Quantum-amplified global-phase spectroscopy on an optical clock transition

Abstract

Optical lattice clocks (OLCs) are at the forefront of precision metrology, operating near a standard quantum limit (SQL) set by quantum noise. Harnessing quantum entanglement offers a promising route to surpass this limit, yet there remain practical roadblocks concerning scalability and measurement resolution requirements. Here, we adapt the holonomic quantum-gate concept to develop a novel Rabi-type "global-phase spectroscopy" (GPS) that utilizes the detuning-sensitive global Aharanov-Anandan phase. With this approach, we are able to demonstrate quantum-amplified time-reversal spectroscopy in an OLC that achieves 2.4(7) dB metrological gain without subtracting the laser noise, and 4.0(8) dB improvement in laser noise sensitivity beyond the SQL. We further introduce rotary echo to protect the dynamics from inhomogeneities in light-atom coupling and implement a laser-noise-canceling differential measurement through symmetric phase encoding in two nuclear spin states. Our technique is not limited by measurement resolution, scales easily owing to the global nature of entangling interaction, and exhibits high resilience to typical experimental imperfections. We expect it to be broadly applicable to next-generation atomic clocks and other quantum sensors approaching the fundamental quantum precision limits.

Figures (1)

• Figure 1: Experimental setup for entangled time-reversal global-phase spectroscopy (GPS)a, Laser-cooled atoms are confined in a 2D optical lattice (red) inside a high-finesse optical cavity. A transverse lattice along the $y$ axis is created via retro-reflection off the (square) mirror. Squeezing and probing light (green) is sent through the cavity along the $z$ axis, while the clock laser (yellow) is aligned with the transverse lattice. The blue arrow represents the RF field used for rotations of the nuclear Zeeman ground states $\{ \ket{\uparrow}, \ket{\downarrow} \}$. The objects in the picture are rendered not to scale. b, Simplified energy level diagram with states $\ket{\downarrow}\equiv \ket{{}^1\text{S}_0, m_I=-\frac{1}{2}}$, $\ket{\uparrow}\equiv \ket{{}^1\text{S}_0, m_I=+\frac{1}{2}}$, $\ket{\text{c}_\downarrow}\equiv \ket{{}^3\text{P}_0, m_I=-\frac{1}{2}}$, $\ket{\text{c}_\uparrow}\equiv \ket{{}^3\text{P}_0, m_I=+\frac{1}{2}}$, $\ket{\text{e}}\equiv \ket{{}^3\text{P}_1, m_F=+\frac{3}{2}}$, quantized along the $z$ axis from panel a. The arrows represent the three control fields from panel a. The cavity mode (vertical gray line) is tuned on resonance with the $\ket{\uparrow}\rightarrow\ket{e}$ transition. c, In GPS, the clock laser drives the optical qubit state along the closed trajectory (yellow curve) on the unit-radius Bloch sphere, encoding a geometric Aharonov-Anandan phase, which equals half of the enclosed area, $A/2$, after a single cyclic evolution. The area $A$ depends on clock laser oscillator (LO) detuning, providing a method to measure LO frequency while operating nominally on atomic resonance. d, Illustration of quantum amplification based on time-reversal. The initial coherent spin state (CSS) is squeezed by a green laser pulse and rotated by $\pi/2$ by an RF pulse before the clock LO pulse is applied to induce a shift of $A/2$ that is mapped back onto the $S_z$ axis by another $\pi/2$ RF pulse. Unsqueezing $-\chi S_z^2$ subsequently amplifies the signal to $M\times A/2$ along the $S_y$ axis (with $M$ constant and independent of $A$ in the vicinity of $A=0$ and $A=2\pi$). The blue shading on the generalized Bloch spheres illustrates the Wigner quasi-probability distributions in the ground state manifold, $\{\ket{\uparrow},\ket{\downarrow}\}^{\otimes N}$.