Spin squeezing in optical atomic clocks

Short answer: Spin squeezing is a way to entangle the atoms in an optical clock so the measurement noise falls below the usual quantum limit. In 2023, a Nature paper reported Rydberg-mediated squeezing in a neutral-atom tweezer clock with a stability 1.94 dB below the standard quantum limit, and a Nature Physics paper reported a cavity-based clock with 1.9 dB of verified stability enhancement. A 2020 Nature Communications analysis argues that squeezing helps only below a critical atom number in a strontium lattice clock. These are laboratory results and a model.

The limit being attacked

The Nature Physics abstract explains that state-of-the-art optical atomic clocks are limited by quantum projection noise, which comes from fluctuations in the population of the many atoms. Entanglement can reduce this noise, and the abstract names building scalable systems that show entanglement-based enhancement as a major goal in quantum computing and metrology. It adds that the main challenge is the fragility of entanglement in large quantum systems.

2023: a tweezer array clock

The Nature paper realizes spin squeezing in an optical clock based on a programmable array of interacting optical qubits, using Rydberg-mediated interactions in neutral atoms. The authors generate states with almost four decibels of metrological gain. They perform a synchronous frequency comparison between independent squeezed states and observe a fractional-frequency stability of 1.087 x 10^-15 at one-second averaging, which they say is 1.94 dB below the standard quantum limit and reaches a fractional precision at the 10^-17 level during a half-hour measurement. They also use local phase shifts from the tweezer array to explore squeezing in measurements that run beyond the relative coherence time with the optical local oscillator. They say the protocol may enable techniques for optimal phase estimation and Heisenberg-limited clocks. That outlook is theirs.

2023: a cavity-based clock

The Nature Physics paper presents an optical clock platform integrated with collective strong-coupling cavity quantum electrodynamics for quantum non-demolition measurements. By balancing spin measurement precision against loss of coherence, the authors measure a metrological enhancement for a large atom ensemble beyond the initial coherent spin state. A movable lattice lets the cavity address two independent subensembles, so they can squeeze two clock ensembles in turn and compare them without the influence of clock laser noise. The authors say the clock comparison remains above the effective standard quantum limit, while the performance directly verifies 1.9 dB of clock stability enhancement at the 10^-17 level without subtracting any technical noise.

2020: when squeezing helps

The Nature Communications paper takes a modelling approach. Using an analytic model of the closed servo loop of an optical clock, the authors predict the optimal stability for a given dead time and laser noise, and their analytic predictions agree with numerical simulations. They find that for usual cyclic Ramsey interrogation of a single ensemble with dead time, even with the most stable current lasers, squeezing can only improve stability for ensembles below a critical atom number of about one thousand in a strontium lattice clock. Even with a tenfold laser improvement, the critical number stays below 100,000. They add that smaller, non-scalable ensembles such as ion clocks can already benefit from squeezed states with current lasers.

Limits

The two experiments measure stability against different baselines, and one of them says its comparison stays above the effective standard quantum limit, so the results should not be read as the same achievement. The 2020 model applies to the interrogation scheme it analyses and does not rule out other schemes. None of the abstracts reports a clock used outside the laboratory.

FAQ

What is spin squeezing?

An entangling operation that reduces measurement noise below the standard quantum limit in one quadrature.

How much improvement was shown?

1.94 dB below the standard quantum limit in the 2023 Nature paper, and 1.9 dB verified enhancement in the Nature Physics paper.

Does squeezing always help a clock?

The 2020 model says for single-ensemble cyclic Ramsey interrogation it helps only below a critical atom number of about one thousand in a strontium lattice clock.

Which clocks benefit now?

The same paper says smaller non-scalable ensembles such as ion clocks can already benefit.

Is this a quantum computer?

No. It is quantum metrology using entanglement.