time (11), and will advance searches for new physics (12). Atomic sensors encode their information in a quantum phase θ, whose value is estimated by measuring the population of atoms in different quantum states. Quantum projection noise (13) for an ensemble of N independent atoms limits the uncertainty in the estimate of θ to a variance ∆θ 2 ≥ ∆θ 2 SQL = 1/N , a limit known as the standard quantum limit (SQL) for a coherent spin state (CSS). Entanglement can be used to bypass this limitation in atomic sensors, as well as in microwave (14) and optical (15) fields.A collective measurement that both resolves the quantum noise that appears in θ and induces sufficiently small measuremen...

Laser-cooled and quantum degenerate atoms are being pursued as quantum simulators and form the basis of today's most precise sensors. A key challenge toward these goals is to understand and control coherent interactions between the atoms. We observe long-range exchange interactions mediated by an optical cavity, which manifest as tunable spin-spin interactions on the pseudo spin-½ system composed of the millihertz linewidth clock transition in strontium. This leads to one-axis twisting dynamics, the emergence of a many-body energy gap, and gap protection of the optical coherence against certain sources of decoherence. Our observations will aid in the future design of versatile quantum simulators and the next generation of atomic clocks that use quantum correlations for enhanced metrology.

Researchers demonstrate superradiant emission from the 150-s lifetime strontium clock transition.

The preparation of large, low-entropy, highly coherent ensembles of identical quantum systems is foundational for many studies in quantum metrology [1], simulation [2], and information [3]. Here, we realize these features by leveraging the favorable properties of tweezer-trapped alkaline-earth atoms [4][5][6] while introducing a new, hybrid approach to tailoring optical potentials that balances scalability, high-fidelity state preparation, site-resolved readout, and preservation of atomic coherence. With this approach, we achieve trapping and optical clock excited-state lifetimes exceeding 40 seconds in ensembles of approximately 150 atoms. This leads to half-minute-scale atomic coherence on an optical clock transition, corresponding to quality factors well in excess of 10 16 . These coherence times and atom numbers reduce the effect of quantum projection noise to a level that is on par with leading atomic systems [7,8], yielding a relative fractional frequency stability of 5.2(3) × 10 −17 (τ /s) −1/2 for synchronous clock comparisons between sub-ensembles within the tweezer array. When further combined with the microscopic control and readout available in this system, these results pave the way towards long-lived engineered entanglement on an optical clock transition [9] in tailored atom arrays.

Coherent control of high-quality-factor optical transitions in atoms has revolutionized precision frequency metrology. Leading optical atomic clocks rely on the interrogation of such transitions in either single ions or ensembles of neutral atoms to stabilize a laser frequency at high precision and accuracy. In addition to absolute time-keeping, the precision and coherence afforded by these transitions has enabled observations of gravitational time dilation on short length-scales, and facilitated applications in quantum information. Here, we demonstrate a new platform for interrogation and control of an optical clock transition based on arrays of individual strontium atoms held within optical tweezers that combines key strengths of these two leading approaches. We report coherence times of 3.4 seconds, record single-ensemble duty cycles up to 96% through repeated interrogation, and 4.7 × 10 −16 (τ /s) −1/2 frequency stability commensurate with present-day leading platforms. These results establish optical tweezer arrays, and their associated capacity for microscopic control of neutral atoms, as a powerful tool for coherent control of optical transitions for metrology and quantum information science.

Recent proposals suggest that lasers based on narrow dipole-forbidden transitions in cold alkaline earth atoms could achieve linewidths that are orders of magnitude smaller than linewidths of any existing lasers. Here, we demonstrate a laser based on the 7.5 kHz linewidth dipole forbidden 3 P1 to 1 S0 transition in laser-cooled and tightly confined 88 Sr. We can operate this laser in the badcavity regime, where coherence is primarily stored in the atoms, or continuously tune to the more conventional good-cavity regime, where coherence is primarily stored in the light field. We show that the cold-atom gain medium can be repumped to achieve quasi steady-state lasing, and demonstrate up to an order of magnitude suppression in the sensitivity of laser frequency to changes in cavity length, the primary limitation for the most frequency stable lasers today.

We present the first characterization of the spectral properties of superradiant light emitted from the ultranarrow, 1-mHz-linewidth optical clock transition in an ensemble of cold 87 Sr atoms. Such a light source has been proposed as a next-generation active atomic frequency reference, with the potential to enable high-precision optical frequency references to be used outside laboratory environments. By comparing the frequency of our superradiant source to that of a state-of-the-art cavity-stabilized laser and optical lattice clock, we observe a fractional Allan deviation of 6.7ð1Þ × 10 −16 at 1 s of averaging, establish absolute accuracy at the 2-Hz (4 × 10 −15 fractional frequency) level, and demonstrate insensitivity to key environmental perturbations.