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Quantum enhanced metrology in the optical lattice clock

Chi Shu

Published Jan 1, 2023• 0 citations
OpenAlex

Abstract

High-bandwidth, high-stability clocks offer unique chances to study fundamental physics beyond simple metrology. Today, the most stable clocks are optical lattice clocks and they can reach a fractional stability of 3.1 × 10^−18 at 1 s averaging time. Their applications are ranging from the redefinition of the SI time unit, the Second, to the possible detection of gravitational waves in space. The stability of optical lattice clocks is primarily limited by quantum projection noise and Dick noise. In this thesis, I present our effort in creating a platform for studying quantum enhanced metrology and its application towards optical lattice clocks. We demonstrated the laser cooling in an optical cavity with Raman-sideband cooling and achieved average vibration number of n = 0.2. We utilized cavity feedback squeezing to demonstrate unitary spin squeezing on magnetic sub-levels of 171Yb, achieving 6.5 dB quantum projection noise reduction over the standard quantum limit (SQL). With coherent optical state transfer by ultra stable laser pulses, we successfully transferred the spin squeezed state from magnetic sub-levels to the optical transition, and demonstrated quantum enhanced metrology in the optical lattice clock for the first time. We achieved 4.4 dB of metrological gain over the SQL, which corresponds to a reduction of the averaging time by a factor of 2.8 in clock operation. Furthermore, we studied quantum enhanced metrology with time-reversal-based protocols. We performed a signal amplification through time-reversed interaction protocol between the ground state magnetic sublevels of 171Yb, achieving the largest sensitivity improvement beyond SQL in any interferometers to date at 11.8dB. Besides that, we experimentally studied the connection between quantum information scrambling, by measuring out-of-time-order correlators (OTOCs), and quantum metrology, by measuring metrological gain. We found these values to agree with each other, and concluded that the time-reversal quantum metrology can saturate the attainable gain from the quantum information scrambling.

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High-bandwidth, high-stability clocks offer unique chances to study fundamental physics beyond simple metrology. Today, the most stable clocks are optical lattice clocks and they can reach a fractional stability of 3.1 × 10^−18 at 1 s averaging time. Their applications are ranging from the redefinition of the SI time unit, the Second, to the possible detection of gravitational waves in space. The stability of optical lattice clocks is primarily limited by quantum projection noise and Dick noise. In this thesis, I present our effort in creating a platform for studying quantum enhanced metrology and its application towards optical lattice clocks. We demonstrated the laser cooling in an optical cavity with Raman-sideband cooling and achieved average vibration number of n = 0.2. We utilized cavity feedback squeezing to demonstrate unitary spin squeezing on magnetic sub-levels of 171Yb, achieving 6.5 dB quantum projection noise reduction over the standard quantum limit (SQL). With coherent optical state transfer by ultra stable laser pulses, we successfully transferred the spin squeezed state from magnetic sub-levels to the optical transition, and demonstrated quantum enhanced metrology in the optical lattice clock for the first time. We achieved 4.4 dB of metrological gain over the SQL, which corresponds to a reduction of the averaging time by a factor of 2.8 in clock operation. Furthermore, we studied quantum enhanced metrology with time-reversal-based protocols. We performed a signal amplification through time-reversed interaction protocol between the ground state magnetic sublevels of 171Yb, achieving the largest sensitivity improvement beyond SQL in any interferometers to date at 11.8dB. Besides that, we experimentally studied the connection between quantum information scrambling, by measuring out-of-time-order correlators (OTOCs), and quantum metrology, by measuring metrological gain. We found these values to agree with each other, and concluded that the time-reversal quantum metrology can saturate the attainable gain from the quantum information scrambling.
Optical atomic clocks with unrivaled precision and accuracy have advanced the frontier of precision measurement science and opened new avenues for exploring fundamental physics. A fundamental limitation on clock precision is the standard quantum limit (SQL), which stems from the uncorrelated projection noise of each atom. State-of-the-art optical lattice clocks interrogate large ensembles to minimize the SQL, but density-dependent frequency shifts pose challenges to scaling the atom number. The SQL can be surpassed, however, by leveraging entanglement, though it remains an open problem to achieve quantum advantage from spin squeezing at state-of-the-art stability levels. Here, we demonstrate clock performance beyond the SQL, achieving a fractional frequency precision of 1.1×10^{-18} for a single spin-squeezed clock. With cavity-based quantum nondemolition measurements, we prepare two spin-squeezed ensembles of ∼30 000 strontium atoms confined in a two-dimensional optical lattice. A synchronous clock comparison with an interrogation time of 61 ms achieves a metrological improvement of 2.0(2) dB beyond the SQL, after correcting for state preparation and measurement errors. These results establish the most precise entanglement-enhanced clock to date and offer a powerful platform for exploring the interplay of gravity and quantum entanglement.
Neutral atom optical standards require the highest levels of laser precision to operate near the limit set by quantum fluctuations. We develop state-of-the-art ultra-stable laser systems to achieve a factor of 10 enhancement in clock measurement precision and additionally demonstrate optical linewidths below 50 mHz. The most stable of these lasers reaches its thermal noise floor of 1 × 10-16 fractional frequency instability, allowing the attainment of near quantum-noise-limited clock operation with single-clock instabilities of 3×10-16 at 1 s. We utilize this high level of spectral resolution to operate a 87Sr optical lattice clock in a regime in which quantum collisions play a dominant role in the dynamics, enabling the study of quantum many-body physics. With a fractional level of precision of near 1 × 10-16 at 1 s, we clearly resolve the signatures of many-body interactions. We find that the complicated interplay between the p wave-dominated elastic and inelastic interaction processes between lattice-trapped atoms leads to severe lineshape distortion, shifts, and loss of Ramsey fringe contrast. We additionally explore the theoretical prediction that these many-body interactions will modify the quantum fluctuations of the system and we find that in certain parameter regimes the quantum noise distribution exhibits a quadrature dependence. We further present technological advancements that will permit ultra-stable lasers to operate with reduced thermal noise, leading to a potential gain of an additional factor of 10 in stability. This indicates that laser fractional frequency instabilities of 1 × 10-17 are within experimental reach, as is a fully-quantum-limited regime of optical clock operation.
Building scalable quantum systems that demonstrate genuine performance enhancement based on entanglement is a major scientific goal for fields including computing, networking, simulations, and metrology. The tremendous challenge arises from the fragility of entanglement in increasingly larger sized quantum systems. Optical atomic clocks utilizing a large number of atoms have pushed the frontier of measurement science, building on precise engineering of quantum states and control of atomic interactions. However, today's state-of-the-art optical atomic clocks are limited by the quantum projection noise (QPN) defined by many uncorrelated atoms. Pioneering work on producing spin squeezed states of atoms has shown a path towards integrating entanglement into the best performing clocks. However, to directly demonstrate advantage of quantum entanglement in a working clock we must prevent backaction effects that degrade quantum coherence and introduce uncontrolled perturbations, as well as minimize the influence of technical noise arising from the interrogating clock laser. Here we present a new optical clock platform integrated with collective strong-coupling cavity QED for quantum non-demolition (QND) measurement. Optimizing the competition between spin measurement precision and loss of coherence, we measure a Wineland parameter of -1.8(7) dB for 1.9x104^44 atoms, thus verifying the presence of entanglement. Furthermore, a moving lattice allows the cavity to individually address two independent sub-ensembles, enabling us to spin squeeze two clock ensembles successively and compare their performance. This differential comparison between the two squeezed clocks directly verifies enhanced clock stability of 2.0(3) dB below QPN, and 0.6(3) dB above the standard quantum limit (SQL), at the measurement precision level of 10−17^{-17}−17, without subtracting any technical noise contributions.
Many-body entangled states allow precision measurement beyond the standard quantum limit. Yet they have not been effectively exploited in optical lattice clocks except for proof-of-principle demonstrations. Under the current experimental conditions, taking into account the lattice perturbation, atom-atom interactions, and local oscillator noise, we theoretically evaluate the performance of spin-squeezing-based shallow-lattice Yb optical clocks. The numerical simulation shows that the stability of differential frequency comparison between two Yb ensembles in squeezed spin states potentially accesses the ${10}^{\ensuremath{-}19}$ level at the averaging time of 1 s. The resultant Wineland parameter may be as low as ${\ensuremath{\xi}}_{\text{W}}^{2}=0.027$, corresponding to a reduction of averaging time by a factor of 37, and is limited by the collision-induced degradation of spin squeezing. The metrological gain provided by spin squeezing opens up new opportunities for precision measurement and fundamental physics.
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.