Near-Unitary Spin Squeezing in Yb171

Abstract

Spin squeezing can improve atomic precision measurements beyond the standard quantum limit (SQL), and unitary spin squeezing is essential for improving atomic clocks. We report substantial and nearly unitary spin squeezing in 171 Yb, an optical lattice clock atom. The collective nuclear spin of ∼ 10 3 atoms is squeezed by cavity feedback, using light detuned from the system's resonances to attain unitarity. The observed precision gain over the SQL is limited by state readout to 6.5(4) dB, while the generated states offer a gain of 12.9(6) dB, limited by the curvature of the Bloch sphere. Using a squeezed state within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2). In the future, the squeezing can be simply transferred onto the optical clock transition of 171 Yb.Optical lattice clocks (OLCs) employ ensembles of cold trapped atoms to reach unprecedented fractional accuracy at the level of 10 −18 [1][2][3][4][5]. Such clocks now operate near the standard quantum limit (SQL) set by quantum projection noise, where the precision of a sensor improves as √ N with the number of atoms N . Spin squeezed states (SSSs) [6-22] are many-body entangled states that can overcome the SQL [8,23]. They have simple Gaussian quasi-probability distributions with reduced (squeezed) and enhanced (antisqueezed) quantum noise, respectively, along two orthogonal directions of the collective atomic spin. While for fixed-bandwidth applications the precision depends on the squeezing alone, André et al. [24] have shown that for optimized clocks the antisqueezed direction eventually leaks into the measurement, reducing the gain in precision. In practice, the amount of antisqueezing typically far exceeds the squeezing, and this mechanism can dramatically reduce the precision gain to the point where, e.g., the state with the highest inferred squeezing of 20 dB (and an antisqueezing of 39 dB) [20] would improve the precision of a clock by a mere 2 dB [25]. Thus nearly unitary (area-preserving) squeezing is of high importance for future clock applications. Furthermore, of the most common OLC atoms, spin squeezing in Sr, Ca, Mg or Hg have not been demonstrated so far, and Yb has only been weakly squeezed by ∼ 2 dB [10].In this Letter, we demonstrate for the first time nearunitary optical spin squeezing, as well as the first substantial squeezing in an OLC atom. The observed metro-logical gain of up to 6.5(4) dB is limited by the state detection, while subtraction of the independently determined measurement noise implies that the generated SSSs offer 12.9(6) dB of metrological gain and 15.9(6) dB of spin noise suppression. Under conditions where the squeezing is unitary within 30%, and nearly optimal for clock applications, we demonstrate an interferometer with a factor of 3.7(2) reduction in averaging time over the SQL. In the future, the demonstrated squeezing between the two nuclear sublevels m = ± 1 2 of the electronic ground state 1 S 0 of 171 Yb can be directly used in the OL...

An Atomic-Array Optical Clock with Single-Atom Readout

“…Concerning systematics, AOCs provide fully siteresolved evaluation combined with an essential mitigation of interaction shifts, while being ready-made for implementing local thermometry using Rydberg states [14] in order to more precisely determine black-body induced shifts [1]. In addition, AOCs offer an advanced toolset for generation and detection of entanglement to reach beyond standard quantum limit operation -either through cavities [16,45] or Rydberg excitation [15] -and for implementing quantum clock networks [19]. Further, the demonstrated techniques provide a pathway for quantum computing and communication with neutral alkalineearth-like atoms [8,20,22].…”

“…In parallel, single-atom detection and control techniques have propelled quantum simulation and computing applications based on trapped atomic arrays; in particular, ion traps [10], optical lattices [11], and optical tweezers [12,13]. Integrating such techniques into an optical clock would provide atom-by-atom error evaluation, feedback, and thermometry [14]; facilitate quantum metrology applications, such as quantum-enhanced clocks [15][16][17][18] and clock networks [19]; and enable novel quantum computation, simulation, and communication architectures that require optical clock state control combined with single atom trapping [20][21][22].…”

Coupling atoms to cavities using narrow linewidth optical transitions: applications to frequency metrology

“…In the case of ref. [16], the entanglement demonstrated between nuclear spin states could in principle be transferred directly to the optical transition through the application of an optical rotation from one of the two entangled ground states to the optically excited 3 P 0 state. In order to generate spin squeezed states using the nondestructive measurements presented in ref.…”

“…This requirement presents challenges in experiments like those of refs. [16,17], where the cavity mirrors obscure optical access along the direction of tight atomic confinement, though this limitation could be overcome by additionally confining the atoms along a second direction.…”

Integrable and Chaotic Dynamics of Spins Coupled to an Optical Cavity

“…where S i are SU(M ) spin operators. A fermionic variant, the Sachdev-Ye-Kitaev (SYK) model, was subsequently introduced by Kitaev. While infinite-range spin interactions do not occur in magnetic materials, they can be realized rather naturally in cold atomic ensembles coupled to an optical cavity mode [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In this setup, the delocalized cavity mode mediates infinite-range interactions between the internal states of atoms through the local coupling at each site, regardless of the distance between atoms [23][24][25][26][27][28][29][30][31].…”